TEXAS INSTRUMENTS Calculator Manual L0806875

User Manual: TEXAS TEXAS INSTRUMENTS Calculator Manual TEXAS INSTRUMENTS Calculator Owner's Manual, TEXAS INSTRUMENTS Calculator installation guides

Open the PDF directly: View PDF .
Page Count: 446 [warning: Documents this large are best viewed by clicking the View PDF Link!]

TEXAS

|NSTIRUMENTS

TI-83

GRAPHINGCALCULATOR

GUIDEBOOK

TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR,

Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas

Instruments Incorporated.

IBM is a registered trademark of International Business Machines Corporation.

Macintosh is a registered trademark of Apple Computer, Inc.

Windows is a registered trademark of Microsoft Corporation.

Important

US FCC

Information

Concerning

Radio Frequency

Interference

Texas Instrtu-nents makes no warranty, either expressed or

ilnplied, including but not lilnited to any implied warranties of

inerchantability and fitness for a particular purpose, regarding any

progralns or book rnateriais and rnakes such inateriais availaMe

solely on an "as-is" basis.

In no event shall Texas Instrmnents be liable to anyone for special,

collateral, ineidentai, or eonsequentiai damages in connection with

or arising out of the purchase or use of these inateriais, and the

sole and exclusive liability of Texas Instruments, regardless of the

form of action, shall not exceed the purchase price of this

equipment. Moreover, Texas Instruments shall not be liable for any

claim of any kind whatsoever against the use of these materials by

any other party.

This equiplnent has been tested and found to cornply with the

limits for a Class B digital device, pumuant to Pm't 15 of the F(C

rules. These limits are designed to provide reasonable protection

against harmflfl interference in a residential installation. This

equiprnent generates, uses, and can radiate radio frequency enet}4y

and, if not installed and used in accordance with the instructions,

inay cause hannflll inte_ferenee with radio colnmunications.

However, there is no guarantee that inte_ferenee will not occur in

a particular instailation.

If this equiplnent does cause harrnful interference to radio or

telexdsion reception, which can be determined by turning the

equipment off and on, you can try to correct the inte_ference by

one or inore of the following measures:

• Reorient or relocate the receiving antenna.

• Increase the separation between the equiplnent and receiver.

• Connect the equipment into an outlet on a circuit different

fl_m that to which the receiver is connected.

• Consult the dealer or an experienced radio/television

technician for help.

Caution: Any changes or modifications to this equiprnent not

expressly approved by Texas Instrulnents may void your authority

to operate the equiplnent.

Table of Contents

This nlanual describes how to use the TI-83 Graphing Calculator, Getting

Started is an overview of TI-83 features. Chapter 1 describes how the TI-83

operates. Other chapters describe various interactive features. Chapter 17

shows how to combine these features to solve problems,

Getting Started: TI-83 Keyboard ..........................................

Do This First! TI-83 Menus .............................................

First Steps ...............................................

Entering a Calculation: The Quadratic Formula ..........

Converting to a Fraction: The Quadratic Formula ........

I)isplaJ_ng ('omplex Results: The Quadratic Formula ....

Defining a Function: Box with Lid .......................

Defining a Table of Values: Box with Lid ...............

Zooming In on the Table: Box with Lid .................

Setting tile Viewing Window-: Box with Lid .............

I)isplaJ_ng and Tracing the Graph: Box with Lid .......

Zooming In on tile Graph: Box with Lid ................

Finding the Calculated Maximum: Box with Lid ........

Other TI-83 Features .....................................

Chapter 1 :

Operating the

TI-83

Turning On and Turning Off the TI-83 .................... 1-2

Setting the Display Contrast ............................. 1-3

The Display .............................................. 1-4

Entering Expressions and Instructions ................... 1-6

TI-83 Edit Keys .......................................... 1-8

Setting Modes ........................................... 1-9

Using TI-83 Variable Names ............................. 1-13

Storing Variable Values .................................. 1-14

Recalling Variable Values ................................ 1-15

ENTRY (Last Entry) Storage A_'ea ........................ 1-16

Ans (Last Pmswer) Storage Pa'ea ......................... 1-18

TI-83 Menus ............................................. 1-19

VARS and VARS Y-VARS Menus ......................... 1-21

Equation Operating System (EOS TM) ..................... 1-22

Error Conditions ......................................... 1-24

Introduction iii

Chapter 2:

Math, Angle, and

Test Operations

Getting Started: Coin Flip ................................ 2-2

Keyboard Math Operations .............................. 2-3

MATH Operations ........................................ 2-5

Using tile Equation Solver ............................... 2-8

MATH NUM (Numbe 0 Operations ........................ 2-13

Entering and Using Complex Nmnbers ................... 2-16

MATH CPX (Complex) OperatMns ....................... 2-18

MATH PRB (Probability) Operations ..................... 2-20

ANGLE Operations ....................................... 2-23

TEST (Relational) Operations ............................ 2-25

TEST LOGIC (Boolean) Operations ...................... 2-26

Chapter 3:

Function

Graphing

Getting Started: Graphing a Circle ....................... 3-2

Defining Graphs ......................................... 3-3

Setting the Graph Modes ................................. 3-4

Defining Funetions ...................................... 3-5

Seleeting and Deseleeting Punetions ..................... 3-7

Setting Graph Styles for Flmetions ....................... 3-9

Setting the Viewing Window \Tariahles ................... 3-11

Setting the Graph Format ................................ 3-13

Displaying Graphs ....................................... 3-15

Exploring Graphs with the Free-Moving Cursor .......... 3-17

Exploring Graphs with TRACE ........................... 3-18

Exploring Graphs with the ZOOM Instructions ........... 3-20

Using ZOOM MEMORY .................................. 3-23

Using the CALC (Calculate) Operations .................. 3-25

Chapter 4:

Parametric

Graphing

Getting Started: Path of a Ball ........................... 4-2

Defining and Displaying Parametric Graphs .............. 4-4

Exploring Parametrie Graphs ............................ 4-7

Chapter 5: Getting Started: Polar Rose .............................. 5-2

Polar Graphing Defining and Displaying Polar Graphs ................... 5-3

ExNodng Polar Graphs .................................. 5-6

iv Introduction

Chapter 6:

Sequence

Graphing

Getting Started: Forest and Trees ........................ (;-2

Defining and Displaying Sequence Graphs ............... 6-3

Selecting Axes Combinations ............................ 6-8

Exploring Sequence Graphs .............................. (;-9

Graphing Web Plots ...................................... 6-11

Using Web Plots to Illustrate Convergence ............... 6-12

Graphing Phase Plots .................................... 6-13

Comparing TI-83 and TI-82 Sequence Variables .......... 6-15

Keystroke Differences Between TI-83 and TI-82 ......... 6-16

Chapter 7:

Tables

Getting Started: Roots of a Function ..................... 7-2

Setting Up the Table ..................................... 7-3

Defining the Dependent Variables ........................ 7-4

I)isplaying the Table ..................................... 7-5

Chapter 8:

DRAW

Operations

Getting Started: Drawing a Tangent Line ................. 8-2

Using the DRAW Menu ................................... 8-3

Clearing Drawings ....................................... 8-4

Drawing Line Segments .................................. 8-5

Drawing Horizontal and Vertical Lines ................... 8-6

Drawing Tangent Lines .................................. 8-8

Drawing Functions and Inverses ......................... 8-9

Shading Areas on a Graph ............................... 8-10

Drawing Circles .......................................... 8-11

Placing Text on a Graph ................................. 8-12

UsHlg Pen to Draw on a Graph ........................... 8-13

Drawing PoHlts on a Graph .............................. 8-14

Drawing Pixels .......................................... 8-16

StorH N Graph Pictures (Pic) ............................. 8-17

Recalling Graph Pictures (Pic) ........................... 8-18

StorHlg Graph Databases (GDB) ......................... 8-19

Recalling Graph Dadabases (GDB) ....................... 8-20

Chapter 9:

Split Screen

Getting Started: Exploring the Unit Circle ................ 9-2

Using Split Screen ....................................... 9-3

Horiz (Horizontal) Split Screen ........................... 9-4

G-T (Graph-Table) Split Screen .......................... 9-5

TI-83 Pixels in Horiz aim G-T Modes ..................... 9-6

Introduction v

Chapter 10:

Matrices Getting Started: Systems of Linear Equations ............ 10-2

Defining a Matrix ........................................ 10-3

Viewing and Editing Matrix Elements .................... 10-4

Using Matrices with Expressions ........................ 10-7

I)isplaying and Copying Matrices ........................ 10-8

Using Math Functions with Matrices ..................... 10-9

Using the MATRX MATH Operations ..................... 10-12

Chapter 11:

Lists Getting Started: Generating a Sequence .................. 11-2

Naming Lists ............................................. 11-3

Storing and Displaying Lists ............................. 11-4

Entering List Names ..................................... 11-6

Attaching Formulas to List Names ....................... 11-7

Using Lists in Expressions ............................... 11-9

LIST OPS Menu .......................................... 11-10

LIST MATH Menu ........................................ 11-17

Chapter 12:

Statistics Getting Started: Pendulum Lengihs and Periods ......... 12-2

Setting up Statistical Palalyses ........................... 12-10

Using the Stat List Editor ................................ 12-11

Attaching Formulas to List Names ....................... 12-14

I)etaehi_lg Fornmlas from List Names .................... 12-16

Switching Stat List Editor Contexts ...................... 12-17

Stat List Editor Contexts ................................. 12-18

STAT EDIT Menu ........................................ 12-20

Regression Model Features .............................. 12-22

STAT CALC Menu ........................................ 12-24

Statistical Variables ...................................... 12-29

Statistical Analysis in a Program ......................... 12-30

Statistical Plotting ....................................... 12-31

Statistical Plotting in a Program ......................... 12-37

Chapter 13:

Inferential

Statistics and

Distributions

Getting Started: Mean Height of a Population ............ 13-2

hfferential Star Editors ................................... 13-6

8TAT TESTS Menu ...................................... 13-9

Inferential Statistics Input Descriptions .................. 13-26

Test and Interval Output Variables ....................... 13-28

Distribution Functions ................................... 13-29

Distribution Shading ..................................... 13-35

vi Introduction

Chapter 14:

Financial

Functions

Getting Started: Finzmeing a Car. ........................ 14-2

Getting Started: (;omputing Compound Interest .......... 14-3

Using tile TVM Solver .................................... 14-4

Using tile Financial Functions ........................... 14-5

Calculating Time Value of Money (TVM) ................. 14-6

Calculating (;ash Flows .................................. 14-8

Calculating Amortization ................................ 14-9

Calculating Interest Conversion .......................... 14-12

Finding I)ays between [)ates_)ef'nm N Payment Method ..... l '4-13

Using tile TVM Variables ................................. 14-14

Chapter 15:

CATALOG,

Strings,

Hyperbolic

Functions

Browsing tile TI-83 CATALOG ........................... 17)-2

Entering and Using Strings ............................... 15-g

Storing Strings to String Variables ....................... 1:)-4

String Functions and Instructions in the CATALOG ...... 1.5-6

Hyperbolic Functions in the CATALOG .................. 15-10

Chapter 16:

Programming

Getting Started: Volume of a Cylinder .................... 16-2

Creating and Deleting Progrmns ......................... 16-4

Entering Command Lines and Executing Programs ...... 16-5

Editing Programs ........................................ 16-6

Copying and Renmning Programs ........................ 16-7

PRGM CTL (Control) Instructions ....................... 16-8

PRGM I/O (Input/Output) Instructions ................... 16-16

('ailing Other Programs as Subroutines .................. 16-22

Chapter 17:

Applications

Comparing Test Results Using Box Plots ................ 17-2

Graphing Pieeewise Punetions ........................... 17-4

Graphing Inequalities .................................... 17-5

Solving a System of Nonlinear Equations ................ 17-6

Using a Program to ( reate the Sierpinski Triangle ....... 17-7

Graphing Cobweb Attractors ............................ 17-8

Using a Program to Guess the Coefficients ............... 17-9

Graphing the Unit Circle and Trigonometric (;m_es ...... 17-10

Finding the Area between Curves ........................ 17-11

Using Parametric Equations: Ferris Wheel Problem ...... 17-12

Demonstrating the Fundamental Theorem of Calculus... 17-14

Computing Areas of Regular N-Sided Polygons .......... 17-16

Computing and Graphing Mortgage Payments ........... 17-18

Introduction vii

Chapter 18:

Memory

Management

{'heeLing Awailable MemolTy"............................. 18-2

Deleting Items from MemoKy" ............................ 18-3

Clearing Entries and List Elements ...................... 18-4

Resetting the TI-8:3 ...................................... 18-5

Chapter 19:

Communication

Link

Getting Started: Sending Variables ....................... 19-2

TI-83 LINK ............................................... 19-3

Selecting Items to Send .................................. 19-4

Receiving Items .......................................... 19-5

Transmitting Items ....................................... 19-6

Transmitting Lists to a TI-82 ............................. 19-8

Transmitting from a TI-82 to a TI-83 ..................... 19-9

Backing Up MemoKy" ..................................... 1%10

Appendix A:

Tables and

Reference

Information

TabD of Functions and Instructions ..................... A-2

Menu Map ............................................... A-39

Vm'iables ................................................ A-49

Statistical Formulas ..................................... A-50

Financial Fommlas ...................................... A-.M

Appendix B:

General

Information

BatteKy" Information ...................................... B-2

In Case of Difficulty ..................................... B-4

En'or Conditions ......................................... B-5

Accuracy hfformation .................................... B-10

Support and Service Infommtion ......................... B-12

Win'rarity Information .................................... B-13

Index

viii Introduction

GettingStarted:

Do ThisFirst!

Contents TI-83 Keyboard ..........................................

TI-S3 Menus .............................................

First Steps ...............................................

Entering a Calculation: The Quadratie Fonuula ..........

('onverting to a Fraction: The Quadratie Formula ........

Displaying Complex Results: The Quadratic Formula ....

Defining a Function: Box with Lid .......................

Defining a Table of Values: Box with Lid ...............

Zooming In on the Table: Box with Lid .................

Setting tile Viewing Window-: Box with Lid .............

Displaying and Traeing the Graph: Box with Lid .......

Zooming In on tile Graph: Box with Lid ................

Finding the ('aleulated Maximum: Box with Lid ........

Other TI-83 Features .....................................

TEXAS INSTRUMENTS T1=83

/ \ \.

X=:I..5:B;!:=I_fiB _Y=_;i:.90_;i:_lfi =

STATPLOT TBLSET FORMAT CALC TABLE

Getting Started 1

TI-83 Keyboard

Generally, the keybom'd is dwided into these zones: graphing keys, editing

keys, advanced function keys, and scientific calculator keys.

Keyboard Zones Graphing keys access the interactive graphing features.

Editing keys allow you to edit expressions and values.

Advanced function keys display menus that access the

advanced functions.

Scientific calculator keys access the capabilities of a

standard scientific calculator.

Graphing Keys

Editing Keys

Advanced

FuncffonKeys

Scientific

Calculator Keys

2Getting Started

Using the

Color-Coded

Keyboard

Using the K_

and @ Keys

The keys on the TI-83 are color-coded to help you easily

locate the key you need.

The gray keys are the number keys. The blue keys along the

right side of the keyboard are the conunon math functions.

The blue keys across the top set up and display graphs.

The primaKF function of each key is printed in white on the

key. For example, when you press FMA_], the MATH menu is

displayed.

The secondary function of each key- is pnnted in yellow

above the key-. When you press the yellow [_ key, the

character, abbreviation, or word printed in yellow above

the other keys becomes active for the next keystroke. For

example, when you press [_ and then [M#Y_, the TEST

menu is displayed. This guidebook describes this keystroke

combination as [_ [TEST],

The alpha function of each key is printed in green above

the key. When you press the green @ key, the alpha

character printed in green above the other keys becomes

active for the next keystroke. For example, when you press

@ and then [MATH],the letter Ais entered. This

guidebook describes this keystroke combination as @

[A].

The_key accesses

the second function

printed in yeltow above

each key --'_

The@key

accessesthe alpha

function printedin

green above each key

Getting Started 3

TI-83 Menus

Displaying a Menu

While using your TI-83, you often will need

to access items from its menus,

When you press a key- that displays a menu,

that menu temporarily replaces the screen

where you are working. For example, when

you press _, the MATH menu is displayed

as a full screen.

After you select an item fronl a menu, the

screen where you m'e working usually is

displayed again.

Moving from One Menu to Another

Solne keys access nlore than one lnenu. When

you press such a key, the names of all

accessible menus are displayed on the top

line. When you highlight a menu name, the

items in that menu are displayed. Press [] and

[] to highlight each menu nalne.

Selecting an Item from aMenu

The number or letter next to the current menu

item is highlighted. If the menu continues

beyond the screen, a down arrow ( _ )

replaces the colon ( : ) in the last displayed

item. If you scroll beyond the last displayed

item, an up arrow ( t ) replaces the colon in

the first item displayed.You can select all item

in either of two ways.

• Press [] or [] to lnove the cursor to the

number or letter of the item; press [g_.

• Press the key or key combination fia" the

number or letter next to the item.

Leaving a Menu without Making a Selection

You can leave a lnenu without lnaking a

selection in ally of three ways.

• Press @ to return to the screen

where you were.

• Press [2_] [QUIT] to t_tum to the home

screen.

• Press a key for another lnenu or screen.

[5+9| [

_ NUM CPX PRB

Pao

:*Dec

4:_(

5:_

6:¢Min(

74€Max(

5+9_

_sl_[ CPX PRB[

round(

5:int(

6:Min(

74.max(

round(

3:iPart(

4:?Part(

5:int(

5:Min(

74Max(

MRTH _ CPX PRB

3tiPar.t(

4:?Part(

5:int(

6:Min(

7:max(

8:fOR(

i_lEIgcd(

15+9_ I

4 Getting Started

First Steps

Before starting the sample pr()blems in this chapter, follow the steps on this

page to reset the TI-83 to its factotT settings and cleat" all nlenlot_y-. This

ensures that the keystrokes in this chapter will produce the illustrated results.

To reset the TI-83, follow these steps.

1, Press FOR]to turn on the calculator.

2, Press and release [_, and then press

[MEM] (above []).

When you press [2_], you access the

operation printed in yellow above the next

key that you press. [MEM]is the

operation of the [] key.

The MEMORY menu is displayed.

3. Press 5to select 5:Reset.

The RESET menu is displayed.

4, Press 1to select 1:All Memory,

The RESET MEMORY menu is displayed.

5, Press 2to select 2:Reset.

M1 nlenlot_y- is cleared, and the calculator

is reset to the factor T default settings.

When you reset the TI-83, the display

contrast is reset.

If the screen is vetT light or blank, press

and t_lease D_], and then press and

hold [] to darken the screen.

If the screen is very dark, press and

release [2_, and then press and hold []

to lighten the screen.

RRM...

3:Clear Entries

4:ClrRllLists

5:Reset...

_MeMoru..,

a. DeCaults...

Resettin9 memoru

erases all data

and PrograMs.

|MeM oleared

Getting Started 5

Entering a Calculation: The Quadratic Formula

Use the quadratic fornmla to solve the quadratic equations 3X 2 + 5X + 2 = 0

and 2X 2 - X + 3 = 0, Begin with the equation 3X 2 + 5X + 2 = 0,

1, Press 3 _ @ [n] (above 1_]) to 3÷R: 5÷B: 2÷C|

store the coefficient of the X 2 tenn.

2, Press @ [ : ] (above [_). The colon

allows you to enter more than one

instruction on a line,

3, Press 6 _ @ [B] (above _) to

store the coefficient of the X term. Press

@ [ : ] to enter a new instruction on

the same line. Press 2_ @ [c]

(above _) to store the constant.

4, Press [NY_ to store the values to the

variables A, B, and C.

The last wdue you stored is shown on the

right side of the display. The cursor moves

to the next line, ready for your next entt3z,

Press[] [] @ [B] [] _ [<] @ [B]

D [] 4_ [A]_ [c] []17113[] 2

@ [A] [] to enter the expression for

one of the solutions for the quadratic

formula,

-b+2a

÷R: 5÷B: 2÷C 2

Press _ to find one solution for the

equation 3X 2 + 5X + 2 = 0.

The answer is shown on the right side of

the display. The cursor nloves to the next

line, ready for you to enter the next

expression.

6 Getting Started

Converting to a Fraction: The Quadratic Formula

You can show the solution as a fl'action.

1. Press [_ to display the MATH lnenu.

Press 1 to select 1:)Frac froln the MATH

lnenu,

When you press 1, AnsJ,Frac is displayed on

the home screen. Arts is a variable that

contains the last calculated answer.

NUN CPX PRB

Pao

3:_

4:_#(

5: *#

6:¢Min(

7¢€Ma× (

(-B+#(BZ-4RC))/(

2R) %6666666667

Rns*Fr, ac|

Press 1_ to convert the result to a

fl'action.

(-B+4-(BZ-4RC) )/(

2R)

To save keystrokes, you can recall the last expression you entered, and then

edit it for a new calculation.

Press [2_ [ENTRY](above [gNT_) to recall

the fraction conversion entry, and then

press Fffffd][ENTRY]again to recall the

quadratic-fornmla expression,

5, Press [] to nlove the cursor onto the + sign

in the fornmla, Press [] to edit the

quadratic-fornmla expression to become:

6, Press 1_ to find the other solution for

the quadratic equation 3X 2 + 5X + 2 = 0.

I-B+E(BZ-4RC))/(

R) -.6666666667

Rns*Fpac -2/3

(-B+E(BZ-4RC))/(

2R)|

2R) -.6666666667

Rns_Frac -2/31

(-B-.r(BZ-4RC))/(

_R) -1

Getting Started 7

Displaying Complex Results: The Quadratic Formula

Now solve the equation 2X 2 - X + 3 = 0. When you set a+bi complex number

mode, the TI-83 displays complex results.

Press 1_ [] [] [] [] [] [] (6 times), and

then press [] to position the cursor over

a+bi. Press @ to select a+bi coinplex-

number mode.

2, Press [_ [QU*T] (above _E]) to return to

the home screen, and then press @ to

cleat" it.

zG-T

Press 2_ @ [A] @ [: ] [] 1

[c] F_q.

The coefficient of the X 2 term, the

coefficient of the X term, and the constant

for the new equation are stored to A, B,

and C, respectively.

eR:-leB:3aC 3

Press [_ [ENTRY] to recM1 the store

instruction, and then press [_ [ENTRY]

again to recall the quadratic-fornmla

expression,

2+R: -1+B:3+C 3

Press @ to find one solution for the

equation 2X 2 - X + 3 = 0.

12+R:-I+B:3+C

i25-I. 198957881t

Press [2_ [ENTRY]repeatedly until this

quadratic-fornmla expression is displayed:

Press @ to find the other solution for

the quadratic equation: 2X 2 - X + 3 = 0.

(-B-g(BZ-4RC))/_

2R)

.25-1.198957881t

(-B+E(BZ-4RC))/(

2R)

i25+1.198957881t

Note: An alternative for solving equations for real numbers is to use the built-in Equation

Solver (Chapter 2).

8 Getting Started

Defining a Function: Box with Lid

Take a 20 enl. x 25 enl. sheet of paper and cut X × X squm'es fronl two comers,

Cut X × 12,5 cm. rectangles from the other two corners as shown in the

diagram below, Fold the paper into a box with a lid. What value of X would

give your box the nlaxinmln volume V? [ _se the table and graphs to determine

the solution,

Begin by defining a function that describes the

volunle of the box.

From the diagram: 2X + A = 20

2X + 2B = 25

V=ABX

Substituting: V = (21) - 2X) (25/2 - X) X

1. Press [] to display the Y= editor, which is

where you define functions for tables and

graphing.

Press[] 20[] 2 _ [] [] 25[] 2[]

[] _ [_ to define the

volume function as Y1 in terms of X.

lets you enter Xquickly, without

having to press @. The highlighted =

sign indicates that Y1 is selected.

_ x B

PloL:L Plot;' PICL3

","?t =I

\y._=

xY_=

"_y_=

,..y_=

,,y_=

xY?=

\'14tB<20-2X) <25/2

-X)X

_Yz=l

,..y_=

xYfi=

Getting Started 9

Defining a Table of Values: Box with Lid

The table feature of the TI-83 displays numeric inforlnation about a function.

You can use a table of values fl'om the function defined on page 9 to estimate

an answer to the problem,

1, Press [2_ [TBLSET] (a|)ove _) to

display the TABLE SETUP menu,

2, Press [gNT_ to accept TblStart=0.

3. Press 1[ggY_ to define the table increment

ATbI=I. Leave Indpnt: Auto and

Depend: Auto so that the table will be

generated automatically,

4. Press [2_ [TABLE](above _) to display

the table,

Notice that the nlaxilnuln value for Y1

(box's volunm) occurs when Xis about 4,

between 3and 5.

TABLESETUP

Tb IStart=O

aTbl=l

Indent:

Depend:

X 91

1 207

Z3_6

_99

hOB

63t_

X=O

X V1

E_t2

F231

B lhh

10 0

X=12

5, Press and hold [] to scroll the table until a

negative result for Y1 is displayed.

Notice that the nmxinmm length of X for

this problem occurs where the sign of Y1

(box's volume) changes from positive to

negative, between 10 and 11,

6, Press[2_ [TBLSET].

Notice that TblStart h_s changed to 6 to

reflect the first line of the table as it was

last displayed, (In step 5, the first value of

X displayed in the table is 6.) TRBLE SETUP Rsk

TblStart=6

_Tbl=l

IndPn÷: P._ _.

Depend:

10 Getting Started

Zooming In on the Table: Box with Lid

You can adjust the way a table is displayed to get lnore inforlnation about a

defined function. With smaller values for aTbl, you can zoom in on the table.

Press 3_to set TblStart. Press [] 1

[gNT_ to set ATbl.

This adjusts the table setup to get a nlore

accurate estimate of Xfor lnaxilnuln

volunle Y1. TABLESETUP

TblStart=3

_Tbl=. 1

IndPnt: r=Rg_t_

Depend: r=_r;J_

2, Press[2_ [TABLE], X91

_.6 4±0.11

3. Press [] and [] to scroll the table. :<;' _.0.z6

KB hOg,gtl

2,.9 h09.19

Notice that tile nlaxinluln value for Y1 is _ 't0a

410.26, which occurs at X=3.7. Therefore, u06.x9

h0h.3B

the nlaxinmln occurs where 3.6<X<3.8, X=4.2

Press [2_ [TBLSET]. Press 3[] 6 _ to

set TblStart. Press [] 01 [gNT_ to set ATbl.

Press [2_ [TABLE], and then press [] and []

to scroll the table.

Four equivalent nlaxinluln values are

shown, 410.60 at X=3.67, 3.68, 3.69, and

3.70.

TRBLE SETUP

TblStart=3.6

_Tbl=.Ol

IndPnt: _ Rsk

Depend: _ Rsk

gYI

K67 hi0&6

3,68 h10,?.6

K69 h10.;':6

3.? h:t0._:6

h:t0.23

X=3, 72

X Y_

-_:.6B hlO.Z6

3.69 h10,_':6

3.? hlO,Z6

3.71 h10.25

_.72 h10.2_

V, =410, 261226

X V_

3.66 h10.2_

3.6}'

K6B

K69 h10,?.6

3.7 h10,;':6

3.71 h10._:5

2;.72 ht0.23

V, =410, 264064

Press [] and [] to inove the cursor to 3.67.

Press [] to lnove the cursor into tile Y1

colulnn,

Tile value of Y1 at X=3.67 is displayed on

the bottoln line in full precision as

410.261226.

Press [] to display tile other nlaxinlunls.

The value of Y1 at X=3.68 in full precision is

410.264064, at X=3.69 is 410.262318, and at

X=3.7 is 410.266.

The lnaxilnuln volulne of the box would

occur at 3.68 if you could lneasure and cut

the paper at .01-eln. increments.

Getting Started 11

Setting the Viewing Window: Box with Lid

You also can use the graphing features of the TI-83 to find the nlaxinlunl value

of a previously defined function. When the graph is activated, the viewing

window defines the displayed portion of the coordinate plane. The values of

the window variables determine tile size of tile xqewing window.

Press _ to display tile window

editor, where you can view and edit the

values of the window variables.

WINDOW

XMin=-lO

XMax=lO

XscI=I

VMin=-lO

VMax=lO

Vscl=l

Xres=l

:_Ymax

Xscl

j Xmm

Xma× /

iZ Ysd

Ymin \

WINDOW

Xmin=O

XMax=20/2I

Xscl=l

VMin=-lO

YMax=IO

Yscl=l

Xres=l

WINDOW

XMin=O

Xmax=lO

XS61=I

VMin=O

VMax=500

Yscl=100

Xres=l

The standard window variables define the

viewing window _ shown. Xmin, Xmax,

Ymin, and Ymax define the boundm'ies of

the display. Xscl and Yscl define the

distance between tick nmrks on the Xand

Y taxes. Xres controls resolution.

2. Press 0_ to define Xmin.

3. Press 20 [] 2 to define Xmax using an

expression.

4. Press [g_gO. The expression is evaluated,

and 10 is stored in Xmax. Press [gffT_] to

accept Xscl as 1.

5. Press 0[ggggm500 [ggggm100 [g_gN 1[ggggm

to define the remaining window variables.

12 Getting Started

Displaying and Tracing the Graph: Box with Lid

Now that you have defined the function to be graphed and the window in

which to graph it, you can display- and explore the graph. You call trace along a

function using the TRACE feature.

1. Press _ to graph the selectedfunctionillthe viewing window. I_i/f .-_.-_-, Nj

The graph of Y1--(20 - 2X)(25/2 -X)X is

displayed.

Press [] to activate the free-moving graph

cursor,

The Xand Ycoordinate values for the

position of the graph cursor are displayed

on the bottom line.

3. Press _], [], [], and [] to move the free-

moving cm\sor to the apparent nlaxinmln

of the function.

As you move the cursor, the Xand Y

coordinate values are updated continually.

Getting Started 13

4. Press _. The trace cursor is displayed

on the Y1 function.

The function that you are tracing is

displayed in the top-left corner.

Press [] and [] to trace along Y1, one X dot

at a time, evaluating Y1 at each X.

You also can enter your estimate for the

nlaxinmln value of ×.

6. Press a [] 8. When you press a number key

while in TRACE, the X= prompt is displayed

in the bottom-left corner.

7. Press [gNT_.

The trace cursor jumps to tile point on the

Y1 function evaluated at X=a.8.

Press [] and [] until you are on the

nlaxinlunl Y wdue.

This is the nlaxinlunl of YI(X) for the X

pixel values. The actual, precise nl_kxinlunl

may lie between pixel values.

?t: G:'_)-::"}D_.::'_/::"-}{)}:

t/ ',..

[?t:{20-2g:l{2gc'2:-{,l)g

'¢l=€.RO-l_g)(2g/l_-l{)g

?t:G_O-_:8)(2:gd_-R):_

14 Getting Started

Zooming In on the Graph: Box with Lid

To help identify nlaxinlulns, nlininlulns, roots, and intersections of functions,

you can magnify the viewing window at a specific location using tile ZOOM

instructions.

1. Press _ to display- the ZOOM lnenu.

This menu is a typical TI-83 menu. To

select an item, you can either press the

number or letter next to the item, or you

can press [] until the item number or letter

is highlighted, and then press [_.

2. Press 2to select 2:Zoom In.

The graph is displayed again. The cursor

has changed to indicate that you m'e using

a ZOOM instruction.

With the cm_sor near the nlaxinlunl vMue

of the function (as in step 8 on page 14),

press [_.

The new viewing window is displayed.

Both Xmax-Xmin and Ymax-Ymin have

been adjusted by factors of 4, the default

values for the zoom factors.

MEMORY

3:Zoom Out

4:ZOeoiMal

5:ZS_uare

6:ZStandard

?4ZTPig

X=.3.7;_.3LI0_.Y=_:tl.=90.3;: .

Press _ to display the new window

settings.

WINDOW

Xmin=2.4734042_.

XMax=4.9734042...

Xsol=l

YMin=348.79032...

YMaX=473.79032...

Yscl=100

Xres=l

Getting Started 15

Finding the Calculated Maximum: Box with Lid

You can use aCALCULATE menu operation to calculate alocal maxinmm of a

function.

Press [2_ [CALC] (above _) to display

the CALCULATE menu. Press 4 to select

4:maximum.

The graph is displayed again with a

Left Bound? prompt,

Press [] to trace along the curve to a point

to tile left of the nlaxinluln, and then press

[N!N.

A _ at the top of the screen indicates the

selected bound.

ARight Bound? prompt is displayed.

3. Press [] to trace along the curve to a point

to the right of the nlaxinluln, and then

press [g_gm.

A _ at the top of the screen indicates the

selected bound.

AGuess? prompt is displayed.

Gu¢_=?

X=_.O69i_g9 Y=_06.9_216

4. Press [] to trace to a point neat" the

inaxiinuin, and then press [ggT_q.

Or, press 3[] 8, and then press [ggT_q to

enter a guess for the nmxinmm.

When you press a number key in TRACE,

the X= prompt is displayed in the bottom-

left corner.

Notice how the values for the calculated

nlaxinlunl compare with the nlaxinlunls

found with the free-moving cursor, the

trace cursor, and the table.

Note: In steps2 and 3 above,youcan entervalues

directlyfor Left BoundandRight Bound,in thesame

way as describedin step 4.

16 Getting Started

Other TI-83 Features

Getting Started has introduced you to basic TI-83 operation. This guidebook

describes in detail the features you used in Getting Started. It also covers the

other features and capabilities of the TI-83.

Graphing You can store, graph, and analyze up to 10 functions

(Chapter 3), up to six parametric functions (Chapter 4), up

to six polar functions (Chapter 5), and up to three

sequences (Chapter 6). You can use DRAW operations to

annotate graphs (Chapter 8).

Sequences You can generate sequences and graph thenl over time. Or,

you can graph them as web plots or as phase plots

(Chapter 6).

Tables You can create function evaluation tables to analyze nlany

functions sinmltaneously (Chapter 7).

Split Screen You can split the screen horizontally to display- both a

graph and a related editor (such msthe Y= editor), the

table, the stat list editor, or the home screen, Ms(), you can

split the screen verticMly to display a graph and its table

sinmltaneously (Chapter 9),

Matrices You can enter and save up to 10 matrices and perform

standard matrix operations on them (Chapter 10).

Lists You can enter and save as nlany lists as lllelllOl_y-allows for

use in statistical analyses. You can attach fornmlas to lists

for automatic computation. You can use lists to evaluate

expressions at nmltiple values sinmltaneously and to graph

a family of curves (Chapter 11).

Statistics You can perform one- and two-variable, list-based

statistical analyses, including logistic and sine regression

analysis. You can plot the data as a histogram, xyLine,

scatter plot, modified or regulm" box-and-whisker plot, or

normal probability plot. You can define and store up to

three stat plot definitions (Chapter 12).

Getting Started 17

Inferential

Statistics You can perform 16 hypothesis tests and confidence

inte_'als and 15 distribution functions. You can display

hypothesis test results graphically or numerically

(Chapter 13).

Financial

Functions You can use tilne-value-of-lnoney (TVM) functions to

analyze financial instruments such as annuities, loans,

mortgages, leases, and sa_lngs. You can analyze the value

of money over equal time periods using cash flow

functions. You can amortize loans with the amortization

functions (Chapter 14).

CATALOG The CATALOG is a convenient, alphal_etieal list of all

functions and instructions on the TI-83. You can paste any

function or instruction from the CATALOG to the current

cursor location (Chapter 15).

Programming You can enter and store programs that include extensive

control and input!output instructions (Chapter 16).

Communication

Link The TI-83 has a port to connect and conlnlunieate with

another TI-83, a TI-82, the Calculator-Based Laborato_sJ u

(CBL 2TM, CBL TM) System, a Calculator-Based Ranger TM

(CBWM), or a personal computer. The unit-to-unit link

cable is included with the TI-83 (Chapter 19).

18 Getting Started

1Operating

the TI-83

Contents Turning On and Turning Off tile TI-83 .................... 1-2

Setting the Display Contrast ............................. 1-3

Tile Display" .............................................. 1-4

Entering Expressions and Instructions ................... 1-6

TI-83 Edit Keys .......................................... 1-8

Setting Modes ........................................... 1-9

Using TI-83 Variable Names ............................. 1-13

Storing Variable Values .................................. 1-14

Recalling Variable Values ................................ 1-15

ENTRY (Last Entry) Storage Area ........................ 1-16

Ans (Last Answer) Storage Area ......................... 1-18

TI-8:_ Menus ............................................. 1-19

VARS and VARS Y-VARS Menus ......................... 1-21

Equation Operating System (EOS TM) ..................... 1-22

En'or Conditions ......................................... 1-24

TEXAS INSTRUMENTS TI-83

Sol Eng

123456789

Degree

Pol Se_

Dot

Si_ul

Horiz G-T

STAT PLOT TBLSET FORMAT CALC TABLE

Operating tile TI-83 1-1

Turning On and Turning Off the TI-83

Turning On the

Calculator

Turning Off the

Calculator

Batteries

To turn on the TI-83, press ION].

• If you previously had turned off the calculator by

pressing K_] [OFF], the TI-83 displays the home screen

as it was when you last used it and clears any error.

• If Automatic Power Down m (APD TM) hal p_eviously

turned off the calculator, the TI-83 will return exactly as

you left it, including the display, cursor, and any em)r.

To prolong the life of the batteries, APD turns off the TI-83

automatically after about five minutes without any actixqty.

To turn offthe TI-83 manually, press [_ [OFF].

• All settings and memory contents are retained by

Constant Memo_y TM.

• Any er_)r condition is cleared.

The TI-83 uses four AAA alkaline batteries and has a user-

replaceable backup lithium batte_Ty- (CR1616 or CR1620).

To replace batteries without losing any information stored

in memory, follow the steps in Appendix B.

1-2 Operating the TI-83

Setting the Display Contrast

Adjusting the

Display Contrast

When to Replace

Batteries

You can adjust the display contrast to suit your viewing

angle and lighting conditions. As you change the contrast

setting, a number from 0 (lightest) to 9 (darkest) in the

top-right corner indicates the current level. You may not be

able to see the number if contrast is too light or too dark.

Note: The T1-83 has 40 contrast settings, so each number 0through 9

represents four settings.

The TI-83 retains tile contrast setting in nlenlol_y- when it is

turned off.

To adjust the contrast, follow these steps.

1. Press and release the D_] key.

2. Press and hold [] or [], which are below and above the

contra_t sjnnbol (yellow, half-shaded circle).

• [] lightens the screen.

• [] darkens the screen.

Note: If you adjust the contrast setting to 0, the display may become

completely blank. To restore the screen, press and release _, and

then press and hold [] until the display reappears.

When the batteries are low, a low-battelT message is

displayed when you turn on the calculator.

Your battePies

ape lou.

Recommend

change of

batteries,

To replace the batteries without losing any- information in

memory, follow tile steps in Appendix B.

Generally-, the calculator will continue to operate for one

or two weeks after the low-batte<F message is fil_t

displayed. After this period, the TI-83 will turn off

automatically and the unit will not operate. Batteries nmst

be replaced. All nmmow is retained.

Note: The operating period following the first low-battery message

could be longer than two weeks if you use the calculator infrequently.

Operating the TI-83 1-3

The Display

Types of

Displays

Home Screen

Displaying

Entries and

Answers

Returning to the

Home Screen

Busy Indicator

The TI-83 displays both text and graphs. Chapter 3

describes graphs. Chapter 9 describes how the TI-83 can

display- a horizontally or vertically split screen to show

graphs and text simultaneously.

The home screen is the prima_T screen of the TI-83. On

this screen, enter instructions to execute and expressions

to evaluate. The answers are displayed on the same screen.

When text is displayed, the TI-83 screen can display a

nlaxinmm of eight lines with a nmxinmm of 16 characters

per line. If all lines of the display are full, text scrolls off

the top of the display. If an expression on the home screen,

the Y= editor (Chapter 3), or the program editor

(Chapter 16) is longer than one line, it wraps to the

beginning of the next line. In numeric editors such as the

window screen (Chapter 3), a long expression scrolls to

the right and left.

VC]mn an enhT is executed on the home screen, the answer

is displayed on the right side of the next line.

io9(2) Entry

• 3010299957 Answer

The mode settings control the way the TI-83 interprets

expressions and displays answers (page 1-9).

If an answer, such as a list or matrix, is too long to display

entirely on one line, an ellipsis (...) is displayed to the right

or left. Press [] and [] to scroll the answer.

ILl Entry

1{25.12 874.2 36_ Answer

To return to the honle screen fronl any- other screen, press

[_ [QUIT].

When the TI-83 is calculating or graphing, a vertical

moving line is displayed as a busy indicator in the top-right

corner of the screen. When you pause a graph or a

program, the busy indicator becomes a vertical moving

dotted line.

1-4 Operating the TI-83

Display Cursors In most cases, the appearance of the cursor indicates what

will happen when you press the next key- or select the next

menu item to be pasted as a character.

Cursor Appearance Effect of Next Keystroke

EntKF Solid rectangle A character is entered at the

• cursor; any existing character is

ove_wvritten

Insert Underline A character is inserted in front of

Second Reverse a_TOW A 2nd character (yellow on the

[] keyboard) is entered or a 2nd

operation is executed

Alpha Reverse A An alpha character (green on the

[] keyboard) is entered or SOLVE is

executed

Full Checkerboard No ently; the lnaxilnuln ehara('te_

rectangle are entered at a prompt or lnelnory

iiiiiii is full

If you press @ during an insertion, the cursor becomes

an underlined A (A) ff you p_ss [_ during an insertion, the

underline cursor becomes an underlined I' (I').

Graphs and editors sometimes display additional cursors,

which are described in other chapters.

Operating the TI-83 1-5

Entering Expressions and Instructions

What Is an

Expression?

Entering an

Expression

Multiple Entries

on a Line

An expression is a group of numbers, variables, functions

and their arguments, or a combination of these elements.

An expression evaluates to a single answer. On the TI-83,

you enter an expression in the same order _.s you would

write it on paper. For exalnple, xR 2 is an expression.

You can use an expression on tile home screen to calculate

an answer. In most places where a value is required, you

can use an expression to enter a value.

(i/3) z I WINDOW [

• 111111111 Xmin=-10

Xmax=2x I

To create an expression, you enter numbers, variables, and

functions from the keyboard and menus. AI_ expression is

coinpleted when you press [gNY_, regardless of the cursor

location. The entire expression is evaluated according to

Equation Operating System (EOS TM) rules (page 1-22), and

the answer is displayed.

Most TI-83 functions and operations are s3qnbols

comprising several characters. You nmst enter the symbol

from the keyboard or a menu; do not spell it out. For

example, to calculate the log of 45, you nmst press [UfN 45.

Do not enter the letters t., O, and 6. If you enter LOG, the

TI-83 inteqorets the enttT as implied nmltiplication of the

variables L, O, and G

Calculate 3.76 + (-7.9 + _5) + 2 Iog 45.

a[E]r6@DDrDg@

[d 5DD

@21 q 45D 2. 642575252

To enter two or more expressions or instructions on a line,

separate them with colons (@ [:]). All instructions are

stored together in last enttT (ENTRY; page 1-16).

15+R:2+B:R/B 2.51

1-6 Operating the TI-83

Entering a

Number in

Scientific

Notation

Functions

Instructions

Interrupting a

Calculation

To enter a number in scientific notation, ff)llow these

steps.

1. Enter the part of the number that precedes the

exponent. This value can be an expression.

2. Press [_ [EE]. Eis pasted to the cursor location.

3. If the exponent is negative, press D, and then enter the

exponent, which can be one or two digits.

l(19/2) £-2 .0951

When you enter a number in scientific notation, the TI-83

does not automatically display answers in scientific or

engineering notation. The mode settings (page 1-9) and the

size of the number determine the display- format.

A function returns a value. For example, +, -, +, _(, and log(

are tlle functions in the example on page 1-6. In general, the

first letter of each function is lowercase on the TI-83. Most

functions take at least one a_gument, as indicated by _m open

parenthesis ( ( ) following the name. For exalnple, sin(

_qui_s one argument, sin(value).

An instruction initiates an action. For example, ClrDraw is

an instruction that clears any- drawn elements from a

graph. Instructions cannot be used in expressions. In

general, the first letter of each instruction name is

uppercase. Some instructions take more than one

argument, as indicated by an ()pen parenthesis ( ( ) at the

end of the name. For example, Circle( requires three

arguments, Circle(X,Y, radius).

To intetTupt a eMeulation or graph in progress, which

would be indicated by the busy indicator, press [_].

When you interrupt a calculation, the menu is displayed.

• To return to the home screen, select 1:Quit.

• To go to the location of the interruption, select 2:Goto,

When you interrupt a graph, a partial graph is displayed.

• To return to the home screen, press @ or any

nongraphing key.

• To restart graphing, press a graphing key or select a

graphing instruction.

Operating the TI-83 1-7

TI-83 Edit Keys

Keystrokes

[] or []

Result

Moves the cursor within an expression; these keys repeat.

Moves the cursor from line to line within an expression that

occupies more than one line; these key-s repeat.

On the top line of an expression on the honle screen, [] nloves

the cursor to the beginning of the expression.

On the bottom line of an expression on the home screen, []

nloves the cursor to the end of the expression.

Moves the cursor to the beginning of an expression.

Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

On a line with text on the home screen, clears the current line.

On a blank line on the honle screen, clears everything on the

home screen.

In an editor, clears the expression or value where the cursor is

located; it does not store a zero.

Deletes a character at the cursor; this key repeats.

[_ tINS] Changes the cursor to __ ; inserts chm'acters in front of the

underline cursor; to end insertion, press [2_] [,NS] or press [], [],

[], or [].

[_ Changes the cursor to n; the next keystroke performs a 2nd

operation (an operation in yellow above a key- and to the left); to

cancel 2nd, press [2_] again.

@ Changes the cursor to i51;the next keystroke pastes an alpha

character (a character in green above a key and to the right) or

executes SOLVE (Chapters 10 and 11); to cancel @, press

@ or press _, [], [], or [].

[_ [A-LOCK] Changes the cursor to r/l;sets alpha-lock; subsequent keystrokes

(on an alpha key) paste alpha characters; to cancel alpha-lock,

press @; name prompts set alpha-lock automatically.

Pastes an X in Func Inode, a Tin Par Inode, a O in Pol Inode, or an

nin Seq mode with one keystroke.

1-8 Operating the TI-83

Setting Modes

Checking Mode

Settings

Changing Mode

Settings

Setting aMode

from a Program

Mode settings control how the TI-83 displays and

interprets numbers and graphs. Mode settings are retained

by the Constant Meln(aTy- feature when the TI-83 is turned

off. All numbet_, including elements of matrices and lists,

are displayed according to the current mode settings.

To display- the mode settings, press [Mff_]. The current

settings are highlighted. Defaults are highlighted below.

The following pages describe the mode settings in detail.

Normal Sci Eng Numeric notation

Float 0123456789 Nulnber of deeilnal places

Radian Degree Unit of angle men,sure

Func Par Pol Seq Type of graphing

Connected Dot Whether to connect graph points

Sequential Simul Whether to plot sinmltaneously

Real a+b ire^0 iReal, rectangular cplx, or polar eplx

Ful 1 H0ri z G T Full screen, two split-screen modes

To change nlode settings, follow these steps.

1. Press [] or [] to lnove the cm\sor to the line of the

setting that you want to change.

2. Press [] or [] to nlove the cursor to the setting you

want.

3. Press [ggY_,

You call set a mode fronl a program by entering the name

of the mode as all instruction; for example, Func or Float.

Fronl a blank eonlnland line, select the nlode setting fronl

the mode screen; the instruction is pasted to the cursor

location.

PROGRRM: TEST

:FuncI I

Operating the TI-83 1-9

Normal, Sci, Eng

Float,

0123456789

Notation modes only 'affect the way an answer is displayed

on the home screen. Numeric answers can be displayed

with up to 10 digits and a two-digit exponent. You can

enter a number in any- format.

Normal notation mode is the usual way we express

numbers, with digits to the left and right of the decimal, as

in 12345.67.

Sci (scientific) notation mode expresses number,s in two

pm'ts. The significant digits display- with one digit to the left

of the decimal. The app_)priate power of 10 displays to the

right of E, t_sin 1.234567E4.

Eng (engineering) notation mode is similm" to scientific

notation. However, the number can have one, two, or three

digits before the decimal; and the power-of-10 exponent is

a nmltiple of three, as in 12.34567E3.

Note: Ifyou select Normal notation, but the answer cannot display in

10 digits (or the absolute value is tess than .00I ), the TF83 expresses

the answer in scientific notation.

Float (floating) decimal mode displays up to 10 digits, plus

the sign and decimal.

0123456789 (fixed) decimal mode specifies the number of

digits (0 through 9) to display to the right of the decimal.

Place the cursor on the desired number of decimal digits,

and then press [ENYE_.

The decimal setting applies to Normal, Sci, and Eng

notation modes.

The decimM setting applies to these numbers:

• An answer displayed on the home screen

• Coordinates on a graph (Chapters 3, 4, 5, and 6)

• The Tangent( DRAW instruction equation of the line, x,

and dy/dx values (Chapter 8)

• Results of CALCULATE operations (Chapters 3, 4, 5,

and 6)

• The regression equation stored after the execution of a

regression lnodel (Chapter 12)

1-10 Operating the TI-83

Radian, Degree

Func, Par, Pol,

Seq

Connected, Dot

Angle modes control how the TI-83 inteq)rets angle values

in trigonometric functions and polar/rectangular

conversions.

Radian mode intelprets angle values as radians. Answers

display- in radians.

Degree mode interprets angle vMues as degrees. Answers

display- in degrees.

Graphing modes define the graphing paralneters. Chapters

3, 4, 5, and 6 describe these nlodes in detail.

Func (function) graphing mode plots functions, where Yis

a function of X (Chapter 3).

Par (parametric) graphing mode plots relations, where X

and Yare functions of T (Chapter 4).

Pol (polar) graphing mode plots functions, where r is a

function of 0 (Chapter 5).

Seq (sequence) graphing mode plots sequences (Chapter 6).

Connected plotting mode draws a line connecting each

point eMeulated for the selected functions.

Dot plotting mode plots only the e;flculated points of the

selected functions.

Operating the TI-83 1-11

Sequential, Simul Sequential graphing-order mode evaluates and plots one

function completely before the next function is evaluated

and plotted.

Simul (sinmltaneous) graphing-order mode evaluates and

plots all selected functions for a single wdue of X and then

evMuates and plots them for the next value of X.

Note: Regardless of which graphing mode is selected, the TI-83 wil!

sequentially graph all stat plots before it graphs any functions.

Real, a+bi, re^Of Real mode does not display complex results unless

complex numbers are entered as input.

Two complex modes display- complex results.

• a+bi (rectangulm" complex mode) displays complex

numbers in the form a+bi.

• re^0i (polar complex mode) displays complex numbers

in the fornl re^Oi.

Full, Horiz, G-T Full screen mode uses the entire screen to display- a graph

or edit screen.

Each split-screen nlode displays two screens

sinmltaneously.

•Horiz (horizontal) mode displays the current graph on

the top half of the screen; it displays the home screen or

an editor on the bottom h'alf (Chapter 9),

•G-T (graph-table) mode displays the current graph on

the left half of the screen; it displays the table screen on

the right half (Chapter 9).

1-12 Operating the TI-83

Using TI-83 Variable Names

Variables and

Defined Items

Notes about

Variables

On the TI-83 you can enter and use several types of data,

including real and complex numbe_\s, matrices, lists,

functions, stat plots, graph databases, graph pictures, and

strings.

The TI-83 uses ansigned names for variables and other

items saved in nlenlol_yL For lists, you 'also can create your

own five-character names.

Variable Type Names

Real numbers A, B,..., Z, 0

Complex numbers A, B,..., Z, 0

Matrices [A], [B], [C], . . . , [J]

Lists Cl, L2, L3, L4, LS, L6, and user-

defined haines

Functions Y1, Y2,..., Yg, Yo

Parametric equations XIT and YIT, ... , X6T and Y6T

Polar functions rl, r2, r3, r4, r5, r6

Sequence functions u, v, w

Stat plots Plot1, Plot2, Plot3

Graph databases GDB1, GDB2,..., GDB9, GDB0

Graph pictures Picl, Pic2,..., Pic9, Pic0

Strings Strl, Str2,..., Str9, Str0

System variables Xmin, Xmax, and others

• You can create as many list names as nlenlo_y- will Mlow

(Chapter 11).

•Progranls have user-defined nanles and share nlenlory

with variables (Chapter 16).

• FI_)lll the honle screen or fronl a progranl, you can store

to matrices (Chapter 10), lists (Chapter 11), strings

(Chapter 15), system variables such me Xmax (Chapter

1), TblStatt (Chapter 7), and all Y= functions (Chapters

3, 4, 5, and 6),

• FI_Olll an editor, you can store to matrices, lists, and

Y= functions (Chapter 3).

• FI_Olll the honle sereen_ a progranl, or all editor, you can

store a value to a lnatrix element or a list element.

• You can use DRAW STO menu items to store and reeM1

graph datab_kses and pictures (Chapter 8).

Operating the TI-83 1-13

Storing Variable Values

Storing Values in

aVariable

Displaying a

Variable Value

Values are stored to and recalled fronl nlenlol_- using

variable names. When an expression containing the name

of a variable is evMuated, the vMue of the variable at that

time is used.

To store a value to a vm'iable fronl the home screen or a

program using the _ key, begin on a blank line and

follow these steps.

1. Enter the value you want to store. The value can be an

expression.

2. Press _. -> is copied to the cursor location.

3. Press @ and then the letter of the variable to which

you want to store the value.

4. Press [gg_O. If you entered an expression, it is

evaluated. The value is stored to the variable.

[5+8_'3÷Q 517[

To display- the value of a vm'iable, enter the name on a

blank line on the home screen, and then press IgOr.

I° 5171

1-14 Operating the TI-83

Recalling Variable Values

Using Recall

(RCL)

To recall and copy variable contents to the current cursor

location, follow these steps. To leave RCk, press @.

1. Press [2_] ERCL]. Rcl and the edit cursor are displayed on

the bottom line of the screen.

Enter the name of the variable in any of five ways.

• Press @ and then the letter of the variable.

• Press [g_ [LIST], and then select the name of the list,

or press [g_ [Ln].

• Press _, and then select the name of the matrix.

• Press [V_g] to display the VARS menu or _ [] to

display the VARS Y-VARS menu; then select the type

and then the name of the variable or function.

• Press NRgM] [_, and then select the name of the

program (in the program editor only).

The variable name you selected is displayed on the

bottom line and the cursor disappeat\s.

100+

Rol 0

Press IENTEEI.The variable contents are inserted where

the cursor w_s located befot_ you began these steps.

1100+517I I

Note: You can edit the characters pasted to the expression without

affecting the value in memory.

Operating the TI-83 1-15

ENTRY (Last Entry) Storage Area

Using ENTRY

(Last Entry)

Accessing a

When you press [g_ on the holne screen to evaluate an

expression or execute an instruction, the expression or

instruction is placed in a storage area called ENTRY (last

ent_T). When you tu_ off the TI-83, ENTRY is retained in

lllelllOl_y',

To recall ENTRY, press 12_ [ENTRY].The last entry is

pasted to the cur_nt cursor location, where you can edit

and execute it. On the home screen or in an editor, the

current line is clea_d and the last entry is pasted to the

line.

Because the TI-83 updates ENTRY only when you press

[g_, you can recall the previous entry even if you have

begun to enter the next expression.

5[] 75+7 12

F_a] [ENTRY] 5 +711

The TI-83 retains as many previous entries as possible in

ENTRY, up to a capacity of 128 bytes. To scroll those

entries, press [_ [ENTRY] repeatedly. If a single ent_T is

more than 128 bytes, it is retained for ENTRY, but it cannot

be placed in the ENTRY storage area.

I_A 1÷1::1 12

I_ 2+B

2_B

[_ 2+BI

[ENTRY]

If you press [2@] [ENTRY] after displaying the oldest stored

enttT, the newest stored entry is displayed again, then the

next-newest entry, and so on,

[ENTRY]

2eB

1+RII

1-16 Operating the TI-83

Reexecuting the

Multiple Entry

Values on a Line

After you have pasted the last entt'y to the home screen

and edited it (if you chose to edit it), you can execute the

entry-. To execute the last ent_T, press [_T_].

To reexecute the displayed entry, press _ again. Each

reexecution displays an answer on the right side of the

next line; the entry- itself is not redisplayed.

F_°_ @ NO+N 0

@N[]I_@N N+I÷N:NZ

To store to ENTRY two or more expressions or

instructions, separate each expression or instruction with

a colon, then press [_T_. All expressions and instructions

separated by colons are stored in ENTRY.

When you press K_ [ENTRY], all the expressions and

instructions separated by colons are p_sted to the current

cursor locatkm. You can edit any of the entries, and then

execute all of them when you press [_R].

For the equation A=_r 2, use trial and error to find the radius of a

circle that covers 200 square centimeters. Use 8 as your first

guess.

[:][_ [_-]@ R[_7 [_E_

F_ [E.TR¥]

[] 7[_ [INS] [] 95

F_t_q

8÷R:_RZ I

201.0619298

8÷R:=RZI

8+R:_Rz

201.0619298

7.95+R:_Rz

198.5565097

Continue until the answer is as accurate as you want.

Clearing ENTRY Clear Entries (Chapter 18) cleats all data that the TI-83 is

holding in the ENTRY storage area.

Operating the TI-83 1-17

Ans (Last Answer) Storage Area

Using Ans in an

Expression

Continuing an

Expression

Storing Answers

When an expression is evaluated successfully- fronl the

home screen (Jr from a program, the TI-83 stores the

answer to a storage at_a called Ans (last answer). Ans nlay

be a real or complex number, a list, a lnatrix, or a string.

When you turn off the TI-83, the value in Ans is t_tained in

nlenlol_y.

You can use the variable Ans to represent the last answer in

most places. Press [2_] tANS] to copy the vm'iable name Ans

to the cm'sor location. When the expression is evaluated, the

TI-83 uses the value of Ans in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters.

Then calculate the yield per square meter if the plot produces a

total of 147 tomatoes.

1[]TN4C32

147 [] _ [ANS]

1.7.4.2 714[

147/Rn_ 5882s5291

You can use Ans as the first enhTy in the next expression

without entering the value again or pressing [_ tANS].On

a blank line on the home screen, enter the function. The

TI-83 pastes the vm'iable name Ans to the screen, then the

function.

s[]2 5/2 2.5

_gDg[N_ffl Rns*9.9 24.75

To store an answer, store Ans to a variable before you

evMuate another expression.

Calculate the area of a circle of radius 5 meters. Next, calculate

the volume of a cylinder of radius 5 meters and height 3.3 meters,

and then store the result in the variable V.

I_ [_]s []

N3D3

__v

xSZ

78.53981634

Rns*3.o I

Rns+U 259.1813939

259.1813939

1-18 Operating the TI-83

TI-83 Menus

Using a TI-83

Scrolling a Menu

You can access lnost TI-83 operations using lnenus. When

you press a key or key- combination to display a menu, one

or more menu names appear on the top line of the screen.

• The menu name on the left side of the top line is

highlighted. Up to seven items in that menu are

displayed, beginning with item 1, which 'also is

highlighted.

• A number or letter identifies each menu item's place in

the menu. The order is 1 through 9, then 0, then A, B, C,

and so on. The LISTNAMES, PRGM EXEC, and PRGM

EDIT menus only label items 1 through 9 and 0.

• When the menu continues beyond the displayed items, a

down arrow ( $ ) replaces the colon next to the last

displayed item.

• When a menu item ends in an ellipsis, the item displays

a secondat7 menu or editor when you select it.

To display any other menu listed on the top line, press []

or [] until that menu name is highlighted. The cursor

location within the initial menu is irrelewmt. The menu is

displayed with the cursor on the first item.

Note: The Menu Map in Appendix A shows each menu, each

operation under each menu, and the key or key combination you press

to display each menu.

To scroll down the menu items, press []. To scroll up the

menu items, press [].

To page down six menu items at a time, press @ []. To

page up six menu items at a time, press @ []. The

green arrows on the calculator, between [] and [], are the

page-down and page-up symbols.

To wrap to the last menu item directly fronl the first menu

item, press []. To wrap to the first menu item directly fi'om

the last menu item, press [].

Operating the TI-83 1-19

Selecting an Item

from a Menu

Leaving a Menu

without Making a

Selection

You can select an item from a menu in either of two ways,

• Press the number or letter of the item you want to

select. The cursor can be anywvhere on the menu, and

the item you select need not be displayed on the screen,

• Press [] or [] to move the cursor to the item you want,

and then press [E6T_.

After you select an item from a menu, the TI-83 typically

displays the previous screen,

Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT

menus, only items 1 through 9 and 0 are labeled in such a way that

you can select them by pressing the appropriate number key. To move

the cursor to the first item beginning with any alpha character or 6,

press the key combination for that alpha character or e. If no items

begin with that character, then the cursor moves beyond it to the next

item.

Calculate :_27.

You can leave a menu without making a selection in any- of

four ways.

• Press [_] [QUIT] to return to the home screen.

• Press @ to return to the prexdous screen.

• Press a key or key- combination for a different menu,

such as [M_ or [_ [LIST].

• Press a key or key combination for a different screen,

such as [] or _ [TABLE],

1-20 Operating the TI-83

VARS and VARS Y-VARS Menus

VARS Menu

Selecting a

Variable from the

VARS Menu or

VARS Y-VARS

You can enter the haines of functions and systeln varial>les

in an expression or store to them directly.

To display the VARS inenu, press _. All VARS inenu

items display secondm:y- menus, which show the names of

the system variables. 1:Window, 2:Zoom, and 5:Statistics

each access lnore than one secondaYy lnenu,

VARS Y VARS

i: Window...

2 : Zoom.,.

3: GDB...

4:Picture.,.

5:Statistics.,.

6: Table...

7: String..,

X/Y, T/O, and U/VNV variables

ZX/ZY, ZT/ZO, and ZU wuiables

Graph database vmiables

Picture variables

XY, Z, EQ, TEST, and PTS vmiables

TABLE vmiables

String variables

To display the VARS Y-VARS menu, press _ [].

1:Function, 2:Parametric, and 3:Polar display seconda[3_

menus of the Y= function vmiables.

VARS Y VARS

i: Function...

2: Parametric...

3:Polar...

4:On/Off...

Yn functions

X_?,T,Y'rtT functions

rn functions

Lets you select/deselect functions

Note: The sequence variables (u, v, w) are located on the keyboard

as the second functions olin, 1%1,and El.

To select a variable fronl the VARS or VARS Y-VARS menu,

follow these steps.

1. Display the VARS or VARS Y-VARS menu.

• Press [_ to display the VARS menu.

• Press _ [] to display the VARS Y-VARS lnenu.

2. Select the type of variable, such as 2:Zoom from the

VARS menu or 3:Polar froln the VARS Y-VARS menu. A

secondm:y- menu is displayed.

3. If you selected 1:Window, 2:Zoom, or 5:Statistics from

the VARS menu, you can press [] or [] to display ()the["

secondal_y- lnenus,

4. Select a variable name from the menu. It is pasted to the

CUrSOr location.

Operating the TI-83 1-21

Equation Operating System (EOS TM)

Order of

Evaluation The Equation Operating System (EOS TM) defines the order

in which functions in expressions are entered and

evaluated on the TI-83. EOS lets you enter numbers and

functions in a simple, straightfot_vard sequence.

EOS evaluates the functions in an expression in this order:

1 Single-argument functions that precede the

argument, such as ¢(, sin(, or log(

2 Functions that are entered after the argument,

such _ks2, -1, 1, o, r, and conversions

3 Powers and roots, such as 2^5 or 5x¢32

4 Pernmtations (nPr) and combinations (nOr)

5 Multiplication, implied nmltiplication, and

division

6 Addition and subtraction

7 Relational functions, such _ > or <

8 Logic operator and

9 Logic operators or and xor

Within a priority level, EOS evaluates functions fronl left to

right.

Calculations within parentheses are ewduated first.

Multiargument functions, such as nDeriv(A2,A,6), are

evaluated as they are encountered.

1-22 Operating the TI-83

Implied

Multiplication

Parentheses

Negation

The TI-83 recognizes implied nmltiplication, so you need

not press [] to express nmltiplication in all cases. For

example, the TI-83 intel_rets 2_, 4sin(46), 5(1+2), and (2"5)7

as implied nmltiplication.

Note: TI-83 implied multiplication rules differ from those of the TI-82.

For example, the TI-83 evaluates 1/2X as (1/2)*X, while the TI-82

evaluates 1/2X as 1/(2"X) (Chapter 2).

All calculations inside a pair of pm'entheses are completed

first. For example, in the expression 4(1+2), EOS first

evaluates the portion inside the pm'entheses, 1+2, and then

nmltiplies the answer, 3, by 4.

4.1+2 I_

4(1+2)

You can omit tile ('lose parenthesis ( )) at tile end of an

expression. All ()pen parenthetical elements are closed

automatic_dly at the end of an expression. This is Mso true

for open parenthetical elements that precede the store or

display-conversion instructions.

Note: An open parenthesis following a list name, matrix name, or Y=

function name does not indicate implied multiplication. It specifies

elements in the list (Chapter I1) or matrix (Chapter 10) and specifies a

value for which to solve the Y= function.

To enter a negative number, use the negation key. Press []

and then enter the number. On the TI-83, negation is in the

third level in the EOS hierm'chy. Functions in the fil\st

level, such as squaring, ale ewduated before negation.

For example, -X 2, evaluates to a negative number (or 0).

[ _se parentheses to square a negative number.

-2z _ 12->R

(-2) z _ -AZ 42

( -A )z-4

Note:Use the[] key forsubtractionand the[] keyfornegation.If

you press [] to enter a negative number, as in 9[] [] 7, or if you

press [] to indicate subtraction, as in !) [] 7, an error occurs. If you

press @ A [] @ B, it is interpreted as implied multiplication

(A*-B).

Operating the TI-83 1-23

Error Conditions

Diagnosing an

Error

Correcting an

Error

The TI-83 detects errot\s while performing these tasks.

• Ewduating an expression

• Executing an instruction

• Plotting a graph

• Storing a value

VClmnthe TI-83 detects an error, it returns an etTor

message as a menu title, such _ts ERR:SYNTAX or

ERR:DOMAIN. Appendix B describes each error type and

possible reasons for tile etTor.

ERR: S_,"NTRX I

_a[IQuit I

2: Goto

• If you select 1:OuR (or press [_ [QUIT]or @), then

tile home screen is displayed.

• If you select 2:Goto, then the prexqous screen is

displayed with the cut\sot at or neat" the error location.

Note: If a syntaxerroroccurs in thecontentsof a Y= functionduring

program execution, thenthe Goto option returnsto the Y=editor, not

to theprogram.

To eotTect an error, follow these steps.

1. Note the error type (ERR:e_9"or type).

2. Select 2:Goto, if it is available. The previous screen is

displayed with the cursor at or neat" the error location.

3. Determine the error. If you cannot recognize the error,

refer to Appendix B.

4. Correct the expression.

1-24 Operating the TI-83

Math,Angle,andTest

Operations

Contents Getting Started: Coin Flip ................................ 2-2

Keyboard Math Operations .............................. 2-3

MATH Operations ........................................ 2-5

Using the Equation Solver ............................... 2-8

MATH NUM (Number) Operations ........................ 2-13

Entering and Using Complex Nmnbers ................... 2-16

MATH CPX (Complex) Operations ....................... 2-18

MATH PRB (Probability) Operations ..................... 2-20

ANGLE Operations ....................................... 2-23

TEST (Relational) Operations ............................ 2-24

TEST LOGIC (Boolean) Operations ...................... 2-26

'_ TEXAS iNSTRUMENTS T1=83

Q^3+PZ-125=O

-Q=4.6415888336...

P=5

bound={-50,50}

-le_t-rt=O

STAT PLOT TBLSET FORMAT CALC TABLE

Math, Angle, and Test Operations 2-1

Getting Started: Coin Flip

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to model flipping a fair coin 10 times. You want to track

how many of those 10 coin flips result in heads. You want to perform this

sinmlation 40 times. With a fair coin, the probability of a coin flip resulting in

heads is 0.5 and the probability of a coin flip resulting in tails is I).5.

1. Begin on tile home screen. Press [_ [] to

display the MATH PRB menu. Press 7 to

select 7:randBin( (random Binomial).

randBin( is pasted to the home screen. Press

10 to enter the number of coin flips. Press

[]. Press [] 5to enter the probability of

heads. Press []. Press 40 to enter the

number of sinmlations. Press D-

2. Press _ to evaluate the expression. A

list of 40 elements is displayed. The list

contains the count of heads resulting from

each set of 10 coin flips. The list has 40

elements because this sinmlation was

performed 40 times. In this example, the

coin came up heads five times in the first

set of 10 coin flips, five times in the second

set of 10 coin flips, and so on.

3. Press [_ [_ [L1][gNTgmto store the data

to the list name L1.You then can use the

data for another activity, such as plotting a

histogram (Chapter 12).

4. Press [] or [] to view the additional counts

in the list. Ellipses (...) indicate that the list

continues beyond the screen.

Note: Since randBin( generates random

numbers, your list elements may differ from those

in the example.

_andBin(10,.5,40

_andBin( 10,. 5,40

{5574663_.

Rgs_L_ 4 6 6 3 ...

andBin( 10,. 5, 40

5 5 7 4 6 6 3 ,..

..£._._L_6 5 7 5 ...

2-2 Math, Angle, and Test Operations

Keyboard Math Operations

Using Lists with

Math Operations

+ (Addition),

-(Subtraction),

* (Multiplication),

/(Division)

Math operations that are valid ff)rlists return a list

calculated element by element. If you use two lists in the

same expression, they nmst be the same length.

{1,2}+{3, 4}+5

{9 113

You can use +(addition, E]), - (subtraction, E]), *

(nmltiplieation, [_), and /(division, []) with real and

complex numbers, expressions, lists, and lnatrices. You

cannot use /with matrices.

valueA+valueB

valueA*valueB

valueA -valueB

valueA / valueB

Trigonometric

Functions

^(Power),

2(Square),

,[( (Square Root)

-1 (inverse)

You can use the trigonometric (trig) functions (sine, [gN];

cosine, [Ugg]; and tangent, _) with real number\%

expressions, and lists. The current angle mode setting

'affects interpretation. For example, sin(a0) in Radian mode

tetut]ls -.9880316241; in Degree mode it returns .5.

sin(value) cos(value) tan(value)

You can use the inverse trig functions (aresine, [g_] [StN-1];

arccosine, [g_] [c05-t]; and arctangent, [g_] [TAN-t])with

real nmnbers, expressions, and lists. The current angle

mode setting affects interpretation.

sin -1(value) cos -1(value) tan -1(value)

Note: The trig functions do not operate on complex numbers.

You can use ^ (power, [_), 2 (square, [77]),and _/( (square

root, [g_] [4]) with teal and complex numbers, expressions,

lists, and nmtrices. You cannot use _( with matrices.

value^power value 2 _[(value)

You can use -1 (inverse, [] ) with real and complex

numbers, expressions, lists, and matrices. The

nmltiplieative inverse is equivalent to the reciprocal, l/x.

value-1

15' .21

Math, Angle, and Test Operations 2-3

log(,

10^(,

In(

e^( (Exponential)

e(Constant)

-(Negation)

(Pi)

You can use log( (logarithln, FO_), 10^( (power of 10, [_

[10x]), and In( (natural log, @) with real or eolnplex

nulnbers, expressions, and lists,

log(value) lO^{power) In(value)

e^( (exponential, [2_ [ex]) returns the constant eraised to

a power. You can use e^( with real or complex numbers,

expressions, and lists.

eA(t)owe_ ,')

le^(5)148.41315911

e(constant, [g_] [el) is stored as a constant on the TI-83.

Press Kfid][el to copy eto the cursor location. In

calculations, the TI-83 uses 2.718281828459 for e.

e2.718281828

- (negation, D) returns the negative of value. You can use -

with real or complex numbers, expressions, lists, and

matrices.

-value

EOS rules (Chapter 1) determine when negation is

evaluated. For example, -A2t_turns a negative nulnber,

because squaring is evaluated before negation. Use

parentheses to square a negated number, as in (-A)2,

2+R: {-RZ, ( -R>a, -

2z, ( -2)z}

{-4 4 -4 4}

Note: On the TI-83, the negation symbol (-) is shorter and higher than

the subtraction sign (-), which is displayed when you press D.

(Pi, [g_ [_]) is stored as a constant in the TI-83, In

calculations, the TI-83 uses 3.1415926535898 for _.

Ix 3.1415926541

2-4 Math, Angle, and Test Operations

MATH Operations

MATH Menu

_Frac,

_Dec

To display the MATH menu, press [MKTgl.

MATH NUMCPX PRB

1: _Fra c Displays the answer as a fraction.

2:_Dec

3:3

4:3_(

5: x#

6: fMin(

7: fMax(

8:nDeriv(

9: fnlnt(

O: Solver.,.

Displays the answer as a decimal.

Calculates the cube.

Calculates the cube root.

Calculates the x t;_root.

Finds the nlininmln of a function.

Finds the nlaxinlunl of a function.

(3olnputes the numerical derivative.

(Tonlputes tile function integral.

Displays the equation solver.

_Frac (display at a fraction) displays an answer _L_its

rational equivalent. You can use _Frac with real or complex

numbers, expressions, lists, and matrices. If the answer

cannot be simplified or the resulting denominator is more

than three digits, the decimal equivalent is returned. You

can only use _Frac following value.

value _Frac

_Dec (display as a decimal) displays an answer in decimal

form. You can use *Dec with real or complex numbet_,

expressions, lists, and matrices. You can only use _Dec

following value.

value _Dec

I/2+I/3_Frac o/61

Ans_Deo

.8333333333

Math, Angle, and Test Operations 2-5

3(Cube),

3_r( (Cube Root)

x_ (Root)

fMin(,

fMax(

3(cube) returns the cube of value. You can use 3with real

or complex numbers, expressions, lists, and square

nmtrices.

value 3

3_( (cube root) returns the cube root of value. You can use

3_( with real or complex numbers, expressions, and lists.

3_(value)

{2,3,4,5}3{8 27 64 125}

_J'(Rns){2 3 4 5}

x_ (xth root) returns the x th root of value. You can use x_

with real or complex numbers, expressions, and lists.

xthrootX-_ value

5 N'32 2

fMin( (function nlininlunl) and fMax( (function nlaxinlunl)

retun_ the value at which the local ndninmm or local

nmxinmnl value of expression with respect to variable

occurs, between/ower and upper values for variable, fMin(

and fMax( are not valid in expression. The accuracy" is

controlled by tolerance (if not specified, the default is

iE-5),

fMin(expression,variable,lower,upper[,toleranoe])

fMax(expression,variable,lower, upper[,toleranoe])

Note: In this guidebook, optional arguments and the commas that

accompany them are enclosed in brackets ([ ]).

f'Min(_in(R), R, -_

-I. 570797171

r_x(sir,(A), R,-:_

• 1.570797171

2-6 Math, Angle, and Test Operations

nDeriv(

fnlnt(

nDeriv( (numerical derivative) returns an approximate

derivative of expression with respect to variable, given the

value at which to calculate the derivative and e (if not

specified, the default is 1E-3). nDeriv( is valid only for real

numbers,

nDeriv(expression,variable,value[,a])

nDeriv( uses the s:nnmetrie difference quotient method,

which approximates the numerical derivative value as the

slope of the secant line through these points.

f(x+e)-f(x-e)

f'(x) =2e

As e becomes smaller, the approxinmtion usually- becomes

nlore accurate.

nDer iv(RA3, R, 5,.

01 ) 75,0001

nDeriv(R^3o R, 5,.

0001 ) 75

You can use nOeriv( once in expression. Because of the

method used to calculate nDeriv(, the TI-83 can return a

false derivative value at a nondifferentiable point.

fnlnt( (function integral) returns the numerical integral

(Gauss-Kronrod method) of expression with respect to

variable, given/ower limit, upper limit, and a tolerance (if

not specified, the default is 1E-5). fnlnt( is valid only- for real

nunlbers.

fnlnt(expression,variable,lower, upper[,tolerance])

?nlnt(A_,R,O&l)

•3333330333

Tip: To speed the drawing of integration graphs (when fnlnt( is used

in a Y= equation), increase the value of the Xres window variable

before you press _.

Math, Angle, and Test Operations 2-7

Using the Equation Solver

Solver

Entering an

Expression in the

Equation Solver

Solver displays the equation solver, in which you can solve

for any variable in an equation, The equation is assunled to

be equal to zero. Solver is valid only for real numbers.

Vcl_en you select Solver, one of two screens is displayed.

• The equation editor (see step 1 picture below) is

displayed when the equation wu'iable eqn is empty,

• The interactive solver editor (see step 3 picture on page

2-9) is displayed when an equation is stored in eqn.

To enter an expression in the equation solver, assunling

that the variable eqn is empty, follow these steps.

1, Select 0:Solver from the MATH menu to display- the

equation editor.

EQUATION SOLVER

e_n: 0=|

2, Enter the expression in any of three ways,

• Enter the expression directly into the equation

solver,

• Paste a Y= vmiable name from the VANS Y-VANS

lnenu to the equation solver,

• Press [_ [act_], p_kste a Y= variable name from the

VANS Y-VANS lnenu, and press [_, The

expression is pasted to the equation solver.

The expression is stored to the variable eqn as you

enter it.

EQURTION SOLVER

e_n: O=Q"3+P z-125

2-8 Math, Angle, and Test Operations

Entering and

Editing Variable

Values

3, Press _ or [_. The interactive solver editor is

displayed.

1%35 -1 5=8

P=8 1...

bound={ -1 E99,

• The equation stored in eqn is set equal to zero and

displayed on the top line.

• Variables in the equation are listed in tile order in

which they appear in the equation. Any values stored

to the listed variables also are displayed.

• The default lower and upper bounds appeal" in the

last line of the editor (bound={-1E99,1E99}).

• A 4 is displayed in the first colunul of the bottonl line

if tile editor continues beyond the screen.

Tip: To usethe solverto solve an equationsuchas K=.SMV2, enter

eqn:0=K-.SMV 2 inthe equationeditor.

When you enter or edit a value for a variable in the

interactive solver editor, the new value is stored in

nlenlol_y- to that varialfle.

You can enter an expression for a variable value. It is

ewduated when you move to the next varialfle.

Expressions nmst resolve to real numbers at each step

during the iteration.

You can store equations to any VAR8 Y-VARS variables,

such as Y1 or r6, and then reference the w_riables in tile

equation. The interactive solver editor displays all

varialfles of all Y= functions referenced in the equation.

EQURTION SSL_)ER Ie_n: 8=V., +7

Y_+7=Obound=C=BR=SX=8{ -i E99, I.,.

Math, Angle, and Test Operations 2-9

Solving for a

Variable in the

Equation Solver

To solve for a variable using the equation solver after an

equation has been stored to eqn, follow these steps.

1. Select 0:Solver from the MATH menu to display the

interactive solver editor, if not already displayed.

I% ;P -125=°P=oL.

bound={-1E99,

2. Enter Ol" edit tile value of each known variable. All

variables, except the unknown variable, nmst contain a

value. To move the cm\sor to the next wuiable, press

INto or _.

QQ3;PZ-125=0p=5I 1...

bound={ -1 E99,

3. Enter an initial guess for tile variable for which you are

solving. This is optional, but it may help find the

solution more quickly-. Also, for equations with nmltiple

roots, the TI-83 will attempt to display the solution that

is closest to your guess,

IQ"3+Pp=sQ=4Iz- 125=0 1...

bound={ -I E99,

The default guess is calculated as (upper+ lower)

2-10 Math, Angle, and Test Operations

4. Editbound={lower,upper},lower and upper are the

bounds between which the TI-83 searches for a solution.

This is optional, but it may help find the solution more

quickly. The default is bound={- 1E99,1E99}.

5. Move the cursor to the variable for which you want to

solve and press @ [SOLVE](above the [gNTgNkey-).

Q_'3+PZ-125=0

I,Q=4.6415888336...

P=5

bound={-50,50}

leCt-rt=O

The solution is displayed next to tile variable for

which you solved. A solid square in the fil_t colunm

marks the variable for which you solved and

indicates that the equation is balanced. An ellipsis

shows that tile value continues beyond the screen.

Note: When a number continues beyond the screen, be sure to

press [] to scroll to the end of the number to see whether it

ends with a negative or positive exponent. A very small number

may appear to be a large number until you scroll right to see

the exponent.

The values of the variables are updated in nlenlot'y.

left-rt=diffis displayed in the last line of the editor.

diffis tile difference between the left and right sides

of the equation. A solid square in the first colunm

next to left-rt= indicates that the equation has been

evaluated at the new value of tile variable for which

you solved.

Math_ Angle_ and Test Operations 2-11

Editing an

Equation Stored

to eqn

Equations with

Multiple Roots

Further Solutions

Controlling the

Solution for

Solver or solve(

Using solve( on

the Home Screen

or from a

Program

To edit or replace an equation stored to eqn when the

interactive equation solver is displayed, press [] until the

equation editor is displayed. Then edit the equation.

Sonle equations have nlore than one solution. You can

enter a new initial guess (page 2-10) or new bounds

(page 2-11) to look for additional solutions.

After you solve for a varialfle, you can continue to explore

solutions from the interactive solver editor. Edit the values

of one or more varialfles. When you edit any variable value,

the solid squares next to the previous solution and

left-rt=diff disappear. Move the cursor to the varialfle for

which you now want to solve and press @ [SOLVE].

The TI-83 solves equations through an iterative process. To

control that process, enter bounds that are relatively close

to the solution and enter an initial guess within those

bounds. This will help to find a solution more quickly. Also,

it will define which solution you want for equations with

nmltiple solutions.

The function solve( is available only fronl CATALOG or

from within a program. It returns a solution (root) of

expression for variable, given an initial guess, and lower

and upper bounds within which the solution is sought. The

default for lower" is -1E99. The default for upper is 1E99.

solve( is vMid only for real numbers.

soNe(expression,variable,guess[ ,{lower, upper'} ])

expression is assumed equal to zero. The value of variable

will not be updated in nlenlory, guess nlay be a value or a

list of two values. Values must be sto[_d for eve_Ty"variable

in expression, except variable, before expression is

evaluated./ower and upper nmst be entered in list format.

4. 641588834

2-12 Math, Angle, and Test Operations

MATH NUM (Number) Operations

MATH NUM Menu

abs(

round(

To display the MATH NUM menu, press _ [Z],

MATH NUM CPX PRB

i : ab s ( Al_solute value

2: round( Round

3 : i Part ( Integer part

4 : f Pa r t ( Fractional part

5 : i nt( Greatest integer

6 : mi n (Mininmln value

7 : max ( Maxinlunl value

8 : ] cm( Legist eonlnlon nmltiple

9 :gcd ( Greatest eonnnon divisor

abs( (absolute value) returns the absolute value of real or

complex (modulus) numbers, expressions, lists, and

matrices.

abs(value)

abs ( -256 ) 2561,

abs( {I.25, -5.67}

I {1.25 5.67}

Note: abs( is also available on the MATH CPX menu.

round( returns a nunlber, expression, list, or nlatrix

rounded to #decimals (_<9). If #decimals is omitted, value

is rounded to the digits that are displayed, up to 10 digits.

round(value [,#decimals ])

round (x, 4) 3. 1416

123456789012÷C I

1.23456789E111

C-round(C) !21

123456789012-Iz3

456789000 12

Math, Angle, and Test Operations 2-13

iPart(,

fPart(

int(

iPart( (integer part) returns the integer part or parts of ++al

or complex numbers, expressions, lists, and matrices.

iPart(value)

fPart( (fra('tional paxt) returns the fractional part or p_u'ts of

real or complex numbe_, expressions, lists, and lnatrices.

fPart(value)

iPart (-23.45) -23

f Part ( -23.45)._ 45

int( (greatest integer) returns the largest integer _<real or

complex numbers, expressions, lists, and nmtrices.

int(value)

lint(-23.45) _241

Note:Fora givenvalue,theresultofint(isthesame as theresultof

iPart( for nonnegative numbers and negative integers, but one integer

less than the result of iPart( for negative noninteger numbers.

2-14 Math, Angle, and Test Operations

min(,

max(

Icm(,

gcd(

min( (ndnimum value) returns the smaller of valueA and

valueB or the smallest element in list, If listA and listB are

compared, min( returns a list of the smaller of each pair of

elements, If list and value are compared, min( compares

each element in list with value,

max( (n]axin]on] value) returns the larger of valueA and

valueB or the largest element in list. If listA and listB are

con]pared, max( retm'ns a list of the larger of each pair of

elements. If list and value are compared, max( compares

each element in list with value,

min(valueA,valueB) max(valueA,valueB)

min(list) max(list)

min(listA,listB) max(listA,listB)

min(list,value) max(list,value)

r,,in(3,2+2)= 3[

r,,in( {3, 4, _,}, 4) I

{3 4 4}

r,Jax( {4, 5, 6}) 6

Note: rain( and max( also are available on the LIST MATH menu.

Icm( t_tums the least eonlnlon nmltiple of valueA and

valueB, both of which must be nonnegative integers, When

listA and listB are specified, Icm( retm'ns a list of the lcm

of each pair of elements. If list and value are specified,

Icm( finds the leln of each element in list and value,

gcd( returns the greatest conlnlon divisor of valueA and

valueB, both of which must be nonnegative integers, When

listA and listB are specified, gcd( t'etun_s a list of the ged

of each pair of elements. If list and value are specified,

gcd( finds the ged of each element in list and value,

Icm(valueA,valueB) gcd(valueA,valueB)

Icm(listA,listB) gcd(listA,listB)

Icm(list,value) gcd(list,value)

10M(2,5) 10

god( {48, 66}, {64,

122} ){16 2}

Math, Angle, and Test Operations 2-15

Entering and Using Complex Numbers

Complex-Number

Modes The TI-83 displays complex numbers in rectangular form

and polar forln. To select a complex-nulnber lnode, press

[MffffE],and then select either of the two modes.

•a+bi (rectangular-complex lnode)

•re^0/(polar-colnplex mode)

Sci Eng

Entering

Complex

Numbers

Note about

Radian versus

Degree Mode

Dot

Horiz G-T

On the TI-83, complex numbet\s can be stored to variables.

Also, complex numbers are valid list elements.

In Real mode, COlnplex-nulnber results return an error,

unless you entered a complex number as input. For

example, in Real mode In(-1) returns an error; in a+bi nlode

In(-1) returns an answer.

Real mode

lin<-i;,m l

ERR-'NONRERL RNS i

ilBQuit i

2: Goto

a+bi lnode

Iln( -l>m I

Complex numbers are stored in rectangular form, but you

can enter a complex number in rectangulm' form or polar

form, regm'dless of the mode setting. The components of

complex numbers can be real numbers or expressions that

evMuate to reM numbers; expressions m'e evMuated when

the connnand is executed.

Radian mode is reconnnended for conlplex number

calculations. Internally-, the TI-83 converts all entered trig

values to radians, but it does not convert values for

exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as

e^ (i0) = cos(0) + isin(0) are not generally true because

the values for cos and sin are converted to radians, while

those for e ^ () are not. For example,

e^(i45) = cos(45) + isin(45) is treated internally as

e^ (i45) = cos(_/4) + isin(x/4). Complex identities are

always tree in radian mode.

2-16 Math, Angle, and Test Operations

Interpreting

Complex Results

Rectangular-

Complex Mode

Polar-Complex

Mode

Complex numbers in results, including list elements, are

displayed in either rectangular or polar form, as specified

by the mode setting or by a display conversion instruction

(page 2-19). In the example below, re^0/and Radian modes

are set.

_2+t)-(le'-(x/4t)

1.325654296e^( ....

Rectangular-complex mode recognizes and displays a

complex number in the fore1 a+bi, where a is the ten

component, b is the imagimuy component, and iis a constant

equM to @'1.

-1)

lln< 3.141592654tI

To enter a complex nulnber in rectangular form, enter the

value of a(real component), press [] or [], enter the value

of b(imaginary component), and press [_ [i] (constant).

real component(÷ or -)imaginary cornponenti

14+2t 4+2t I

Polar-complex mode recognizes and displays a complex

number in the form re ^ 0/, where ris the nmgnitude, eis the

b_e of the natm'al log, 0is the angle, and iis a constant equM

in(-I)

3.141592654e^ ( I...

To enter a complex number in polar ff)nn, enter the value

of r (magnitude), press [_ [ex] (exponential function),

enter the value of 0(angle), press [_ [i] (constant), and

then press D.

ma_dtudeea(anglei)

10e._(n/3t)

10e"(I.04719755...

Math, Angle, and Test Operations 2-17

MATH CPX (Complex) Operations

MATH CPX Menu

conj(

real(

imag(

To display the MATH CPX menu, press [_ [] [],

MATH NUM

1:conj(

2:real(

3:imag(

4:angle(

5:abs(

6:_Rect

7:_Polar

CPX PRB

Returns the complex conjugate,

Returns the real part.

Returns the imaginary part,

Returns the polar angle.

Returns the magnitude (modulus),

Displays the result in rectangular form,

Displays the result in polar form,

conj((conjugate) returns the complex conjugate of a

complex number or list of complex numbers,

conj(a+bi) returns a-bi in a+bi nlode,

conj(re^(0i)) returns re^C0/) in re^ei mode,

toni (3+4t) 3-4t1 c°nJ (3e^(4t >>

3e"(2. 28318530?._

real( (real part) returns the real part of a complex number

or list of complex nmnbers,

real(a+bi) returns a,

real(f'e^(0i)) returns _"*cos(O).

r.eal(3+4t) 3[ real (3e_'(4t > >

-I.968938863

imag( (imaginary part) returns the imagining- (nonreal) part

of a complex number or list of complex numbers.

imag(a+bi) t_tunls b.

imag(re^(Oi)) returns _'_sin(O),

Iimag(3+4t ) 41 imag(3e^(4t >>-2.270407486

2-18 Math, Angle, and Test Operations

angle(

abs(

_Rect

)Polar

angle( returns the polar angle of a complex number or list

of complex numbers, calculated as tan -1 (b/a), where b is

the imaginatT part and a is the real part. The calculation is

adjusted by +x in the second quadrant or -x in the third

quadrant.

angle(a+bi) returns tan-l(b/a).

angle(re^(Oi)) returns 0, where -x<O<x.

an91 e (3+4t ) an91 e (38^ (4i.) )

•927295218 -2. 283185387

abs( (absolute value) returns the lnagnitude (lnodulus),

_(real2+imag2) , of a complex nulnber or list of eonlplex

nulnl)ers,

abs(a+bi) returns _ .

abs(re^(Oi)) returns r(nmgnitude),

labs(3+4t ) 51 [abs(3e^(4t )) 31

)Rect (display as reetanguhu') displays a complex t_sult in

rectangular form. It is valid only at the end of an

expression, It is not valid if the result is real,

complex result_Rect returns a+bi.

_Rec.t

1#(-2_.414213562t1

)Polar (display as polar) displays a coInplex result in polar

form, It is valid only at the end of an expression. It is not

valid if the result is real.

corr_plexresult_Polarreturnsre (_).

#(-2)_PolaP

1.4142135628^(I...

Math, Angle, and Test Operations 2-19

MATH PRB (Probability) Operations

MATH PRB Menu To display the MATH PRB menu, press _ E},

MATH NUMCPX PRB

i: rand

2: nPr

3:nCr

4:!

5: randlnt(

6: randNorm(

7: randBin(

Randonl-nunlber generator

Number of pernmtations

Number of combinations

Factorial

Random-integer generator

Random # from Normal distribution

Random # from Binomial distribution

rand rand (random number) generates and returns one or more

random numbers > 0 and < 1. To generate a list of random-

numbers, specify- an integer > 1 for numt'rials (number of

trials). The default for numt'rials is 1.

rand [(num trials)]

Tip: To generate random numbers beyond the range of Oto I, you

can include rand in an expression. For example, rand*5 generates a

random number > 0 and < 5.

With each rand execution, the TI-83 generates the salne

randonl-number sequence for a given seed value. The TI-83

factoFf-set seed value for rand is 0. To generate a different

randonl-number sequence, store any nonzero seed value to

rand. To restore the factoFy--set seed vMue, store 0 to rand

or reset the defaults (Chapter 18).

Note: The seedvaluealso affectsrandlnt(, randNorm(, and

randBin( instructions(page2-22).

r'and

•1272157551

1÷rand 2646513087

rand(3)

{. 7455607728

2-20 Math, Angle, and Test Operations

nPr,

nCr

!(Factorial)

nPr (number of permutations) returns the number of

pernmtations of items taken number at a time. items and

number must be nonnegative integers, Both items and

number can be lists.

items nPr number

nCr (number of combinations) returns the number of

combinations of items taken number at a time. items and

number nmst be nonnegative integers. Both items and

number can be lists.

itemsnCrnumb_"

5 nPe 2 (2_2_i;

5 nCe 2

{2,3> nPP _ 6}

! (factorial) returns the factorial of either an integer or a

nmltiple of .5. For a list, it returns factorials for each

integer or nmltiple of .5. value nmst be _>-.5 and _<69.

value!

£120 24 720}

Note: The factorial is computed recursiveiy using the relationship

(n+t)! = n.n!, until n is reduced to either 0 or -1/2. At that point, the

definition 0!=I or the definition (-1/2)!=_- is used to complete the

calculation. Hence:

n!=n*(n-I )*(n-2)* ... *2* I, if n is an integer >0

n!= n*(n-1 )*(n-2)* ....1/2.-_;, if n+1/2 is an integer >O

n! is an error, if neither n nor n+I/2 is an integer >0.

(The variable n equals value in the syntax description above.)

Math, Angle, and Test Operations 2-21

randlnt(

randNorm(

randBin(

randlnt( (random integer) generates and displays a random

integer within a range specified by lower and upper integer

bounds. To generate a list of random numbers, specify an

integer > 1 for numt,Fials (number of trials); if not

specified, the default is 1.

randlnt(lower,upper[,numtrials])

rand Int ( 1,6)+ra G

dlnt(1,6)

randInt( 1,{26, 3)i5}

randNorm( (random Normal) generates and displays a

random real number fi'onl a specified Normal distribution.

Each generated value could be any real number, but most

will be within the intercal [p-3(_), p+3(o)]. To generate a

list of random numbers, specify- an integer > 1 for

numtrials (number of trials); if not specified, the default

is 1.

randNorm(p,ol,numtrials])

randNorm(O, 1)

.0_7207G175

_ndNo:r,(35,2,10

_34.02r01938 37_.

randBin( (randon] Binomial) generates and displays a

random integer from a specified Binomial distribution.

numtrials (nmnber of trials) lnust be _>1, prob (probability

of success) must be _>0 and _<1. To generate a list of

randonl nunlbers, specify an integer > 1 for

numsimulations (nmnber of sinmlations); if not specified,

the default is 1.

randBin(numtrials,prob[,numsimulations])

randBirKS,,2) 3

randBin(7,. 4, 10)

{332512 2 ...

Note: The seed value stored to rand also affects randlnt(,

randNorm(, and randBin( instructions (page 2-20).

2-22 Math, Angle, and Test Operations

ANGLE Operations

ANGLE Menu

DMS Entry

Notation

°(Degree)

To display the ANGLE menu, press [_ [ANGLE]. The ANGLE

menu displays angle indicatot\_ and instruetions. The

Radian/Degree mode setting affects the TI-S3's

interpretation of ANGLE menu entries.

ANGLE

1: °

2:'

3: r

4: ,DMS

5: R,Pr(

6: R_PO(

7: P_Rx(

8: PmRy(

Degree notation

DMS minute notation

Radian notation

Displays as degree/lninute/seeond

Returns r, given X and Y

Returns 0, given X and Y

Returns x, given R and 0

Returns y, given R and 0

DMS (degrees/minutes/seconds) entlT notation comprises

the degree sjonbol (°), the minute sjonbol ('), and the

second symbol ("). degrees nmst be a real number;

minutes and seconds nlust be real numbers _>0.

degrees°minutes'seconds ''

For exalnple, enter for 30 degrees, 1 minute, 23 seconds. If

the angle nlode is not set to Degree, you nmst use ° so that

the TI-83 call interpret the atgulnent as degrees, minutes,

and seconds.

Degree mode

sin(30° 1'23") I

.5003484441

Radian mode

sin(30° 1'23") I

-. 98421299951

sin(30 °l 23 o)

•5003484441

°(degree) designates an angle or list of angles as degrees,

regardless of the current angle mode setting. In Radian

nlode, you Call use ° to convert degrees to radians.

value °

{value1 ,value2,value3,value_ ,...,value n} °

° also designates degrees (D) in DMS format.

' (minutes) designates minutes (M) in DMS format.

"(seconds) designates seconds (S) in DMS format..

Note: " is not on the ANGLE menu. To enter ", press @ [-].

Math, Angle, and Test Operations 2-23

r(Radians)

_DMS

R_Pr (,

R_,Pe (,

P_-Rx(,

P*Ry(

r (radians) designates an angle or list of angles as radians,

regardless of the cmTent angle mode setting. In Degree

mode, you can use r to convert radians to degrees.

value r

Degree mode

sin (<_/4.') r )

•7071067812

sin( {0, ,/2} _) 1}%w.J

(x/4> r 45

_DMS (degree/minute/second) displays answer in DMS

format (page 2-23). The nlode setting lnust be Degree for

answer to be interpreted as degrees, minutes, and seconds.

_DMS is valid only at the end of a line.

answe_'_DMS

54°32'30"*2 I

109.08333331

Rns*DMS 10905 0

RI_Pr(converts rectangular coordinates to polar

coordinates and returns r, R_PO( converts rectangular

coordinates to polar coordinates and returns O.xand ycan

be lists.

R*Pr(x,y), R*PO(x,y)

R*Pr(-1,O) I

,05 !I Note: Radian mode is set

e,eo( } 14i5926541

PI_Rx( converts polar coordinates to rectangular

coordinates and returns x. PI*Ry( converts polar

coordinates to reetangulm" coordinates and returns y. rand

0can be lists.

P*Rx(r,_,P*Ry(v,_

P*Rx(I,x)

P*R_(I,x) -10 Note: Radian mode is set.

2-24 Math, Angle, and Test Operations

TEST (Relational) Operations

TEST Menu

>_ ->,

<,_<

Using Tests

To display the TEST menu, press [_ [TEST].

This operator... Returns 1 (true) if,..

TEST LOGIC

1 : =Equal

2 : _ Not equal to

3 : > Greater than

4 : > Greater than or equal to

5:<Less than

6 : < Less than or equal to

Relational operators compare valueA and valueB and

return 1 if the test is true or 0 if the test is false, valueA and

valueB can be real numbet_, expressions, or lists. For =

and _ only, valueA and valueB also can be matrices or

complex numbers. If valueA and valueB are matrices, both

nmst have the same dimensions.

Relational operators are often used in programs to eont_x)l

program flow and in graphing to control the graph of a

function over specific values.

valueA =valueB valueA _valueB

valueA >value B valueA >valueB

valueA <valueB valueA <valueB

25=26 el

{i'2'3}<3{i 1 0}

Relational operatot_ are evMuated after lnathelnatieal

functions according to EOS rules (Chapter 1).

• The expression 2+2=2+3 returns 0. The TI-83 performs

the addition first because of EOS rules, and then it

compares 4 to 5.

• The expression 2+(2=2)+3 returns 6. The TI-83 performs

the relational test first because it is in parentheses, and

then it adds 2, 1, and 3.

Math, Angle, and Test Operations 2-25

TEST LOGIC (Boolean) Operations

TEST LOGIC

Boolean

Operators

and,

or_

xor

not(

Using Boolean

Operations

To display the TEST LOGIC menu, press [_ [TEST] [_.

This operator... Returns a 1 (true} if...

TEST LOGIC

1 : an d Both values are nonzero (true).

2: 0cAt least one value is nonzero (tree),

3 : x0c Only one value is zero (false),

4 : n0t ( The value is zero (false).

Boolean operators are often used in programs to control

program flow and in graphing to control the graph of the

function over specific values. Values are interpreted _ts

zero (false) or nonzero (ttlle).

and, or, and xor (exclusive or) return a value of 1 if an

expression is true or 0if an expression is false, according

to the table below, valueA and valueB can be real

numbers, expressions, or lists.

valueA and valueB

valueA or valueB

valueA xor valueB

valueA valueB and or xor

€0 €0 returns 1 1 0

€0 0 returns 0 1 1

0€0 returns 0 1 1

0 0 returns 0 0 0

not( returns 1if value (which can be an expression) is O,

not(value)

Boolean logic is often used with relational tests. In the

following program, the instructions store 4 into C,

PROGRAM::2+R: 3+BBOOLEAN I

:If" R=2 and B=3

:Then: 4eC

:Else: 5eC

:End

2-26 Math_ Angle_ and Test Operations

Contents Getting Started: Graphing a Circle ....................... 3-2

Defining Graphs ......................................... 3-3

Setting tile Graph Modes ................................. 3-4

Defining Funetions ...................................... 3-5

Selecting and Deseleeting Ftmetions ..................... 3-7

Setting Graph Styles for Ptmetions ....................... 3-9

Setting the Viewing Window \Tariables ................... 3-11

Setting the Graph Format ................................ 3-13

DisNaying Graphs ....................................... 3-15

Exploring Graphs with the Free-Mo_ng Cursor .......... 3-17

Exploring Graphs with TRACK ........................... 3-18

Exploring Graphs with the ZOOM Instructions ........... _-20

Using ZOOM MEMORY .................................. G-23

Using the CALC (Calculate) Operations .................. 3-25

_ TEXAS INSTRUMENTS T|=83

STAT PLOT TIBLSET FORMAT CALC TABLE

Fllnction Graphing 3-1

Getting Started: Graphing a Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph a circle of radius 10, centered on the origin in the standard viewing

window. To graph this circle, you nmst enter separate formul_ts for the upper

and lower portions of the circle. Then use ZSquare (zoom square) to adjust the

display- and make tile functions appear as a circle.

In Func mode, press [] to display tile

Y= editor. Press _ [_] 100 [] _ [] []

to enter the expression Y=f(100-X2),

which defines the top half of the circle.

The expression Y=-f(100-X 2) defines the

bottom half of the circle. On the TI-83, you

can define one function in terms of another.

To define Y2=-Y1, press [] to enter the

negation sign. Press FqAgg][] to display- the

VARS Y-VARS menu. Then press _ to

select 1:Function. The FUNCTION seeondatT

menu is displayed. Press 1to select 1:Y1.

Press _ 6 to select 6:ZStandard. This is a

quick way- to reset the window wu'iables to

the standard values. It also graphs the

functions; you do not need to press [ggAPH].

Notice that the functions appear as an

ellipse in the standard xqewing window.

To adjust the display- so that each pixel

represents an equal width and height, press

6 to select 8:ZSquare. The functions

are replotted and now appear as a circle on

the display.

To see the ZSquare window variables, press

and notice the new values for Xmin,

Xmax, Ymin, and Ymax.

_INOOW

Xmin=-15.16129...

Xmax=15.161290...

XsGI=I

Vnin=-lO

9max=lO

Vscl=l

Xres=l

3-2 Function Graphing

Defining Graphs

TI-83--Graphing

Mode Similarities

Defining aGraph

Displaying and

Exploring a

Graph

Saving a Graph

for Later Use

Chapter 3 specifically describes function graphing, but the

steps shown here are similar for each TI-83 graphing

mode. Chapters 4, 5, and 6 describe aspects that are unique

to paralnetric graphing, polar graphing, and sequence

graphing.

To define a graph in any graphing mode, follow these

steps. Some steps are not always necessmT.

1. Press [ff0_] and set the appropriate graph mode

(page 3-4).

2. Press [] and enter, edit, or select one or more functions

in the Y= editor (page 3-5 and 3-7).

3. Deselect stat plots, ifnecessmT (page 3-7).

4. Set the graph style ff)r each function (page 3-9).

5. Press _ and define the viewing window variables

(page 3-11).

6. Press _ [FORMAT] and select the graph format settings

(page 3-13).

After you have defined a graph, press [ffg_] to display- it.

Explore the behavior of the function or functions using the

TI-83 tools described in this chapter.

You can store the elements that define the current graph to

any- of 10 graph database variables (GDB1 through GDBg,

and GDB0; Chapter 8). To recreate the current graph later,

simply recall the graph database to which you stored the

original graph.

These types of information m'e stored in a GDB

• Y= functions

• Graph style settings

• Window settings

• Format settings

You can store a picture of the current graph display to any

of 10 graph picture variables (Picl through Picg, and Pie0;

Chapter 8). Then you can superimpose one or more stored

pictures onto the current graph.

Function Graphing 3-3

Setting the Graph Modes

Checking and

Changing the

Graphing Mode

To display- the mode screen, press [_. The default

settings are highlighted below. To graph functions, you

nmst select Func mode before you enter values for the

window vm'iables and before you enter the functions.

Sci Eng

Setting Modes

from a Program

Dot

Horiz G-T

The TI-83 has four graphing modes.

•Func (function graphing)

•Par (parametric graphing; Chapter 4)

•Pol (polar graphing; Chapter 5)

•Seq (sequence graphing; Chapter 6)

Other mode settings affect graphing results. Chapter 1

describes each mode setting.

•Float or 0123456789 (fixed) decinlal nlode affects

displayed graph coordinates.

•Radian or Degree angle mode affects interpretation of

some functions.

•Connected or Dot plotting mode 'affects plotting of

selected functions.

•Sequential or Simul graphing-order mode affects

function plotting when nlore than one function is

selected.

To set the graphing mode and other nlodes fronl a

program, begin on a blank line in the program editor and

follow these steps.

1. Press [MO_] to display- the lnode settings.

2. Press [], [], [_, and [] to place the cursor on the mode

that you want to select.

3. Press _ to paste the Inode name to the cursor

location.

The nlode is changed when the program is executed.

3-4 Function Graphing

Defining Functions

Displaying

Functions in the

Y= Editor

Defining or

Editing a

Function

To display the Y= editor, press @. You can store up to 10

functions to tile function variables Y1 through Y9, and YO.

You can graph one or more defined functions at once. In

this example, functions Y1 and Y2 are defined and selected.

PI,'.,LI PloLg Pl,:,t_:

-,y1B4"(100-ga:)

.,YaB -YI

\Y_=

..Y_=

,,y_=

-,y_=

To define or edit a function, follow these steps.

1. Press [] to display the Y= editor.

2, Press [] to nlove the cursor to the function you want to

define or edit, To erase a function, press @,

3. Enter or edit the expression to define the function.

• You lnay use functions and variables (including

matrices and lists) in the expression. When the

expression ewduates to a nonreal number, the value

is not plotted; no error is returned.

• The independent variable in the function is X. Func

lnode defines _ as X. To enter X, press

or press @ [x].

• When you enter the first character, the = is

highlighted, indicating that the function is selected.

As you enter the expression, it is stored to the variable

Yn as a use>defined function in the Y= editor.

4. Press [gNY_or [] to l:love the cursor to the next

function.

Function Graphing 3-5

Defining a

Function from

the Home Screen

or aProgram

Evaluating Y=

Functions in

Expressions

To define a function fronl the home screen or a prograln,

begin on a blank line and follow these steps.

1. Press @ [,], enter the expression, and then press

@ [-1 again.

2. Press _.

3. Press _ [] 1to select 1:Function fl'om the

VARS Y-VARS menu,

4. Select the function name, which p_stes the name to the

cursor location on the home screen or program editor.

5. Press _ to complete the instruction.

"expression " _ Yn

I"X z''÷Vt Donel "J',JtI_IX2PI':'tt P10t;: Plot, I

When the instruction is executed, the TI-83 stores the

expression to the designated variable Yn, selects the

function, and displays the message Done.

You can calculate the value of a Y= function Yn at a

specified value of X. A list of values returns a list.

Yn(value)

Yn({valuel ,value2,value3, . ..,value n})

Pl*tl Pl*{2 P10t) IY1 (0) 6

\V1 B. 2Xs-2X+6

,,..z= I '_1 ({0, 1,2,3,4} )

xV_-= ._6 4.2 3.6 5.4 ...

3-6 Function Graphing

Selecting and Deselecting Functions

Selecting and

Deselecting a

Function

Turning On or

Turning Off a Stat

Plot in the Y=

Editor

You can select and deselect (turn on and turn off) a

functkm in the Y= editor. A function is selected when the =

sign is highlighted. The TI-83 graphs only the selected

functions. You can select any or all functions Y1 through

Yg, and Y0.

To select or deselect a function in the Y= editor, follow

these steps.

1. Press [] to display the Y= editor.

2. Move the cursor to the function you want to select or

deselect.

3, Press [] to place the cursor on the functkm's =sign.

4. Press [gg_g] to change the selection status.

When you enter or edit a function, it is selected

automatically. When you clem' a function, it is deselected.

To view and change the OlVOff status of a stat plot in the

Y= editor, use Plot1 Plot2 Plot3 (the top line of the

Y= editor). When a plot is on, its name is highlighted on this

line.

To change the OlgOff status of a stat plot fronl the

Y= editor, press [] and [] to place the cursor on Plot1,

Plot2, or Plot& and then press [g_N.

_lotz Plet_ _ J

",YI =. 2X3-2X+6 -'1---,_ Plott isturnedon.

\Vz= -Yt I

,_.y_=2X+XZ j Plot2 and Plot3 are turned off

\Y_= J

",us =

",'¢_= /

-W= I

Function Graphing 3-7

Selecting and

Deselecting

Functions from

the Home Screen

or a Program

To select or deselect a function fronl the home screen or a

program, begin on a blank line and follow these steps.

1. Press _ [] to display- the VANS Y-VANS menu.

2. Select 4:On/Off to display the ON/OFF secondary menu.

3. Select l:FnOn to turn on one or more functions or

2:FnOff to turn off one or more functions. The

instruction you select is copied to the cursor location.

4. Enter the number (1 through 9, or 0; not the variable

Yn) of each function you want to turn on or turn off.

• If you enter two or more numbers, separate them

with eonunas.

• To turn on or turn off all functions, do not enter a

number after FnOn or FnOff,

FnOn[function#function#,.,, function n]

FnOff[function# function# .... function n]

5, Press [ggTig], When the instruction is executed, the

status of each function in the eutTent mode is set and

Done is displayed.

For example, in Func mode, FnOff :FnOn 1,3 turns off all

functions in the Y= editor, and then turns on Y1 and Y3.

FnOff :FnOn Dlo3e I Pl<,tl Plo_Z Plot._

",Y1B. 2X_-2X+6

_,Y;_= -Y1

",YsBXZ

xy_=

xY_=

\Y_=

,,y_=

3-8 Function Graphing

Setting Graph Styles for Functions

Graph Style

Icons in the Y=

Editor

Setting the Graph

Style

This table describes the graph styles available for function

graphing. Use the styles to visually differentiate functions

to be graphed together, For example, you can set Y1 as a

solid line, Y2 as a dotted line, and Y3 as a thick line,

Icon Style Description

".. Line A solid line connects plotted points; this is

the default in Connected mode

"i Thick A thick solid line connects plotted points

'_.i Above Shading covers the area a*bove the graph

ik Below Shading covet\_ the area below the graph

'1! Path A circular cursor traces the leading edge of

the graph and draws a path

(! Aidmate A circular cursor traces the leading edge of

the graph without drawing a path

". Dot A snlall dot represents each plotted point;

this is the default in Dot mode

Note: Some graph styles are not available in all graphing modes.

Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.

To set the graph style for a function, follow these steps.

1. Press [] to display the Y= editor.

2. Press [] and [] to nlove the cut\sor to the function.

3. Press [] [] to move the cm'sor left, past the = sign, to

the graph style icon in the first colunm. The insert

cm'sor is displayed. (Steps 2 and 3 are interchangeable.)

4. Press _ repeatedly to rotate through the graph

styles. The seven styles rotate in the same order in

which they are listed in the table above.

5. Press [], [], or [] when you have selected a style.

PlotJ. F'1ot;_P1ot:_

",Y1B8sin(X)

_YzB8cos(X)

\Y_=

xY_=

\Y_=

xy_=

Function Graphing 3-9

Shading Above

and Below

When you select _mor 1;.for two or more functions, the

TI-83 rotates through four shading patterns.

• Vertical lines shade the first function with a '_.1or b.

graph style.

• Horizontal lines shade the second.

• Negatively sloping diagonal lines shade the third.

• Positively sloping diagonal lines shade the fom'th.

• The rotation returns to vertical lines for the fifth '_.ior i;.

function, repeating the order described above.

VClmn shaded are_Ls intersect, the patterns overlap.

Setting a Graph

Style from a

Program

Note: When _1or h_,is selected for a Y= function that graphs a family of

curves, such as Yl={1,2,3}X, the four shading patterns rotate for

each member of the family of curves.

To set the graph style fl'onl a program, select H:GraphStyle(

from the PRGM CTL menu. To display this menu, press

[V_ while in the program editor.function# is the nmnber

of the Y= function name in the current graphing mode.

graphstyle# is an integer from 1 to 7 that corresponds to

the graph style, as shown below.

1 = ". (line) 2 = '_i(thick) 3 = ,m(above)

4 = 1'.-.(below) 8= ':) (path) 6= (!

(animate) 7= ". (dot)

GraphStyle(fanction#,graphstyle#)

For example, when this program is executed in Func mode,

GraphStyle(1,3) sets Y1 to '_](above),

:OisPGr'aPh

3-10 Function Graphing

Setting the Viewing Window Variables

The TI-83 Viewing

Window The viewing window is the portion of the coordinate plane

defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale)

defines the distance between tick marks on the x-axis. Yscl

(Y scale) defines the distance between tick marks on the

y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.

_Ymax

Xsc_

Xmax /

_--Yscl

Ymir_ N

WINDOW

Xmin=-lO

XMax=lO

Xscl=l

Ymin=-lO

Ymax=lO

Yscl=l

XPes=l

Displaying the

Window

Variables

Changing a

Window Variable

Value

To display the current window variable values, press

_. The window editor above and to the right shows

the default values in Func graphing mode and Radian angle

nlode. The window variables differ fronl one graphing

mode to another.

Xres sets pixel resolution (1 through 8) for function graphs

only. The default is 1.

• At Xres=l, functions are evaluated and graphed at each

pixel on the x-axis.

• At Xres=8, functions are evaluated and graphed at every

eighth pixel along the x-axis.

Tip: SmalIXres valuesimprovegraph resolutionbut maycausethe

TI-83 to drawgraphs more slowly.

To change a window variable value fronl the window

editor, follow these steps.

1. Press [] or [] to move the cut\sor to the window

variable you want to change.

2. Edit the value, which can be an expression.

• Enter a new wdue, which clears the original value.

• Move the cursor to a specific digit, and then edit it.

3. Press [g_gff], [], or []. If you entered an expression, the

TI-83 ewduates it. The new value is stored.

Note: Xmin<Xmax andYmin<Ymax must be true in orderto graph.

Function Graphing 3-11

Storing to a

Window Variable

from the Home

Screen or a

Program

AX and AY

To store a value, which can be an expression, to a window

variable, begin on a blank line and follow these steps,

1, Enter the value you want to store,

2, Press _.

3, Press _ to display- the VARS menu.

4, Select 1 :Window to display the Func window variables

(X/Y secondmT menu).

• Press [] to display the Par and Pol window variables

(T/0 secondm_y- menu).

• Press [] [] to display the Seq window variables

(UN/W secondary menu).

5, Select the window variable to which you want to store a

value, The name of the variable is pasted to the current

CUrSOr location.

6, Press _ to complete the instruction.

When the instruction is executed, the TI-83 stores the

value to the window variable and displays the vMue.

J14+Xv,ax 14J

The variables AX and AY (items 8 and 9 on the VARS

(1:Window) X/Y seeondmT menu) define the distance from

the center of one pixel to the center of any adjacent pixel

on a graph (graphing accuracy), a× and AY are calculated

from Xmin, Xma×, Ymin, and Yma× when you display- a

graph.

(Xmax - Xmin) (Ymax - Ymin)

AX = AY -

94 62

You can store values to AX and AY. If you do, Xmax and

Ymax m'e cMculated from AX, Xmin, AY,and Ymin.

3-12 Function Graphing

Setting the Graph Format

Displaying the

Format Settings

Changing a

Format Setting

RectGC, PolarGC

To display- the format settings, pl_ss [2_ [FORMAT]. The

default settings are highlighted below.

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

Sets cursor coordinates.

Sets coordinates display on or off.

Sets grid off or on.

Sets axes on or off.

Sets axes label oft"or on.

Sets expression display on or off.

Format. settings define a graph's appearance on the display.

Format settings apply to all graphing modes. Seq graphing

mode has an additional mode setting (Chapter 6).

To change a fornlat setting, follow these steps.

1. Press [_, [}_],[], and [] as necessary- to lnove the cursor

to the setting you want to select.

2. Press [ggYgg]to select the highlighted setting.

RectGC (rectangular graphing coordinates) displays the

cursor location _LSrectangular coordinates Xand Y.

PolarGC (polar graphing coordinates) displays tile cursor

location as polar coordinates R and 0.

The RectGC/PolarGC setting determines which wuiables

are updated when you plot tile graph, move the free-

nloving cursor, or trace.

• RectGC updates X and Y; if CoordOn format is selected,

Xand Y are displayed.

•PolarGC updates X, Y, R, and 0; if CoordOn format is

selected, R and 0 are displayed.

Function Graphing 3-13

CoordOn,

CoordOff

GridOff, GridOn

AxesOn, AxesOff

LabelOff,

LabelOn

ExprOn, ExprOff

CoordOn (coordinates on) displays the cursor coordinates

at the bottom of the graph, If ExprOff format is selected,

the function number is displayed in the top-right corner,

CoordOff (coordinates off) does not display- the function

number or coordinates,

Grid points cover the viewing window in rows that

correspond to the tick marks (page 3-11) on each axis.

GridOff does not display grid points.

GridOn displays grid points.

AxesOn displays the axes.

AxesOff does not display- the axes.

This overrides the LabelOff/LabelOn format setting.

LabelOff and LabelOn determine whether to display labels

for the axes (X and Y), if AxesOn format is also selected.

ExprOn and ExprOff determine whether to display- the

Y= expression when the trace cursor is active. This format

setting also applies to stat plots.

When ExprOn is selected, the expression is displayed in the

top-left comer of the graph screen.

When ExprOff and CoordOn both are selected, the number

in the top-right corner specifies which function is being

traced.

3-14 Function Graphing

Displaying Graphs

Displaying a New

Graph

Pausing or

Stopping aGraph

Smart Graph

To display the graph of the selected function or functions,

press _. TRACE, ZOOM instructions, and CALC

operations display- the graph automatically. As the TI-83

plots the graph, the busy indicator is on. As the graph is

plotted, X and Y m'e updated.

V_l_ile plotting a graph, you can pause or stop graphing.

• Press [ggT_ to pause; then press [ggT_ to resume.

• Press [ON]to stop; then press _ to redraw.

Snlart Graph is a TI-83 feature that redisplays the last

graph ilnlnediately when you press _, but only if all

graphing factors that would cause replotting have

remained the same since the graph was last displayed.

If you performed any of these actions since the graph was

last displayed, the TI-83 will replot the graph based on new

values when you press _.

• Changed a mode setting that affects graphs

• Changed a function in the current picture

• Selected or deselected a function or stat plot

• Changed the value of a variable in a selected function

• Changed a window variable or graph fornlat setting

• Cleared drawings by selecting ¢lrDraw

• Changed a stat plot definition

Function Graphing 3-15

Overlaying

Functions on a

Graph

On the TI-83, you can graph one or more new functions

without replotting existing functions, For example, store

sin(X) to Y1 in the Y= editor and press [_7. Then store

cos(X) to Y2 and press _ again. The function Y2 is

graphed on top of Y1, the original function,

Graphing a

Family of Curves

If you enter a list (Chapter 11) as an element in an

expression, the TI-83 plots the function for each value in

the list, thereby graphing a family of curves. In Simul

graphing-order mode, it graphs 'all functions sequentiMly

for the fit.st element in each list, and then for the second,

and so on.

{2,4,6}sin(X) graphs three functions: 2sin(X), 4 sin(X), and

6sin(X).

Plot1 PIo_Z Plot_

_.YtB£2, 4, 6}sin(X

xy?=

\y_,=

-.y_=

",y_=

-.y_=

{2,4,6}sin({1,2,3}X) graphs 2sin(X), 4sin(2X), and 6 sin(3X).

PI_L1 PlOL_: Plot. _ '_

".YIB(2, 4, 6}sin(

1,2,3}X)

\Yz =

\Y_=

-.y_=

..y_=

Note: When using more than one list, the lists must have the same

dimensions.

3-16 Function Graphing

Exploring Graphs with the Free-Moving Cursor

Free-Moving

Cursor

Graphing

Accuracy

When a graph is displayed, press [], [], [], or [] to nlove

tile cursor around the graph. When you first display- the

graph, no cursor is visible. When you press [], [], [], or [],

the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate

values of the cursor location m'e displayed at the bottom of

the screen if ¢oordOn format is selected. The Float/Fix

decimal mode setting determines tile number of decimal

digits displayed for the coordinate wdues.

To display the graph with no cursor and no coordinate

values, press @ or [gg_g]. When you press [], [], [], or

[], the cursor moves froln the same position.

The flee-moving cursor nloves fronl pixel to pixel on the

screen. When you move the cursor to a pixel that appears

to be on the function, the cursor nlay be neat', but not

actuMly on, the function. The coordinate value displayed at

the bottom of the screen actuMly lnay not be a point on the

function. To lnove the cursor along a function, use

(page 3-18).

The coordinate values displayed as you move the cursor

approximate actuM math coordinates, *accurate to within

the width and height of the pixel. As Xmin, Xmax, Ymin, and

Ymax get closer together (as in a Zoomln) graphing

accuracy ineretkqes, and the coordinate values nlore closely

approxinlate the lnath coordinates.

Free-moving cursor 'on" the curve

Function Graphing 3-17

Exploring Graphs with TRACE

Beginning a

Trace

Moving the Trace

Cursor

Moving the Trace

Cursor from

Function to

Function

Use TRACE to move the cursor from one plotted point to

the next along a function• To begin a trace, press _. If

the graph is not displayed already, press _ to display

it. The trace cursor is on the first selected function in the

Y= editor, at the middle × value on the screen• The cursor

coordinates are displayed at the bottom of the screen if

CoordOn format is selected. The Y= expression is displayed

in the top-left corner of the screen, if ExprOn format is

selected.

To move the TRACE cursor,., do this:

•, , to the previous or next plotted press [] or [].

point,

•.. five plotted points on a function press [g_ [] or K_

(Xres affects this), [].

•.. to any valid Xvalue on a function, enter a value, and

then press [KNT_.

•fronl one function to another, press [] or [].

When the trace cursor nloves along a function, the Ywdue

is calculated from the X value; that is, Y=Yn(X). If the

function is undefined at an X value, the Y value is blank.

'_1='_-_i_*_ J_

..... i ............

g:?,:LB:LLIBgR f:IL:L:LBLIT09

-- -- Trace cursor on the curve

If you nlove the trace cursor beyond the top or bottonl of

the screen, the coordinate values at the bottom of the

screen continue to change appropriately.

To nlove the trace cursor fronl function to function, press

[] and []. The cursor follows the order of the selected

functions in the Y= editor• The trace cursor moves to each

function at the same × value• If ExprOn format is selected,

the expression is updated.

3-18 Function Graphing

Moving the Trace

Cursor to Any

Valid X Value

Panning to the

Left or Right

Quick Zoom

Leaving and

Returning to

TRACE

Using TRACE in

a Program

To move the trace cursor to any valid X value on the

current function, enter the value. When you enter the first

digit, an X= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the X= prompt. The value nmst be

valid for the current viewing window. When you have

coinpleted the enttT, press _ to inove the cursor.

Zt L;t L......

Note: This feature does not apply to stat plots.

If you trace a function beyond the left or right side of the

screen, the viewing window automatically pans to the left

or right. Xmin and Xmax are updated to correspond to the

new viewing window.

While tracing, you can press _ to adjust the viewing

window so that the cursor location beconles the center of

the new xqewing window, even if the cursor is above or

below the display. This allows panning up and down. After

Quick Zoom, the cursor remains in TRACE.

When you leave and return to TRACE, the trace cursor is

displayed in the same location it was in when you left

TRACE, unless Smart Graph has replotted the graph

(page 3-15).

On a blank line in the prograln editor, press _. The

instruction Trace is pasted to the cursor location. When the

instruction is encountered during program execution, the

graph is displayed with the trace cursor on the first

selected function. As you trace, the cursor coordinate

values are updated. When you finish tracing the functions,

press _ to resume program execution.

Function Graphing 3-19

Exploring Graphs with the ZOOM Instructions

ZOOM Menu To display the ZOOM menu, press _, You can adjust the

viewing window of the graph quickly- in several ways. All

ZOOM instructions axe accessible fronl programs.

ZOOM MEMORY

i: ZBox

2: Zoom In

3: Zoom Out

4: ZDecimal

5: ZSquare

6: ZStandard

7: ZTrig

8: Zlnteger

9: ZoomStat

0: ZoomFit

Draws a box to define the viewing window.

Magnifies the graph around the cursor.

Views more of a graph atxmnd the cursor.

Sets aX and aY to O. 1.

Sets equal-size pixels on the Xand Y m,ces.

Sets the standard window variables.

Sets the built-in trig window variables.

Sets integer values on the Xand Y m,ces.

Sets the values for current stat lists.

Fits YMin and YMax between XMin and XMax.

Zoom Cursor

ZBox

When you select 1 :ZBox, 2:Zoom In, or 3:Zoom Out, the

cursor on the graph becomes the zoom cursor (+), a

smaller version of the free-mo_dng cursor (+).

To define a new viewing window using ZBox, follow these

steps,

1, Select l:ZBox from the ZOOM menu. The zoom cursor is

displayed at the center of the screen.

2. Move the zoonl cursor to any spot you want to define as

a cornet" of the box, and then press [N_N. When you

lnove the cm_or away- from the first defined corner, a

smM1, square dot indicates the spot.

3. Press [_, E], [_, or [_. As you lnove the cursor, the sides

of the box lengthen or shorten proportionately on the

screen.

Note: To cancel ZBox before you press _, press @.

4. When you have defined the box, press [_ to replot

the graph.

V]\,, ,,/'

X:3,:L9J.tlBBq t:! .B2:.t:LIB3B

To use ZBox to define another box within the new graph,

repeat steps 2 through 4. To cancel ZBox, press @.

3-20 Function Graphing

Zoom In,

Zoom Out

ZDecimal

ZSquare

Zoom In magnifies the part of the graph that surrounds the

cursor location. Zoom Out displays a greater portion of the

graph, centered on the cut\sor location. The XFact and

YFact settings determine the extent of the zoom.

To zoom in on a graph, follow these steps.

1, Check XFact and YFact (page 3-24); change as needed.

2, Select 2:Zoom In from the ZOOM menu. The zoom

cursor is displayed.

3, Move the zoom cut, or to the point that is to be the

center of the new viewing window,

4, Press [gNYE_, The TI-83 adjusts the viewing window by

XFact and YFact; updates the window variables; and

replots the selected functions, centered on the cursor

location,

5. Zoonl in on the graph again in either of two ways.

• To zoom in at the same point, press [_T_].

• To zoom in at a new point, move the cm\sor to the

point that you want as the center of the new viewing

window, and then press [_T_].

To zoom out on a graph, select 3:Zoom Out and repeat

steps 3 through 5.

To cancel Zoom In or Zoom Out, press @.

ZDecimal replots the functions inunediately. It updates the

window variables to preset values, tks shown below. These

values set AX and AYequal to 0.1 and set the X and Y value

of each pixel to one decimal place.

Xmin=-4.7 Ymin=-3.1

Xmax=4.7 Ymax=3,1

Xscl=l Yscl=l

ZSquare replots the functions immediately. It redefines the

xqewing window based on the cun'ent values of the

window variables. It adjusts in only one direction so that

AX=AY,which makes the graph of a circle look like a circle.

Xscl and Yscl remain unchanged. The midpoint of the

current graph (not the intersection of the axes) becomes

the midpoint of the new graph.

Function Graphing 3-21

ZStandard

ZTrig

Zlnteger

ZoornStat

ZoomFit

ZStandard replots the functions immediately, It updates the

window vm'iables to the standm'd values shown below.

Xmin=-lO Ymin=-lO Xres=l

Xmax=lO Ymax=lO

Xscl=l Yscl=l

ZTrig replots the functions immediately. It updates the

window vm'iables to preset values that are appropriate ffw

plotting trig functions. Those preset values in Radian mode

m'e shown below,

Xmin=-(47/24)_ Ymin=-4

Xmax=(47/24)_ Ymax=4

Xscl=_/2 Yscl=l

Zlnteger redefines the viewing window to the dimensions

shown below, To use Zlnteger, move the cursor to the point

that you want to be the center of the new window, and

then press [_T_]; Zlnteger replots the functions,

AX=I Xscl=lO

AY=I YscI=IO

ZoomStat redefines the viewing window so that all

statistical data points m'e displayed. For regular and

modified box plots, only Xmin and Xmax m'e adjusted.

ZoomFit replots the functions immediately, ZoomFit

recalculates YMin and YMax to include the nlininmm and

nlmNinlunl Yvalues of the selected functions between the

current XMin and XMax. XMin and XMax are not changed.

3-22 Function Graphing

Using ZOOM MEMORY

ZOOM MEMORY

ZPrevious

ZoomSto

ZoomRcl

To display the ZOOM MEMORY menu, p_ss _ [_.

ZOOM MEMORY

1:ZPrevious

2:ZoomSto

3:ZoomRcl

4:SetFactors...

[_ses the pre_ious _iewing window,

Stores the user-defined window,

Recalls the user-defined window.

Changes Zoom In and Zoom Out factors.

ZPrevious replots the graph using the window variables of

the graph that was displayed before you executed the last

ZOOM instruction.

ZoomSto inunediately stores the cmTent viewing window.

The graph is displayed, and the values of the current

window variables are stored in the user-defined ZOOM

variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and

ZXres.

These variables apply to all graphing modes. For example,

changing the value of ZXmin in Func nlode also changes it

in Par mode,

ZoomRcl graphs the selected functions in a user-defined

viewing window. The user-defined viewing window is

determined by the values stored with the ZoomSto

instruction. The window variables are updated with the

user-defined values, and the graph is plotted.

Function Graphing 3-23

ZOOM FACTORS

Checking XFact

and YFact

Changing XFact

and YFact

Using ZOOM

MEMORY Menu

Items from the

Home Screen or

a Program

The zoonl factors, XFact and YFact, are positive numbers

(not necessarily intege_\_) greater than or equal to 1, They

define the magnification or reduction factor used to Zoom

In or Zoom Out around a point,

To display the ZOOM FACTORS screen, where you can

t_iew the current values for XFact and YFact, select

4:SetFactors from the ZOOM MEMORY menu. The values

shown m'e the defaults.

ZOOM FRCTORS I

XFacL=4

VFact=4

You can change XFact and YFact in either of two ways.

• Enter a new value. The original value is cleared

automatically when you enter the first digit.

• Place the cursor on the digit you want to change, and

then enter a value or press [bE[] to delete it,

From the home screen or a program, you can store directly

to any of the user-defined ZOOM vm'iables.

1-5÷ZXr_in:5÷ZXr_,a5

From a program, you can select the ZoomSto and ZoomRcl

instructions fronl the ZOOM MEMORY menu.

3-24 Function Graphing

Using the CALC (Calculate) Operations

CALCULATE

value

To display the CALCULATE nlenu, press I_ [CALC], Use the

items on this menu to analyze tile current graph functions,

CALCULATE

i: value

2: zero

3: minimum

4: maximum

5:intersect

6:dy/dx

7:ff(x)dx

Calculates a function Yvalue for a given X,

Finds a zero (x-intercept) of a function.

Finds a nlininmln of a function,

Finds a nlaxinmln of a function.

Finds an intersection of two functions,

Finds a numeric derivative of a function.

Finds a numeric integral of a function,

value evaluates one or more currently selected functions

for a specified value of X.

Note: Whena valueis displayedfor X, press[_ to clear thevalue.

Whenno valueisdisplayed, press @ to cancelthevalue

operation.

To evaluate a selected function at X, ff)llow these steps.

1, Select 1:value froln the CALCULATE menu, The graph is

displayed with X= in tile bottom-left corner.

2, Enter a real value, which can be an expression, for X

between Xmin and Xmax.

3. Press IE_]. "7i7.J

The cursor is on the first selected function in the Y= editor

at the X value you entered, and the coordinates are

displayed, even if ¢oordOff fornlat is selected.

To nlove the cm'sor fl'om function to function at the

entered Xvalue, press [] or [], To t_store the free-re(Mug

cursor, press [] or [].

Function Graphing 3-25

zero zero finds a zero (x-intercept or root) of a function using

solve(. Functions can have more than one x-intercept

value; zero finds the zero closest to your guess.

The time zero spends to find the eotTect zero value

depends on the accuracy of the values you specify for the

left and right bounds and the accuracy of your guess.

To find a zero of a function, follow these steps.

1. Select 2:zero froln the CALCULATE menu. The current

graph is displayed with Left Bound? in the bottom-left

corner.

Press [] or [] to move the cm\sor onto the function %r

which you want to find a zero.

Press [] or [] (or enter a value) to select the x-value for

the left bound of the interval, and then press I_T_. A

indicator on the graph screen shows the left bound.

Right Bound? is displayed in the bottom-left corner.

Press [] or [] (or enter a value) to select the x-value for

the right bound, and then press IT_. A _ indicator on

the graph screen shows the right bound. Guess? is then

displayed in the bottom-left corner.

Press [] or [] (or enter a value) to select a point near

the zero of the function, between the bounds, and then

press [_T_].

ZCYO

The cursor is on the solution and the coordinates are

displayed, even if ¢oordOff format is selected. To move to

the same x-value for other selected functions, press [] or

[]. To restore the free-moving cursor, press [] or [].

3-26 Function Graphing

minimum,

maximum minimum and maximum find a ndninmln or nl3xinlunl of a

function within a specified inteP_+al to a tolerance of 1E-5.

To find a nlininlunl Or nlaxinlunl, follow these steps.

1. Select 3:minimum or 4:maximum fronl the CALCULATE

nlenu. The current graph is displayed.

2. Select the function and set left bound, right bound, and

guess _ts described for zero (steps 2 through 4; page 3-26).

The cursor is on the solution, and the coordinates ate

displayed, even if you have selected CoordOff format;

Minimum or Maximum is displayed in the bottom-left

c()rner.

To nlove to the salne x-value for other selected functions,

press [] or []. To restore the free-moving cursor, press []

or [].

intersect intersect finds the coordinates of a point at which two or

nlore functions intersect using solve(. The intersection

nmst appear on the display to use intersect.

To find an intersection, follow these steps.

1. Select 5:intersect fi'om the CALCULATE menu. The

current graph is displayed with First curve? in the

bottom-left corner.

c >.J *

Fit_t cul_ve?

ll=0 € Y=.5

2. Press [] or [], if necessatT, to nlove the cursor to the

first function, and then press [gg7_. Second curve? is

displayed in the bottom-left corner.

3. Press [] or [], if necessatT, to nlove the cursor to the

second function, and then press [gg7_.

4. Press [] or [] to nlove the cursor to the point that is

your guess as to location of the intersection, and then

press [gfff_.

The cursor is on the solution and the coordinates are

displayed, even if CoordOff format is selected. Intersection

is displayed in the bottom-left corner. To restore the free-

moving cursor, press [], [], [], or [].

Function Graphing 3-27

dy/dx

ff(x)dx

dy/dx (numerical derivative) finds the numerical derivative

(slope) of a function at a point, with e= 1E-3,

To find a function's slope at a point, follow these steps,

1, Select 6:dy/dx from the CALCULATE menu. The current

graph is displayed.

2, Press [] or [] to select the function for which you want

to find the numerical derivative.

3, Press [] or [] (or enter a value) to select the X value at

which to calculate the deriwttive, and then press [_TE_.

The cursor is on the solution and the numerical derivative

is displayed.

To move to the same x-value for other selected functions,

press [] or [], To _store the free-moving cursor, press []

or [].

j'f(x)dx(numerical integral) finds the numerical integral of a

function in a specified inte[w'al, It uses the fntnt( function,

with a tolerance of e= 1E-3.

To find the numerical derivative of a function, follow these

steps.

1, Select 7:jf(x)dx from the CALCULATE menu. The current

graph is displayed with Lower LimR? in the bottom-left

corner.

Press [] or [] to move the cm\sor to the function for

which you want to calculate the integral.

Set lower and upper limits as you would set left and

right bounds for zero (step 3; page 3-26). The integral

value is displayed, and the integrated area is shaded.

;'t=X_-3_÷:1. [ J

,,f'I-J,

LeLOeV Limit? I,

_= -1•_II Sf(x)4x=_._Z?_li7

Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or

any action that invokes Smart Graph to clear the shaded area.

3-28 Function Graphing

4Parametric

Graphing

Contents Getting Started: Path of a Ball ........................... 4-2

Defining and Displaying Parametrie Graphs .............. 4-4

Exploring Parametric Graphs ............................ 4-7

_TEXAS INSTRUMENTS TF83

STAT PLOT TBLSET FORMAT CALC TABLE

Parametric Graphing 4-1

Getting Started: Path of a Ball

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph the parametric equation that describes the path of a ball hit at an initial

speed of 30 meters per second, at an initial angle of 25 degrees with the

horizontal from ground level. How fat" does the ball travel? When does it hit the

ground? How high does it go? Ignore all forces except gravity.

For initial velocity v0 and angle 0, the position of the ball as a function of time

has horizontal and vertical components.

Horizontal: X1 (t)=tv0cos(0) 1 ,

Vertical: Y1 (t)=tv0sin(0)- g gt 2

The vertical and horizontal vectors of the bali's motion also will be graphed.

Vertical vector: X2(t)=0 Y2(t)=Yl(t)

Horizontal vector: X3(t)=Xl(t) Y3(t)=0

Gravity constant: g=9,8 m/see 2

Press [_3_. Press [] [] [] [] [_ to

select Par mode. Press [] [] [] [_ to

select 8imul R)r sinmltaneous graphing of

all three parametric equations in this

example.

Press @. Press 30 _ [_ 26 [_

[ANGLE] I (to select °) [] [_ to define

XITin terms of T.

Press 30 _ _ 28 [_ [ANGLE]1 [] []

9.8 [] 2 _ [] _ to define YIT.

The vertical component vector is defined

by X2Tand Y2T.

4. Press 0[ggY_ to define X2T.

Press [_ [] to display the VARS Y-VARS

menu, Press 2to display the PARAMETRIC

secondmT nlenu, Press 2 [gN?_7to define

Y2T,

4-2 Parametric Graphing

The horizontal component vector is

defined by X3Tand Y3T,

Press [gAg_ [] 2, and then press 1[gNTgglto

define X3T.Press 0 [gNT_ to define Y3T.

Press [] [] [] _ to change the graph

style to 5 for X3Tand Y3T. Press [] [gNY_

[gNT_ to change the graph style to .41!for

X2Tand Y2T. Press [] [gNY_ [gNT_ to

change the graph style to "0for XlT and Y1T.

(These keystrokes _tssume that all graph

styles were set to "..originally.)

Press _. Enter these values for the

window variables.

Tmin=0 Xmin=-10 Ymin=-5

Tmax=5 Xmax=100 Ymax=15

Tstep=,l Xscl=50 Yscl=10

Press [g_ [FORMAT] [] [] [] [] F_ to set

AxesOff, which turns off the axes.

PI,:,I:t PI,:,L> PlOI:3

91T B30Tsin (25 ° )

-9.8/2TZ

xXzT Be

VaT B'¢1T

",X_T BX1T

V St 1_10

\X_T =

Plo_t PloLZ Plot3

_XITB30Tcos(25 ° )

YITB30Tsin(25 ° )

-9.8/2TZ

_XZT B0

YZT BYI T

_T _1 T

WINDOW

STsteP=,l

XMin=-lO

gMax=100

Xscl=50

Vmin=-5

Vmax=15

Vsol=lO

PolarGC

CoordO££

GridOn

xPrO_£

10. Press _. The plotting action

sinmltaneously shows the ball in flight and

the vertical and horizontal component

vectors of the motion.

Tip: To simulate the ball flying through the air, set

graph style to _)(animate) for XIT and YIT.

11. Press _ to obtain numerical results

and answer the questions at the beginning

of this section.

Tracing begins at Tmin on the first

pm'ametric equation (X1Tand Y1T), As you

press [] to trace the curve, the cursor

follows the path of the ball over time. The

values for X (distance), Y (height), and T

(time) are displayed at the bottom of the

screen.

/---_,.

glT=3OTcg¢_;(_ Y1T=30TSin(_:_

Parametric Graphing 4-3

Defining and Displaying Parametric Graphs

TI-83 Graphing

Mode Similarities

Setting

Parametric

Graphing Mode

Displaying the

Parametric Y=

Editor

Selecting a

Graph Style

The steps for defining a parametric graph are similar to the

steps for defining a function graph. Chapter 4 assumes that

you are familiar with Chapter 3: Function Graphing.

Chapter 4 details aspects of parametric graphing that differ

from function graphing.

To display- the mode screen, press NgffE].To graph

parametric equations, you nmst select Par graphing mode

before you enter window wu'iables and before you enter

tile components of parametric equations.

After selecting Par graphing mode, press [] to display the

_arametric Y= editor.

P10L1 Plo_:2 Plot3

_.X1T=11

YtT----

,,X;_T=

'y';_V=

\X_T=

y__T=

In this editor, you can display and enter both the Xand Y

conlponents of up to six equations, X1T and Y1T through X6T

and YST. Each is defined in terms of the independent

variable T. A common application of parametric graphs is

graphing equations over time.

The icons to the left of XIT through X6Trepresent the graph

style of each parametric equation (Chapter 3). The default

in Par mode is "..(line), which connects plotted points. Line,

'_i (thick),-(! (path), (!(animate), and ". (dot) styles are

available for parametric graphing.

4-4 Parametric Graphing

Defining and

Editing

Parametric

Equations

Selecting and

Deselecting

Parametric

Equations

Setting Window

Variables

To define or edit a parametric equation, follow the steps in

Chapter 3 for defining a function or editing a function. The

independent variable in a paralnetrie equation is T. In Par

graphing mode, you can enter the paralnetric variable Tin

either of two ways.

• Press _.

• Press@ [T].

Two components, Xand Y, define a single parametric

equation. You nmst define both of them.

The TI-83 graphs only the selected parametric equations.

In the Y= editor, a parametric equation is selected when the

= signs of both the Xand Y components are highlighted.

You may select any or all of the equations XIT and YIT

through X6T and Y6T.

To change the selection status, move the cursor onto the =

sign of either the Xor Y colnponent and press [gNYE_. The

status of both the Xand Y components is changed.

To display" the window variable values, press _.

These vmiables define the viewing window. The values

below are defaults for Par graphing in Radian angle mode.

Tmin=O

Tmax=6.2831853,..

Tstep=.1308996...

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

Smallest Tv'Mue to evaluate

Largest Tvalue to evaluate (2x)

T value increment (x/24)

SmMlest X vMue to be displayed

Largest X value to be displayed

Spacing between the X tick nlarks

SmMlest Y vMue to be displayed

Largest Y value to be displayed

Spacing between the Y tick marks

Note: To ensure that sufficient points are plotted, you may want to

change the T window variables.

Parametric Graphing 4-5

Setting the Graph

Format

Displaying a

Graph

To display- the current graph format settings, press [_

[FORMAT], Chapter 3 describes the format settings in detail,

The other graphing modes share these format settings; $eq

graphing mode has an additional axes format setting,

When you press _, the TI-83 plots the selected

parametric equations, It evaluates the Xand Ycomponents

for each value ofT (fronl Tmin to Tmax in intel_'als of

Tstep), and then plots each point defined by X and Y. The

window vm'iables define the viewing window.

As the graph is plotted, X, Y, and T m'e updated.

Snlart Graph applies to parametric graphs (Chapter 3).

Window

Variables and

Y-VARS Menus

You can perform these actions fronl the home screen or a

program.

• Access functions by using the name of the X or Y

component of the equation as a vm'iable.

*.5 -,

NiT 94. r0916375

• Store parametric equations.

"cos(T) "÷Yi"sin(T) "÷Xl TD°neTDone \XzT="XlTBsin(T)yzT=Vin°tITBcos(T)nOtznots I

• Select or deselect parametric equations,

FR0t'f" 1 Done Pl0tl ,otz ,,t, I

",XlT =cos(T)

YiT=sin(T) I

xXzT=

YZT=

• Store values directly to window variables.

360÷Tnax 360

4-6 Parametric Graphing

Exploring Parametric Graphs

Free-Moving

Cursor

TRACE

The free-lnoving cursor in Par graphing works the salne as

in Func graphing.

In RectGC format, nloving the cursor updates the values of

Xand Y; if CoordOn format is selected, Xand Y are

displayed.

In PolarGC format, X, Y, R, and 0 are updated; if CoordOn

format is selected, R and 0 m'e displayed.

To activate TRACE, press _. When TRACE is active,

you can nlove the trace cursor along the graph of the

equation one Tstep at a time. When you begin a trace, the

trace cursor is on the first selected function at Train. If

ExprOn is selected, then the function is displayed.

In RectGC format, TRACE updates and displays the vMues

of X, Y, and T if CoordOn format is on.

In PolarGC format, X, Y, R, 0 and Tare updated; if CoordOn

format is selected, R, 0, and T are displayed. The X and Y

(or Rand 0) values are calculated from T.

To nlove five plotted points at a time on a function, press

[] or [2ffd][_. If you nlove the cursor beyond the top or

bottom of the screen, the coordinate values at the bottom

of the screen continue to change appropriately.

Quick Zoom is available in Par graphing; panning is not

(Chapter 3).

Parametric Graphing 4-7

Moving the Trace

Cursor to Any

Valid TValue

To move the trace cursor to any valid T value on the

current function, enter the number, When you enter the

first digit, a T= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the T= prompt, The wdue nmst be

valid for the current _ewing window, When you have

colnpleted the ent_% press [K_Y_ to lnove the cursor.

PIoI:I PloL2 Plot_

_.X1 T_sir,(T)

YtT_T

XIT=_;ifl(T) _,Ii T=T

}

T=2

XIT=S;n(T) _IT=T

(

T=;_

ZOOM ZOOM operations in Par graphing work the same as in Func

graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin,

Ymax, and Yscl) window vm'iables are affected.

The T window vm'iables (Train, Tmax, and Tstep) are only-

'affected when you select ZStandard. The MARS ZOOM

seeondm_y- menu ZT/Z0 items 1 :ZTmin, 2:ZTmax, and

3:XTstep are the zoom memory variables for Par graphing.

CALC CALC operations in Par graphing work the same as in Func

graphing. The CALCULATE menu items available in Par

graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.

4-8 Parametric Graphing

Polar

Graphing

Contents Getting Started: Polar Rose .............................. 5-2

Defining and Displaying Polar Graphs ................... 5-3

Exploring Polar Graphs .................................. 5-6

TEXAS INSTRUMENTS T1=83

STAT PLOT TBLSET FORMAT CALC TABLE

Polar Graphing 5-1

Getting Started: Polar Rose

Getting Started is a fast-paced introduction. Read the chapter for details.

The polar equation R=Asin(B0) graphs a rose. Graph the rose for A=8 and

B=2.5, and then explore the appearance of the rose for other values of A and B.

Press _ to display the mode screen.

Press [] [] [] [] [] [gfff_] to select Pol

graphing mode. Select the defaults (the

options on tile left) for the other nlode

settings.

Press [] to display- the polar Y= editor.

Press 8NTN2.6 _ [] [g_gO to define

rl.

3. Press _ 6 to select 6:ZStandard and

graph the equation in the standard viewing

window. The graph shows only five petals

of the rose, and the rose does not appear

to be synunetrical. This is because the

standard window sets 0max=2= and defines

the window, rather than the pixels, as

square.

4. Press _ to display the window

variables. Press [] 4[gfi_ [_] to increase the

value of 0max to 4x.

5, Press _ 5to select 5:ZSquare and plot

the graph.

Repeat steps 2 through 5 with new values

for the variables Aand Bin the polar

equation rl=Asin(B0). Observe how the new

values 'affect the graph.

Plot:t Plot2 Plot3

_rl B8sin(2.50)

\r_:=

i_.r_ =

%rfi=

WINDOW

Omin=O

OMaX=4X

Ostee=,1308996...

XMin=-lO

Xmax=lO

XSCI=I

_VMin=-lO

5-2 Polar Graphing

Defining and Displaying Polar Graphs

TI-83 Graphing

Mode Similarities

Setting Polar

Graphing Mode

Displaying the

Polar Y= Editor

Selecting Graph

Styles

The steps for defining a polar graph are similar to the steps

for defining a function graph. Chapter 5 assumes that you

are familiar with Chapter 3: Function Graphing. Chapter 5

details aspects of polar graphing that differ from function

graphing.

To display- the mode screen, press [M6_]. To graph polar

equations, you nmst select Pol graphing mode before you

enter values for the window variables and before you enter

polar equations.

After selecting Pol graphing mode, press [] to display- the

_olar Y= editor.

PI,:,I:I PloL2 Plot3

\rl=

\i-- 2----

M-_3:=

\1,-,tl =

\1.'. _ =

\p6=

In this editor, you can enter and display up to six polar

equations, rl through r6. Each is defined in terms of the

independent variable 0 (page 5-4).

The icons to the left of rl through r6 represent the graph

style of each polar equation (Chapter 3). The default in Pol

graphing mode is "..(line), which connects plotted points.

Line, "i (thick), -(! (path), (! (animate), and ". (dot) styles are

available for polar graphing.

Polar Graphing 5-3

Defining and

Editing Polar

Equations

Selecting and

Deselecting Polar

Equations

Setting Window

Variables

To define or edit a polar equation, follow the steps in

Chapter 3 for defining a function or editing a function. The

independent vm'iable in a polar equation is 0. In Pol

graphing mode, you can enter the polar variable 0 in either

of two ways.

• Press _.

• Press@ [0].

The TI-83 graphs only the selected polar equations. In the

Y= editor, a polar equation is selected when the =sign is

highlighted. You nlay select any- or M1of the equations.

To change the selection status, nlove the cursor onto the

= sign, and then press [_.

To display- the window variable values, press _.

These variables define the viewing window. The values

below are defaults for Pol graphing in Radian angle mode.

Omin=O

Omax=6.2831853,..

Ostep=.1308996...

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

SmMlest 0 value to evMuate

Largest 0 vMue to evaluate (2=)

Increment between @values (=/24)

SmMlest X vMue to be displayed

Largest X value to be displayed

Spacing between the X tick marks

SmMlest Y value to be displayed

Largest Y value to be displayed

Spacing between the Y tick marks

Note: To ensure that sufficient points are plotted, you may want to

change the 0 window variables.

5-4 Polar Graphing

Setting the Graph

Format

Displaying a

Graph

Window

Variables and

Y-VARS Menus

To display the current graph format settings, press [2_]

[FORMAT].Chapter 3 describes the forlnat settings in detail.

The other graphing lnodes share these format settings.

When you press _, the TI-83 plots the selected polar

equations. It evMuates R for each value of 0 (from 0min to

0max in intervals of 0step) and then plots each point. The

window variables define the viewing window.

As the graph is plotted, X, Y, R, and 0 are updated.

Slnart Graph applies to polm" graphs (Chapter 3).

You can perfornl these actions fronl the honle screen or a

program.

• Access functions by using the name of the equation as a

wuiable

rl +r.z 8

• Store polar equations,

"51_1"÷1"i Done \r?:=\rll_5OPl°tlP10t_: Plot3 I

• Select or deselect polar equations.

FnOff 1 Done Plott PIotZ Plot_ I

xr I=50 I

• Store values directly to window variables.

IO+Orqih OI

Polar Graphing 5-5

Exploring Polar Graphs

Free-Moving

Cursor

TRACE

Moving the Trace

Cursor to Any

Valid e Value

ZOOM

CALC

The ffee-mo_ing cursor in Pol graphing works the same as

in Func graphing. In RectGC fonnat, moving tile cursor

updates the values of Xand Y; if CoordOn format is

selected, Xand Y are displayed. In PolarGC format, X, Y, R,

and 0 are updated; if CoordOn format is selected, Rand 0

m'e displayed.

To activate TRACE, press _. When TRACE is active,

you can nlove the trace cursor along the graph of the

equation one 0step at a time. When you begin a trace, tile

trace cursor is on the first selected function at 0min. If

ExprOn fornlat is selected, then the equation is displayed.

In RectGC format, TRACE updates the values of X, Y, and 0;

if CoordOn format is selected, X, Y, and 0 are displayed. In

PolarGC format, TRACE updates X, Y, R, and 0; if CoordOn

format is selected, Rand 0 m'e displayed.

To nlove five plotted points at a time on a function, press

Kffa][] or Kffa][Z]. If you move tile trace cursor beyond tile

top or bottonl of the selden, the coordinate values at the

bottonl of the screen continue to change appropriately.

Quick Zoom is available in Pol graphing mode; panning is

not (Chapter 3).

To nlove the trace cursor to any valid 0 value on the

current function, enter the number. When you enter the

first digit, a 0= prompt and the number you entered are

displayed in tile bottom-left corner of tile screen. You can

enter an expression at the 0= prompt. The value must be

valid for the current viewing window. When you complete

tile enhT, press _ to nlove the cursor.

ZOOM operations in Pol graphing work the same as in Func

graphing. Only the X(Xmin, Xmax, and Xscl) and Y (Ymin,

Ymax, and Yscl) window variables are affected.

The 0 window variables (0rain, 0max, and Ostep) are not

'affected, except when you select ZStandard. The VARS

ZOOM seeondmTy- menu ZT/ZO items 4:Z0min, 5:Z0max, and

6:Z0step m'e zoom nlemoKy-varialfles ff_r Pol graphing.

CALC operations in Pol graphing work the sanle as in Func

graphing. The CALCULATE nlenu items available in Pol

graphing are 1:value, 2:dy/dx, and 3:dr/d0.

5-6 Polar Graphing

Sequence

Graphing

Contents Getting Started: Forest and Trees ........................ 6-2

Defining and Displaying Sequence Graphs ............... 6-3

Selecting Axes ('ombinations ............................ 6-8

Exploring Sequence Graphs .............................. 6-9

Graphing Web Plots ...................................... 6-11

Using Web Plots to Illustrate Convergence ............... 6-12

Graphing Phase Plots .................................... 6-13

Comparing TI-83 and TI-82 Sequence Variables .......... 6-1.5

Keystroke Differences Between TI-83 and TI-82 ......... 6-16

'_ TEXAS iNSTRUMENTS T1=83

u= -.Bu(7_-:1.)+3.6

-,_ I=

-% l

........ ....

>'_=:L5 I' "_ "%_

X=l.F_61172 i'=1._ _:61172

STATPLOT TBLSET FORMAT CALC TABLE

Sequence Graphing 6-1

Getting Started: Forest and Trees

Getting Started is a fast-paced introduction. Read the chapter for details.

A small forest of 4,0!)0 trees is under a new forestw plan. Each year 20 percent

of the trees will be hmwested and 1,000 new trees will be planted. Will the

forest eventually- disappear? Will the forest size stabilize? If so, in how many

yeat\_ and with how many trees?

Press IM65E].Press [] [] [] [] [] [] IgffTgR]

to select Seq graphing mode.

Press [_ [FORMAT] and select Timeaxes

format and ExprOnformat if neeessatT.

Soi Eng

0123456789

Degree

ar Pol

UM MW UW

PolaPGC

CoopdO_

GridOn

RxesO_

LabelOn

3. Press @. If the graph-style icon is not ".

(dot), press [] [], press [g_-gRquntil ". is

displayed, and then press [] [].

4. Press [_ [] ato select iPart( (integer

pro't) because only whole trees are

harvested. After each annual hatw'est, 80

percent (.80) of the trees remain. Press []

8[_ [u] [] _ [] 1 [] to define the

number of trees after each harvest. Press

[] 1000 [] to define the new trees. Press []

4000 to define the number of trees at the

beginning of the program.

5. Press [_ 0 to set nNin=0. Press [] 60

to set nNax=fi0, nNin and nMax evaluate

forest size over 50 years. Set the other

window variables.

PlotStart=l Xmin=0 Ymin=0

PlotStep=l Xmax=50 Ymax=6000

Xscl=10 Yscl=1000

Press _. Tracing begins at nMin (the

start of the foresttT plan). Press [] to trace

the sequence year by year. The sequence is

displayed at the top of the screen. The

values for n(number of years), X (X=n,

because nis plotted on the x-axis), and Y

(tree count) are displayed at the bottom.

When will the forest stabilize? With how

many trees?

PI_I PI_tZ Plot3

_Min=l

'..u(_bBiPart(.Bu(

_-I)+1000)

u(_Min)B4000

".v(_)=

v(_Min)=

".u(_)=

lu=iPart(.Bu(_-l)+lOO0) I

6-2 Sequence Graphing

Defining and Displaying Sequence Graphs

TI-83 Graphing

Mode Similarities

Setting Sequence

Graphing Mode

The steps for defining a sequence graph are similar to the

steps for defining a function graph. Chapter 6 assumes that

you are familiar with Chapter 3: Function Graphing.

Chapter 6 details aspects of sequence graphing that differ

froln function graphing.

To display- the mode screen, press [M6D_.To graph

sequence functions, you nmst select 8eq graphing mode

before you enter window wu'iables and before you enter

sequence functions.

Sequence graphs automatically plot in Simul mode,

regardless of the current plotting-order mode setting.

TI-83 Sequence

Functions u, v,

and w

The TI-83 has three sequence functions that you can enter

from the keyboard: u, v, and w. They are above the [7], [],

and [] keys.

You call define sequence functions in terms off

• The independent variable n

• The previous term in the sequence function, such as

u(n-1)

• The term that precedes tile previous term in tile

sequence function, such as u(n-2)

• The previous term or the term that precedes the

previous term in another sequence function, such as

u(n-1) or u(n-2) t_ferenced in the sequence v(n).

Note: Statements in this chapter about u(n) are also true for v(n) and

w(n); statements about u(n-1) are also true for v(n-1) and w(n-1);

statements about u(n-2) are also true for v(n-2) and w(n-2).

Sequence Graphing 6-3

Displaying the

Sequence Y=

Editor

Selecting Graph

Styles

Selecting and

Deselecting

Sequence

Functions

After selecting Seq mode, press [] to display- the sequence

Y= editor.

nMin=l

",.u(n)=

u(nMin)=

"..v(n)=

v(nMin)=

"..u(n)=

u(nMin)=

In this editor, you can display and enter sequences for u(n),

v(n), and w(n), Also, you can edit the value for nMin, which

is the sequence window variable that defines the nlininluln

nvalue to evaluate.

The sequence Y= editor displays the nMin value because of

its relevance to u(nMin), v(nMin), and w(nMin), which are the

initial values for the sequence equations u(n), v(n), and

w(n), respectively.

nMin in the Y= editor is the same as nMin in the window

editor. If you enter a new value for nMin in one editor, the

new value for nMin is updated in both editors.

Note: Useu(nMin), v(nMin), or w(nMin) only with a recursive

sequence,whichrequires an initialvalue.

The icons to the left of u(n), v(n), and w(n) represent the

graph style of each sequence (Chapter 3). The default in

$eq mode is ". (dot), which shows discrete values. Dot,

"..(line), and "i (thick) styles m'e available for sequence

graphing. Graph styles m'e ignored in Web format.

The TI-83 graphs only the selected sequence functions. In

the Y= editor, a sequence function is selected when the =

signs of both u(n)= and u(nMin)= are highlighted.

To change the selection status of a sequence function,

move the cut\sor onto the = sign of the function name, and

then press [g_. The status is changed for both the

sequence function u{n) and its initial value u(nMin).

6-4 Sequence Graphing

Defining and

Editing a

Sequence

Function

Nonrecursive

Sequences

To define or edit a sequence function, follow the steps in

Chapter 3 for defining a function. The independent vmiable

in a sequence is n.

In Seq graphing mode, you can enter the sequence vmiable

in either of two ways.

• Press _.

• Press [g67][CATALOG][N].

You can enter the function name from the keyboard.

• To enter the function name u, press [gh_][u] (above [_).

• To enter the function name v, press [g6_ [v] (above [_).

• To enter the function name w, press [g67][w] (above [_).

Generally, sequences are either nonrecursive or recursive.

Sequences are evaluated only at consecutive integer

values, nis always a series of consecutive integers, starting

at zero or any positive integer.

In a nonrecursive sequence, the nth term is a function of

the independent variable n. Each term is independent of all

other terms.

For example, in the nonrecursive sequence below, you can

calculate u(6) directly, without fit\_t calculating u(1) or any

%exdous terlll,

PloL1 PloL2 Plot3

_Hin=l

,.u(_)B2*n

u(_Min)B

"..v(_)=

v(_Min)=

"'.u(_)=

u(_Min)=

The sequence equation above returns the sequence

2, 4, 6, 8,10, . . . for n=1,2,3,4,5,....

Note: You may leave blank the initial value u(nMin) when calculating

nonrecursive sequences.

Sequence Graphing 6-5

Recurslve

Sequences

In a reem\Mve sequence, the nth term in the sequence is

defined in relation to the previous term or the term that

precedes the previous term, represented by u(n-1) and

u(n-2). A reem\Mve sequence may also be defined in

relation to n, as in u(n)=u(n- 1)+n.

For example, in the sequence below you cannot calculate

u(5) without first calculating u(1), u(2), u(3), and u(4).

plo1:1 PloL2 pl,:a:_: I

_Min=l I

"..u(_)B2*u(n-1 )

u(.n[_in)B1

Using an initial value u(nMin) = 1, the sequence above

returns 1, 2, 4, 8, 16,...

Tip: On the TI-83, you must type each character of the terms. For

example, to enter u(n-1), press _ [u] [] _ [] [] lB.

Recursive sequences require an initial value or values,

since they reference undefined terms.

• If each term in the sequence is defined in relation to the

pre_dous term, as in u(n-1), you nmst specify an initial

value for the first tenn.

PloLi plol:._ Plot3

nMin=l

..u (n) B. 8u (n- 1 )+5

u(nMin)B100

If each term in the sequence is defined in relation to the

term that precedes the previous term, as in u(n-2), you

nmst specify- initial values for the first two terms. Enter

the initial values as a list enclosed in braees ({ }) with

commas separating the values.

Plot't PloI:2 Plot3

nMin=l

I..u(n)Bu(n-1 )+u(n

-2) }[ u(r_Min)B{l,O

The value of the first term is 0 and the value of the second

term is 1 for the sequence u(n).

6-6 Sequence Graphing

Setting Window

Variables To display- the window variables, press _, These

variables define the viewing window. The values below are

defaults for Seq graphing in both Radian and Degree angle

nlodes,

nMin=1

nMax:10

PlotStart:1

PlotStepffil

Xmin:-10

Xmax=lO

Xscl=l

Ymin=-lO

Ymax=lO

Yscl=l

Smallest nvalue to ev'gduate

Largest nvalue to evaluate

First term number to be plotted

Incremental nvalue (for graphing only)

Smallest X value to be displayed

Largest X value to be displayed

Spacing between the X tick marks

Smallest Y value to be displayed

Largest Y value to be displayed

Spacing between the Y tick marks

nMin must be an integer k O, nMax, PlotStart, and PlotStep

nmst be integers _>1,

nMin is the smallest nwdue to evaluate, nMin also is

displayed in the sequence Y= editor, nMax is the largest n

value to evaluate. Sequences are evaluated at u(nMin),

u(nMin+l), u(nMin+2), ... ,u(nMax).

PlotStart is the first term to be plotted. PlotStart=l begins

plotting on tile first term in tile sequence. If you want

ph)tting to begin with the fifth term in a sequence, for

exalnple, set PlotStart=& The first four terms are evaluated

but are not plotted on the graph.

PlotStep is the incremental nwdue for graphing only.

PlotStep does not 'affect sequence evaluation; it only

designates which points are plotted on the graph. If you

specify PlotStep=2, the sequence is ewduated at each

consecutive integer, but it is plotted on the graph only at

evew other integer.

Sequence Graphing 6-7

Selecting Axes Combinations

Setting the Graph

Format

Setting Axes

Format

Displaying a

Sequence Graph

To display- the current graph format settings, press [_

[FORMAT], Chapter 3 describes the format settings in detail,

The other graphing modes share these format settings, The

m,ces setting on the top line of the screen is available only

in Seq mode,

Time Web uv vw uw

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

Type of sequence plot (m,ces)

Rectangular or polar output

Cursor coordinate display mdoff

Grid display off or on

Axes display on or off

Axes label display- off or on

Expression display on or off

For sequence graphing, you can select fronl five axes

formats. The table below shows the values that are plotted

on the x-axis and y-m'ds for each axes setting.

Axes Setting

Time

Web

x-axis

u(n-1), v(n-1),w(n-1)

u(n)

v(n)

u(n)

y-axis

u(n), v(n),w(n)

v(n)

w(n)

See pages 6-11 and 6-12 for nlore information on Web

plots. See page 6-13 for more information on phase plots

(uv, vw, and uw m,ces settings).

To plot the selected sequence functions, press _. As a

graph is plotted, the TI-83 updates X, Y, and n.

Snlart Graph applies to sequence graphs (Chapter 3).

6-8 Sequence Graphing

Exploring Sequence Graphs

Free-Moving

Cursor

TRACE

Moving the Trace

Cursor to Any

Valid nValue

The free-moving cursor in Seq graphing works the same as

in Func graphing. In RectGC fonnat, nloving tile cursor

updates the values of Xand Y; if CoordOn format is

selected, Xand Yare displayed. In PolarGC fornlat, X, Y, R,

and 0 are updated; if CoordOn format is selected, R and 0

m'e displayed.

The axes fornlat setting affects TRACE.

When Time, uv, vw, or uw axes format is selected, TRACE

moves the cursor along the sequence one PlotStep

increment at a time. To nlove five plotted points at once,

press [_ [] or [_ [].

• When you begin a trace, the trace cursor is on the first

selected sequence at the term number specified by

PlotStart, even if it is outside the viewing window.

• Quick Zoom applies to all directions. To center the

viewing window on the current cursor location after

you have moved the trace cursor, press [_. The

trace cursor t_tun_s to nMin.

In Web format, the trail of the cursor helps identify points

with attracting and repelling behavior in the sequence.

When you begin a trace, the cursor is on the x-axis at the

initial wdue of the first selected function.

Tip: To move the cursor to a specified nduring a trace, enter a value

for n, and press _. For example, to quickly return the cursor to the

beginning of the sequence, paste nMin to the n= prompt and press

To nlove the trace cursor to any valid nvMue on the

current function, enter the number. When you enter the

first digit, an n= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the n= prompt. The value nmst be

valid for the current viewing window. When you have

completed the entKy-,press [gfff_ to move the cursor.

U=U(:O-1)+U(:O-Z)

I . , .:": "

;o=_: " "

}1=5"I_ ?=3

Sequence Graphing 6-9

ZOOM

CALC

Evaluating u, v,

and w

ZOOM operations in Seq graphing work the same as in

Func graphing, Only the X (Xmin, Xmax, and Xscl) and Y

(Ymin, Ymax, and Yscl) window variables are affected.

PlotStart, PlotStep, nMin, and nMax are only affected when

you select ZStandard. The VARS Zoom secondary lnenu ZU

items 1through 7are the ZOOM MEMORY variables for Seq

graphing.

The only CALC operation available in Seq graphing is value.

• When Time axes format is selected, value displays Y (the

u(n) value) for a specified nvalue.

• When Web axes format is selected, value draws the web

and displays Y (the u(n) value) for a specified nvalue,

• When uv, vw, or uw axes format is selected, value

displays X and Y according to the axes format setting.

For example, for uv axes format, X represents u(n) and

Y represents v(n),

To enter the sequence names u, v, or w, press [2_] [u], [v], or

[w], You can evaluate these names in any- of three ways,

• Calculate the nth value in a sequence.

• Calculate a list of values in a sequence.

• Generate a sequence with u(nstart,nstop[,nstep]), nstep

is optional; default is 1.

"nz"+u:u(3) 9

u({1,3,5,7,9})

{i 925 49 81}

u(1,9,2)

{1 9 25 49 81}

6-10 Sequence Graphing

Graphing Web Plots

Graphing a Web

Plot

Valid Functions

for Web Plots

Displaying the

Graph Screen

Drawing the Web

To select Web axes format, press [_ [FORMAT] [] [E_], A

web plot graphs u(n) versus u(n-1), which you can use to

study long-term behavior (convergence, divergence, or

oscillation) of a reeursive sequence. You can see how the

sequence lnay change behavior as its initial value changes.

V_l_en Web axes format is selected, a sequence will not

graph properly or will generate an error.

• It must be recursive with only one recursion level

(u(n-1) but not u(n-2)).

• It cannot reference ndirectly.

• It cannot reference any defined sequence except itself.

In Web format, press _ to display the graph screen.

The TI-83:

• Draws a y=x reference line in AxesOn format.

• Plots the selected sequences with u(n-1) as the

independent variable.

Note: A potential convergence point occurs whenever a sequence

intersects the y=x reference line. However, the sequence may or may

not actually converge at that point, depending on the sequence's initial

value.

To activate the trace cursor, press _. The screen

displays the sequence and the emTent n, X, and Y values (X

represents u(n-1) and Y represents u(n)). Press []

repeatedly to draw the web step by step, starting at nMin.

In Web format, the trace cursor follows this course.

1. It starts on the x-axis at the initial value u(nMin) (when

PlotStart=l).

2. It lnoves vertically (up or down) to the sequence.

3. It lnoves horizontally to the y=x reference line.

4. It repeats this vertical and horizontal movenlent as you

continue to press [].

Sequence Graphing 6-11

Using Web Plots to Illustrate Convergence

Example:

Convergence

Press [] in Seq mode to display the sequence Y= editor.

Make sure the graph style is set to ". (dot), and then

define nMin, u(n) and u(nMin) as shown below.

_Min=lPl_lPloL_ PloL_ )+

u(_Min)B{-4}

"-.v(n)=

v(nMin)=

".uO?)=

Press [_ [FORMAT] _ to set Time axes ff)rmat,

Press [_ and set the variables as shown below.

nMin=l Xmin=0 Ymin=-10

nMax=25 Xmax=25 Ymax=l 0

PlotStart=l Xscl=l Yscl=l

PlotStep=l

4. Press [g_ to graph the sequence.

5, Press [_ [FORMAT]and select the Web axes setting.

6. Press [_ and change the variables below.

Xmin=-10 Xmax=10

Press [g_ to graph the sequence.

Press _, and then press [] to draw the web. The

displayed cursor coordinates n, X (u(n-1)), and

Y(u(n)) change accordingly. When you press [], a new n

value is displayed, and the trace cursor is on the

sequence. When you press [] again, the nvalue remains

the same, and the cursor moves to the y=x reference line.

This pattern repeats as you tra_'e the web.

u=-.au(._._-:t:,*_:.e t.-*

N'--_.?_:EII?2 I?=1,?_:El172

6-12 Sequence Graphing

Graphing Phase Plots

Graphing with uv,

vw, and uw

Example:

Predator-Prey

Model

The phase-plot m,ces settings uv, vw, and uw show

relationships between two sequences. To select a

phase-plot axes setting, press [_ [FORMAT],press [] until

the cursor is on uv, vw, or uw, and then press [_.

Axes Setting x-axis y-axis

uv u(n) v(n)

vw v(n) w(n)

uw u(n) w(n)

Use the predator-prey model to determine the regionM

populations of a predator and its pt_y that would maintain

population equilibrium for the two species.

This example uses the model to determine the equilibrium

populations of wolves and rabbits, with initial populations

of 200 rabbits (u(nMin)) and 50 wolves (v(nMin)).

These are the wu'iables (given values are in pm'entheses):

R = number of rabbits

M = rabbit population growth rate without wolves (.05)

K = rabbit population death rate with wolves (.001)

W = number of wolves

G = wolf population growth rate with rabbits (.0002)

D = wolf population death rate without rabbits (.03)

n= time (in months)

Rn= Rn_I(I+M-KWn_I)

W, = W,_I(I+GRn_I-D )

1, Press [] in Seq mode to display the sequence Y= editor.

Define the sequences and initial wdues for Rnand Wnas

shown below. Enter the sequence Rnas u(n) and enter

the sequence Wnas v(n).

Plot:l. Plot::" F'lot2, l

nMir,=l I

".l.l(_) BM(_- 1 )*( 1+1

•05-. 00 l*v(n-1 ) )l

-.u(n) By (_- 1)*( 1+

•0002.u (n-1)-. 03

)v(nMin)B{50}

".t0(n)=

u_(r_Min)=

Sequence Graphing 6-13

2, Press _ [FORMAT] _ to select Time axes format,

3, Press _ and set the variables as shown below.

nMin=O Xmin=O Ymin=O

nMax=400 Xmax=400 Ymax=300

PlotStart=l Xscl=100 Yscl=100

PlotStep=l

4, Press [ghT_] to graph the sequence,

5, Press _ [] to individually trace the number of

rabbits (u(n)) and wolves (v(n)) over time (n),

Tip: Press a number, and then press _ to jump to a specific n

Press [g_] [FORMAT] [] [] _ to select uv axes

format,

Press _ and change these variables as shown

below.

Xmin=84 Ymin=25

Xmax=237 Ymax=75

Xscl=50 Yscl=lO

Press _. Trace both the number of rabbits (X) and

the number of wolves (Y) through 400 generations,

I g=160.LIB_.=:B y=6;',66;'BLI9

Note: When you press [_, the

equation for uis displayed in the

top-left corner. Press [] or [] to

see the equation for v.

6-14 Sequence Graphing

Comparing TI-83 and TI-82 Sequence Variables

Sequences and

Window

Variables

Refer to the table if you are familim" with the TI-82. It

shows TI-83 sequences and sequence window vm'iables, as

well as their TI-82 counterparts.

TI-83

In the Y= editor:

u(n)

u(nMin)

v(n)

v(nMin)

w(n)

w(nMin)

In the window editor:

nMin

nMax

PlotStart

PlotStep

TI-82

UnStart (window variable)

VnStart (window vm'iable)

not available

nStart

nMax

nMin

not available

Sequence Graphing 6-15

Keystroke Differences Between TI-83 and TI-82

Sequence

Keystroke

Changes

Re%r to the table if you are familiar with the TI-82. It

conlpares TI-83 sequence-name sy_tax and variable sy_tax

with TI-82 sequence-name syntax and variable syntax.

TI183 /TI-82 On TI183, press: On TI-82, press:

n/n_ _ [,]

u(n) /Un _ [u] _ [Y-VARS] [] []

D_D

v(n)/vn _ [i r_ [¥-VARS][] []

D_D

w(n) _ [w] not available

D_D

u(n-1)lUn-1 _ [u] _ [Un-l]

D_DmD

v(n-1)/vn-1 I_ [v] I_ [vn-_]

I]]_E]mD

w(n-1) _ [w] not available

[]_•mD

6-16 Sequence Graphing

Tables

Contents Getting Started: Roots of a Function ..................... 7-2

Setting Up the Table ..................................... 7-3

Defining the Dependent Variables ........................ 7-4

Displaying the Table ..................................... 7-5

'_ TEXAS iNSTRUMENTS T1=83

XY_ Y2

0 0 0

1"1 "_

2 h 0

21 15

h_hE

511_ 10_

X= -1

STAT PLOT TBLSET FORMAT CALC TABLE

Tables 7-1

Getting Started: Roots of a Function

Getting Started is a fast-paced introduction. Read the chapter for details.

Evaluate the function Y = X :_- 2X at each integer between -10 and 10. How

many sign changes occur, and at what Xvalues?

Press _ [] [] [] FENY_to set Func

graphing mode.

Press @. Press _ _ 3to select 3

Then press [] 2_ to enter the

function Y1=X3-2X.

Press [_ [TBLSET] to display- the TABLE

SETUP screen. Press [] 10 _to set

TblStart=-10, Press 1_to set ATbI=I.

Press _ to select Indpnt: Auto

(automatically generated independent

values). Press [] [gNT_ to select

Depend: Auto (automatically generated

dependent values).

Press [_ [TABLE]to display the table

screen.

Press [] until you see the sign changes in

the value of Y1. How many sign changes

occur, and at what X values?

Plol:l P1*{_ Pl_l:_

-.Y1BX x-2X

,,yz=

b.Y_=

•,.y _=

\Yg=

".YG=

\YT=

TABLE SETUP

TbIStart= -10

_Tbl=l

Indent: _ Ask

Depend: _ Ask

XY_

"9 "7tl

"B "h96

"? "329

"6 "_.Oh

"_: "Jig

"h "gtl

X= -10

X YI

"2 "h

"1 1

0 0

1 "t

X=3

7-2 Tables

Setting Up the Table

TABLE SETUP

Screen

TblStart, ATbl

Indpnt: Auto,

Indpnt: Ask,

Depend: Auto,

Depend: Ask

Setting Up the

Table from the

Home Screen or

aProgram

TodisplaytheTABLESETUPscreen, press[_[TBLSET].

TRBLE SETUP Rsk

TblStart=O

_Tbl=l

IndPnt:

Depend: i Rsk

TblStart (table start) defines the initial value for the

independent variable. TblStart applies only when the

independent variable is generated automatically (when

Indpnt: Auto is selected).

ATbl (table step) defines the increment for the independent

variable.

Note: In Seq mode, both TblStart and ATbl must be integers.

Selections Table Characteristics

Indpnt: Auto Values are displayed automatically in both

Depend: Auto the independent-variable colunm and in all

dependent-variable colunms.

Indpnt: Ask The table is empty; when you enter a value

Depend: Auto for the independent variable, all

corresponding dependent-variable values

are cah:ulated and displayed automatically.

Indpnt: Auto Values are displayed autonmtically for the

Depend: Ask independent variable; to generate a value

for a dependent variable, move the cursor

to that cell and press [E_.

Indpnt: Ask The table is empty; enter values for the

Depend: Ask independent variable; to generate a value

for a dependent variable, move the cm:sor

to that cell and press [EN_,

To store a value to TblStart, ATbl, or TblInput from the

home screen or a program, select the variable name from

the VARB TABLE seconda[w menu. TblInput is a list of

independent-variable values in the cmTent table.

When you press [2_ [TBLSET] in the program editor, you

can select IndpntAuto, IndpntAsk, DependAuto, and

DependAsk.

Tables 7-3

Defining the Dependent Variables

Defining

Dependent

Variables from

the Y= Editor

Editing

Dependent

Variables from

the Table Editor

In the Y= editor, enter the functions that define the

dependent vmiables. Only functions that are selected in the

Y= editor are displayed in the table. The current graphing

mode is used. In Par mode, you nmst define both

components of each parametric equation (Chapter 4).

To edit a selected Y= function fronl the table editor, follow

these steps.

1. Press [_ [TABLE]to display" the table, then press [] or

[] to move the cursor to a dependent-variable column.

2. Press [] until the cursor is on the function name at the

top of the colunm. The function is displayed on the

bottonl line.

20't

Vt BX_-2X

3, Press [ggT_. The cursor moves to the bottonl line. Edit

the function.

X ml

o o

I"t

.-, it

LI _6

_; I15

I_ 20_

71BII_-2X

X m

o o

t "1

620_

V1BX:-4X

Press [ggT_ or []. The new values are calculated. The

table and the Y= function are updated automatically.

X Y1

Yt =O

Note: You also can use this feature to view the function that

defines a dependent variable without having to leave the table.

7-4 Tables

Displaying the Table

The Table To display- the table, press [_q [TABLE].

Current cell

Independent- X _ 1 4, Y z Dependent-

variable values to _ -_9.iz variable values in

11 "hh.86 "_:h.86

in the first lZ -h?.eB -_:Z.BE the second and

column 13 -_Z.I_6 -6Z.eE third columns

1h "_'.gB "G6.98 _. --

1 1_ "_ 9"_ "E.q.Z --

16 "6h._:B "?h,59

Y1 = -39, 173120459

Current cell's full value

Note: The table abbreviates the values, if necessary.

Independent and

Dependent

Variables

Clearing the

Table from the

Home Screen or

a Program

The current graphing lnode determines which independent

and dependent varial)les are displayed in the table

(Chapter 1). In the tal)le above, for example, the

independent variable X and the dependent wuiables Y1 and

Y2 are displayed because Func graphing mode is set.

Graphing Mode Independent Dependent

Variable Variable

Func (function) X Y1 through Yg, and

Par (parametric) TX1T/Y1T through

X6T/Y6T

Pol (polar) 0 rl through r6

Seq (sequence) n u(n), v(n), and w(n)

From the home screen, select the CIrTable instruction fronl

the CATALOG. To clear the table, press [ggY_.

From a program, select 9:CIrTable from the PRGM I/0 menu

or from the CATALOG. The talfle is cleared upon execution.

If IndpntAsk is selected, 'all independent and dependent

varialfle values on the table are cleared. If DependAsk is

selected, all dependent variable values on the talfle are

cleared.

Tables 7-5

Scrolling

Independent-

Variable Values

If Indpnt: Auto is selected, you can press [] and [] in the

independent-variable colunm to display more wdues. As

you scroll the colunm, the corresponding dependent-

variable values also are displayed. All dependent-variable

values may not be displayed if Depend: Ask is selected.

X YI Yz

1"t "_

z 4 ¢

4 _6 4B

5 115 105

6 204 192

X=O

X YI Yz

1"t I"_

4 io

.3 21 1_:

18.r.

X= -1

Note: You can scroll back from the value entered for TblStart. As you

scroll, TblStart is updated automatically to the value shown on the top

line of the table. In the example above, TblStart=0 and ATbI=I

generates and displays values of X=0,..., 6; but you can press [] to

scroll back and display the table for X=-I,..., 5.

Displaying Other

Dependent

Variables

If you have defined more than two dependent variables,

the first two selected Y= functions are displayed initially-.

Press [] or [] to display dependent variables defined by

other selected Y= functions. The independent wuiable

always remains in the left colunm, except during a trace

with Par graphing nlode and G-T split-screen nlode set.

XYz Y_

"_ "6 ":LB

"2 "6 "10

"1 "4 "LI

O_O

1G 2

Z:L=I ;L

Y_= -28

Tip: To simultaneously display on the table two dependent variables

that are not defined as consecutive Y= functions, go to the Y= editor

and deselect the Y= functions between the two you want to display.

For example, to simultaneously display Y4 and Y7 on the table, go to

the Y= editor and deselect Y5 and Y6.

7-6 Tables

8Dnrs Wuctions

Contents Getting Started: Drawing a Tangent Line ................. 8-2

Using the DRAW Menu ................................... 8-3

Clearh]g Dra,_lngs ....................................... 8-4

Drawing Line Segments .................................. 8-5

Drawing Horizontal and Vertical Lines ................... 8-(;

Drawing Tangent Lines .................................. 8-8

Drawing Functions and hwerses ......................... 8-9

Shading Areas on a Graph ............................... 8-10

Drawing ('ircles .......................................... 8-11

Plaeing Text on a Graph ................................. 8-12

Using Pen m Draw on a Graph ........................... 8-1:3

Drawing Points on a Graph .............................. 8-14

Drawing Pixels .......................................... 8-16

Storing Graph Pictures (Pies) ............................ 8-17

Recalling Graph Pictures (Pics) .......................... 8-18

Storing Graph Databases (GDBs) ........................ 8-19

Recalling Graph Databases (GDBs) ...................... 8-20

4_ TEXAS INSTnUMENTS T1=83

STAT PLOT TBLSET FORMAT CALC T._,B LE

DRAW Instructions 8-1

Getting Started: Drawing a Tangent Line

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to find the equation of the tangent line at X = _2 for the

function Y= sinX.

Before you begin, select Radian and Func

mode from the mode screen, if necessaw.

1. Press [] to display- the Y= editor. Press

[g_ _ [] to store sin(X) in Y1.

2. Press _ 7to select 7:ZTrig, which

graphs the equation in the ZOOlll Trig

window.

P1,'.,tl Plot_ Pl(,t3

".Y1Bsin(X)

%yz=

",Yx=

-.y_=

-,y_=

,,y_=

xY_'=

/-7--,. /-7_

"..>" ".L/

Press [g_ [DRAW] 6 to select 6:Tangent(.

The tangent instruction is initiated.

4. Press_ [4] 2[] [] 2.

Press [ggg_. The tangent line is drawn; the

Xvalue and the tangent-line equation are

displayed on the graph.

tl==in(:4)

/-7_. /-7\

".,_i_1 -,,_i___

1{=0 ?=0

tl=sih((X)

_.--.. /2"-..

-,_i_1 ",2/

4=,r(2)/211

_[//

8-2 DRAW Instructions

Using the DRAW Menu

DRAW Menu

Before Drawing

on a Graph

Drawing on a

Graph

To display the DRAW menu, press [_ [DRAW]. The TI-S3's

interpretation of these instructions depends on whether

you accessed the menu fronl the honle screen or the

program editor or directly- from a graph.

DRAW POINTS STO

1 : C1rDraw Clears all drawn elements.

2: Line(

3: Horizontal

4: Vertical

5: Tangent(

6: DrawF

7: Shade(

8: Drawlnv

9: Circle(

O: Text(

A: Pen

Draws a line segment between 2 points,

Draws a horizontal line.

Draws a vertical line.

Draws a line segment tangent to a function.

Draws a function.

Shades an area between two functions.

Draws the inverse of a function.

Draws a circle.

Draws text on a graph screen.

Activates the free-form drawing tool.

The DRAW instructions draw on top of graphs. Therefore,

before you use the DRAW instructions, consider whether

you want to perform one or more of the following actions,

• Change the mode settings on the mode screen,

• Change the fornlat settings on the format screen.

• Enter or edit functions in the Y= editor,

• Select or deselect functions in the Y= editor.

• Change the window variable values.

• Turn stat plots on or off.

• Clear existing drawings with ClrDraw (page 8-4).

Note: If you draw on a graph and then pedorm any of the actions

listed above, the graph is reptotted without the drawings when you

display the graph again.

You can use any DRAW menu instructions except Drawlnv

to draw on Func, Par, Pol, and Seq graphs. Drawlnv is valid

only in Func graphing. The coordinates for all DRAW

instructions ate the display's x-coordinate and y-coordinate

values.

You can use most DRAW menu and DRAW POINTS menu

instructions to draw directly on a graph, using the cursor

to identify the coordinates. You also can execute these

instructions from the home screen or from within a

progranl. If a graph is not displayed when you select a

DRAW menu instruction, the home screen is displayed.

DRAW Instructions 8-3

Clearing Drawings

Clearing

Drawings When

a Graph Is

Displayed

Clearing

Drawings from

the Home Screen

or aProgram

All points, lines, and shading drawn on a graph with DRAW

instructkms are temporm'y.

To elem' drawings from the currently displayed graph,

select 1 :ClrDraw from the DRAW menu, The current graph

is replotted and displayed with no drawn elements,

To clem' drawings on a graph fronl the holne screen or a

program, begin on a blank line on the home screen or in

the program editor. Select 1:CIrDraw from the DRAW menu.

The instruction is copied to the cursor location. Press

When CIrDraw is executed, it clears 'all drawings from the

current graph and displays the message Done. When you

display the graph again, all drawn points, lines, circles, and

shaded areas will be gone.

ClrOraw Done

Note:Beforeyoucleardrawings,youcanstore them withStorePic

(page 8-17).

8-4 DRAW Instructions

Drawing Line Segments

Drawing a Line

Segment Directly

on a Graph

Drawing a Line

Segment from

the Home Screen

or a Program

To draw a line segment when a graph is displayed, follow

these steps.

1. Select 2:Line( from the DRAW menu.

2. Place the cursor on the point where you want the line

segment to begin, and then press [_E_.

3. Move the cursor to the point where you want the line

segment to end. The line is displayed _s you move the

cursor. Press [ggY_.

R=5,3191_Bgl/I=_.qSi_t_9

To continue drawing line segments, repeat steps 2 and 3.

To cancel Line(, press @.

Line( also draws a line segment between the coordinates

(X1 ,Y1) and (X2,Y2). The values nlay be entered ZLS

expressions.

Line(X1,Y1,X2,Y2)

Line (0, 0, 6, 9)11

To erase a line segment, enter Line(X1,Y1,X2,Y2,0)

Line(2, 3, 4, 6, 0)11 /,

DRAW Instructions 8-5

Drawing Horizontal and Vertical Lines

Drawing a Line

Directly on a

Graph

To draw a horizontal or vertical line when a graph is

displayed, follow these steps.

1, Select 3:Horizontal or 4:Vertical from the DRAW menu. A

line is displayed that nloves as you nlove the cursor.

2. Place the cm'sor on the y-coordinate (for horizontal

lines) or x-coordinate (for vertical lines) through which

you want the drawn line to pass.

3. Press [_ to draw the line on the graph.

To continue drawing lines, repeat steps 2 and 3.

To cancel Horizontal or Vertical, press @,

8-6 DRAW Instructions

Drawing a Line

from the Home

Screen or a

Program

Horizontal (horizontal line) draws a horizontal line at Y=y.

y can be an expression but not a list.

Horizontal y

Vertical (vertical line) draws a vertical line at X=x, x can be

an expression but not a list,

Vertical _"

To instruct tile TI-83 to draw more than one horizontal or

vertical line, separate each instruction with a colon ( : ).

Ho_-izor,÷_al 7: Vet

t_al 4: Vertical ......................

DRAW Instructions 8-7

Drawing Tangent Lines

Drawing

aTangent Line

Directly

on a Graph

Drawing

aTangent Line

from the Home

Screen or

a Program

To draw a tangent line when a graph is displayed, follow

these steps,

1, Select 5:Tangent( fron] the DRAW nlenu.

2. Press [] and [] to move the cm_or to the function for

which you want to draw the tangent line. The cmTent

graph's Y= function is displayed in the top-left corner, if

ExprOn is selected.

3. Press [] a_d [] or enter a number to select the point on

the function at which you want to draw the tangent line.

4. Press [E_. In ffunc mode, the X value at which the

tangent line wa_ drawn is displayed on the bottom of

the screen, along with the equation of the tangent line.

In all other nlodes, the dy/dx value is displayed.

X=i,gt;_:

Tip: Change the fixed decimal setting on the mode screen if you want

to see fewer digits displayed for X and the equation for Y.

Tangent( (tangent line) draws a line tangent to expression

in terms of X, such as Y1 or X2, at point X=value. Xcan be

an expression, expression is interpreted as being in Func

nlode,

Tangent(expression,value)

Tangent ('gi, 3)|

8-8 DRAW Instructions

Drawing Functions and Inverses

Drawing a

Function DrawF (draw function) draws expression at a function in

terms of Xon the current graph, When you select 6:DrawF

froln the DRAW menu, the TI-83 returns to the home screen

or the program editor, DrawF is not interactive,

DrawF expression

[Ir.at0F t?1-5 II ...... ./_-.._ .(_. .....

Note: You cannot use a list in exp'_vssion to draw a family of curves.

Drawing an

Inverse of a

Function

Drawlnv (draw inverse) draws the inverse of expression by

plotting Xvalues on the y-axis and Yvalues on the x-axis.

V_lmn you select 8:Drawlnv from the DRAW menu, the TI-83

returns to the home screen or the program editor. Drawlnv

is not interactive. Drawlnv works in Func mode only.

Drawlnv expression

Drato Inv '.?ill . .@__SI.

Note: You cannot use a list ine_pression to draw a familyof curves.

DRAW Instructions 8-9

Shading Areas on aGraph

Shading a Graph To shade an area on a graph, select 7:Shade( fronl the

DRAW menu. The instruction is pasted to the home screen

or to the program editor.

Shade( draws loweffune and uppeffunc in terms of X on

the current graph and shades the area that is specifically

above lowerfane and below uppe_2fune. Only the areas

where lowerfane <uppeffunc are shaded.

Xleft and Xright, if included, specify- left and right

boundaries for the shading. Xleft and Xright nmst be

numbers between Xmin and Xmax, which axe the defaults.

patte_ specifies one of four shading patterns.

pattern= 1vertical (default)

pattern= 2horizontal

pattern= 3negative--slope 45°

pattern=4 positive--slope 45°

patres specifies one of eight shading resolutions.

patres= 1shades every pixel (default)

patres=2 shades evetF- second pixel

patres=3 shades every third pixel

patres=4 shades eve_- fourth pixel

patres=5 shades every fifth pixel

patres=6 shades eve_Ty-sixth pixel

patres=7 shades evetsz seventh pixel

patres=8 shades every eighth pixel

Shade(lowerfanc,uppe_:func[._left._right,patte_,patres])

Shade(X_-8X, X-2), ....... ____...;.:(

8-10 DRAW Instructions

Drawing Circles

Drawing a Circle

Directly on a

Graph

Drawing a Circle

from the Home

Screen or a

Program

To draw a circle directly on a displayed graph using the

cursor, follow these steps,

1, Select 9:Circle( fronl the DRAW menu.

2, Place the cursor at the center of the circle you want to

draw. Press [NTEN.

3. Move the cursor to a point on the circumference. Press

[ggTE_ to draw the circle on the graph.

Note: This circle is displayed as circular, regardless of the window

variable values, because you drew it directly on the dispiay. When

you use the Circle( instruction from the home screen or a

program, the current window variables may distort the shape.

To continue drawing circles, repeat steps 2 and 3, To

cancel Circle(, press @.

Circle( draws a circle with center (X,Y) and radius. These

values can be expressions.

Circle(X,Y, radius)

Ciwcle(O, 0, 7)1

Tip: When you use Circle( on the home screen or from a program,

the current window values may distort the drawn circle. Use ZSquare

(Chapter 3) before drawing the circle to adjust the window variables

and make the circle circular.

DRAW Instructions 8-11

Placing Text on a Graph

Placing Text

Directly on a

Graph

Placing Text on a

Graph from the

Home Screen or

aProgram

Split Screen

To place text on a graph when the graph is displayed,

follow these steps,

1, Select 0:Text( from the DRAW menu.

2, Place the cursor where you want the text to begin.

3, Enter the characters. Press @ or [_ [A-LOCK] to

enter lettet\s and 0. You nlay enter TI-83 functions,

variables, and instructions. The font is proportional, so

the exact number of characters you can place on the

graph varies. As you type, the characters are placed on

top of the graph.

To cancel Text(, press @,

Text( places on the current graph the chara('ters

comprising value, which can include TI-83 functions and

instructions. The top-left corner of the first character is at

pixel (row,column), where row is an integer between

0 and 57 and column is an integer between 0 and 94. Both

row and colnft_firt can be expressions.

Text(row,column,value,value.. ,)

value can be text enclosed in quotation marks ( " ), or it

can be an expression. The TI-83 will evaluate an

expression and display the result with up to 10 characters.

Text(42,50,"Vt=.

2XX-2X+6 )|

..... ......

I ?'I=._:X_-_:X+G

On a Horiz split screen, the nlaxinlunl value for row is 25,

On a G-T split screen, the nlaxinlunl value for ro_t_)is 45,

and the nlaxinlunl value for column is 46,

8-12 DRAW Instructions

Using Pen to Draw on a Graph

Using Pen to

Draw on a Graph

Pen draws directly on a graph only, You cannot execute

Pen from the home screen or a progranL

To draw on a displayed graph, follow these steps.

1. Select A:Pen from the DRAW menu,

2. Place the cursor on the point where you want to begin

drawing. Press [_ to turn on the pen,

3. Move the cursor. As you move the cursor, you draw on

the graph, shading one pixel at a time,

4. Press [_ to turn off the pen,

For example, Pen was used to create the arrow pointing to

the local minimunl of the selected function.

..... E.,dL

To continue drawing on the graph, nlove the cursor to a

new position where you want to begin drawing again, and

then repeat steps 2, 3, and 4. To cancel Pen, press @.

DRAW Instructions 8-13

Drawing Points on a Graph

DRAW POINTS

Drawing Points

Directly on a

Graph with

Pt-On(

To display- the DRAW POINTS menu, press [_a] [DRAW] [_.

The TI-83's interpretation of these instructions depends on

whether you accessed this nlenu froth the home screen or

the program editor or directly froth a graph.

DRAW POINTS ST0

i : Pt On( Turns on apoint.

2: Pt Off(

3: Pt Change(

4: Pxl On(

5: Pxl Off(

6: Pxl Change(

7: pxl Test(

Turns off a point.

Toggles a point on or off.

Turns on a pixeL

Turns off a pixel.

Toggles a pixel on or off,

Returns 1 if pixel on, 0 if pixel off,

To draw a point on a graph, follow these steps.

1, Select 1:Pt-On( from the DRAW POINTS menu,

2. Move the cursor to the position where you want to draw

the point.

3. Press [ggY_ to draw the )oint.

R:Ll,_6e0mgl y:LI.BM]?O.:I?

To continue drawing points, repeat steps 2 and 3. To

cancel Pt-On(, press @.

8-14 DRAW Instructions

Erasing Points

with Pt-Off(

Changing Points

with Pt-Change(

Drawing Points

from the Home

Screen or a

Program

To erase (turn off) a drawn point on a graph, follow these

steps,

1. Select 2:Pt-Off( (point off) from the DRAW POINTS

nlenu,

2. Move the cursor to the point you want to erase.

3. Press _ to ertkse the point.

To continue ertLsing points, repeat steps 2 and 3. To cancel

Pt-Off(, press @.

To change (toggle on or off) a point on a graph, %llow

these steps.

1. Select 3:Pt-Change( (point change) from the DRAW

POINTS menu.

2. Move the cursor to the point you want to change.

3. Press I_ to change the point's on/off status.

To continue changing points, t_peat steps 2 and 3. To

cancel Pt-Change(, press @.

Pt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off(

tutlls the point off. Pt-Change( toggles the point on or off.

mark is optional; it determines the point's appearance;

specify 1, 2, or 3, where:

1=•(dot; default) 2= [] (box) 3=+(cross)

Pt-On(x,y[,mark])

Pt-Off(x,y[ ,mark ])

Pt-Change(x,y)

Pt.-0n ( 2, 5, 2> :Pt,-

Note: If you specified mark to turn on a point with Pt-On(, you must

specify mark when you turn off the point with Pt-Off(. Pt-Change(

does not have the mark option.

DRAW Instructions 8-15

Drawing Pixels

TI-83 Pixels A pixel is a square dot on the TI-83 display. The Pxl- (pixel)

instructions let you turn on, turn off, or reverse a pixel

(dot) on the graph using the cursor. When you select a

pixel instruction from the DRAW POINTS menu, the TI-83

retm'ns to the home screen or the program editor. The

_ixel instl_ctions are not interactive.

p; jq

Turning On and

Off Pixels with

Pxl-On( and

Pxl-Off(

Using pxI-Test(

Split Screen

PxI-On( (pixel on) turns on the pixel at (row,column),

where row is an integer between 0 and 62 and column is an

integer between 0 and 94.

PxI-Off( turns the pixel off. Pxl-Change( toggles the pixel on

and off.

Pxl-On(row,column)

Pxl-Off(row,column)

Pxl-Change(_'ow,column)

pxI-Test( (pixel test) returns 1 if the pixel at (row,column)

is turned on or 0 if the pixel is tunled off on the curl_nt

graph, row nmst be an integer between 0 and 62. column

nmst be an integer between 0 and 94.

pxI-Test(row,colu'rnn)

On a Horiz split screen, the maxinmm value for row is 30

for PxI-On(, PxI-Off(, Pxl-Change(, and pxI-Test(.

On a G-T split screen, the nlaxinlunl value for row is 50 and

tile nlaxinlunl value for column is 46 for PxI-On(, PxI-Off(,

Pxl-Change(, and pxI-Test(.

8-16 DRAW Instructions

Storing Graph Pictures (Pics)

DRAW STO Menu

Storing aGraph

Picture

To display the DRAW STO menu, press [g_ [DRAW] [_,

When you select an instruction fronl the DRAW STO menu,

the TI-83 returns to the home screen or the program editor.

The picture and graph database instructions are not

interactive.

DRAW POINTS STO

1:StorePic

2:RecallPic

3:StoreGDB

4:RecalIGDB

Stores the current picture.

Recalls a saved picture.

Stores the current graph datal)ase.

Recalls a saved graph database.

You can store up to 10 graph pictures, each of which is an

image of the cmTent graph display-, in picture wuialfles

Pie1 through Picg, or PicO.Later, you can superimpose the

stored picture onto a displayed graph from the home

screen or a program.

A picture includes drawn elements, plotted functions, axes,

and tick marks. The picture does not include axes labels,

lower and upper bound indicators, prompts, or cursor

coordinates. Any parts of the display- hidden by these items

m'e stored with the picture.

To store a graph picture, follow these steps.

1. Select 1:StorePic fronl the DRAW STO menu. StorePic is

DL_ted to the current cursor location.

2. Enter the number (from 1 to 9, or 0) of the picture

variable to which you want to store the picture. For

example, if you enter 3, the TI-83 will store the picture

to Pic3.

5tor.ePio 3

Note: You alsocan selecta variablefromthe PICTURE

secondarymenu(_ 4). The variableispastednextto

8torePic.

3. Press [ggTE_ to display- the current graph and store the

picture.

DRAW Instructions 8-17

Recalling Graph Pictures (Pics)

Recalling aTo

Graph Picture 1.

Deleting a Graph

Picture

recall a graph picture, follow these steps,

Select 2:RecallPic ffonl the DRAW STO menu, RecallPic

is pasted to the current cursor location,

Enter the number (from 1to 9, or 0) of the picture

varial)le from which you want to recall a picture. For

example, if you enter 3, the TI-83 will recall the picture

stored to Pic3.

Reoal IPio 3

Note: You also can select a variable from the PICTURE

secondary menu (_ 4). The variable is pasted next to

RecallPic.

3, Press I_ to display- the current graph with the

picture superimposed on it,

Note: Pictures are drawings. You cannot trace a curve that is part of a

picture.

To delete graph pictures from memo[3z, use the

MEMORY DELETE FROM menu (Chapter 18).

8-18 DRAW Instructions

Storing Graph Databases (GDBs)

What Is a Graph

Database.'?

Storing a Graph

Database

A graph database (GDB) contains the set of elements that

defines a pm'ticular graph. You can recreate the graph froln

these elements. You can store up to 10 GDBs in variables

GDB1 through GDB9, or GDB0 and recall them to recreate

graphs.

A GDB stores five elements of a graph.

• Graphing mode

• Window variables

• Format settings

• All functions in the Y= editor and the selection status of

each

• Graph style for each Y= function

GDBs do not contain drawn items or stat plot definitions.

To store a graph database, follow these steps.

1, Select 3:StoreGDB from the DRAW STO menu. StoreGDB

is pasted to the current cursor location,

2. Enter the number (from 1to 9, or 0) of the GDB variable

to which you want to store the graph database. For

example, if you enter 7, the TI-83 will store the GDB to

GDB7,

StoreGDB 7

Note: You also can select a variable from the GDB secondary

menu ([_ 3). The variable is pasted next to $toreGDB.

3, Press 1_ to store the current database to the

specified GDB variable.

DRAW Instructions 8-19

Recalling Graph Databases (GDBs)

Recalling a

Graph Database

Deleting a Graph

Database

CAUTION: When you recall a GDB, it replaces all existing

Y= functions. Consider storing the cutTent Y= functions to

another database before recalling a stored GDB.

To recall a graph database, follow these steps.

1. Select 4:RecalIGDB from the DRAW STO menu.

RecalIGDB is pasted to the current cursor location.

2. Enter the number (from 1to 9, or 0) of the GDB variable

from which you want to recall a GDB. For example, if

you enter 7, the TI-83 will recall the GDB stored to

GDB7,

Reoal IGDB 7

Note: You alsocan selecta variablefromthe GDB secondary

menu(_ 3). The variableis pastednextto RecalIGDB.

3, Press [_ to replace the current GDB with the

recalled GDB. The new graph is not plotted. The TI-83

changes the graphing mode automatically, if necessat T.

To delete a GDB fronl nlemo_T, use the MEMORY DELETE

FROM menu (Chapter 18).

8-20 DRAW Instructions

SplitScreen

Contents Getting Started: Exploring tile Unit Circle ................ 9-2

Using Split Screen ....................................... 9-3

Horiz (Horizontal) Split Screen .......................... 9-4

G-T (Graph-Table) Split Screen .......................... 9-5

TI-83 Pixels in Horiz and G-T Mode ...................... 9-6

'_ TEXAS INSTRUMENTS T1=83

','t==in_)JoX IoY 1

_'.', l _, .._,75 1.2,_3

1.07 1.1177_:

2.337 .97:_9

X=.BO:_h7:_O h 1.605 .ggg4

?=.7190761B

STATPLOT TBLSET FORMAT CALC TABLE

Split Screen 9-1

Getting Started: Exploring the Unit Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Use G-T (graph-table) split-screen mode to explore the unit circle and its

relationship to the numeric values for tile connnonly used trigonometric angles

of 0°, 30 °, 45°, 60 °, 90 °, and so on.

Press [g6m to display the mode screen.

Press [] [] [] [g_ to select Degree

mode. Press [] [] [g_ to select Par

(parametric) graphing mode.

Press [] [] [] [] [] [] [g_ to select G-T

(graph-table) split-screen mode.

Press [_ [FORMAT]to display" the format

screen. Press [] [] [] [] [] [] [g_ to

select ExprOff.

Press [] to display" the Y= editor for Par

graphing mode. Press [g6_ _ []

[ggg_] to store cos(T) to XIT, Press [gF_

[] _ to store sin(T) to YIT.

Press _ to display the window

editor. Enter these values for the window

variables.

Train=0 Xmin=-2.3 Ymin=-2.5

Tmax=360 Xmax=2.3 Ymax=2.fi

Tstep=l 5 Xscl=l Yscl=l

Press _. On the left, the unit circle is

graphed parametrically in Degree mode

and the trace cursor is activated. When

T=0 (from the graph trace coordinates),

you can see from the table on the right

that the value of XlT (cos(T)) is 1and YIT

(sin(T)) is 0. Press [] to move the cursor to

the next 15°angle increment. As you trace

around the circle in steps of 15°, an

approximation of the standard value for

each angle is highlighted in the table.

li X1, V1T

i 0

.g .Bfl6

.zsne ._ss_

T=_O 0 1

g:.BSfi02B_

9-2 Split Screen

Using Split Screen

Setting a Split-

Screen Mode To set a split-screen lnode, press [MO0_,and then nlove the

cursor to tile bottol:l line of the l:lode screen.

• Select Horiz (horizontal) to display- the graph screen and

another screen split horizontally.

• Select G-T (graph-table) to display the graph screen and

table screen split vertically.

Sci Eng Sci Eng

Dot

The split screen is activated when you press any key that

applies to either half of the split screen.

Sonle screens m'e never displayed +is split screens. For

example, if you press _ in Roriz or G-T inode, the inode

screen is displayed as a full screen. If you then press a key

that displays either half of a split screen, such as _,

the split screen returns.

VC]mnyou press a key or key combination in either Horiz or

6-7 mode, the cursor is placed in the half of the display- for

which that key applies. For example, if you press _,

the cursor is placed in the half in which the graph is

displayed. If you press [g_ [TABLE],the cursor is placed in

the half in which the table is displayed.

The TI-83 will remain in split-screen lnode until you

change back to Full screen mode.

Split Screen 9-3

Horiz (Horizontal) Split Screen

Horiz Mode

Moving from Half

to Half in Horiz

Mode

Full Screens in

Horiz Mode

In Horiz (horizontal) split-screen lnode, a horizontal line

splits tile screen into tc ) and bottom halves.

\ViBsin(X z)

,.YzBcos(XZ )

\Y._=

The top half displays the graph.

The bottom half displays any of these editors.

• Home screen (four lines)

• Y= editor (four lines)

• Stat list editor (two rows)

• Window editor (three settings)

• Table editor (two rows)

To use the top half of tile split screen:

• Press [g_ or _.

• Select a ZOOM or CALC operation.

To use tile bottonl half of tile split screen:

• Press any key or key combination that displays the

home screen.

• Press [] (Y= editor).

• Press [gT_ [g_ (stat list editor).

• Press _ (window editor).

• Press [2_ [TABLE](table editor).

All other screens are displayed as full screens in Horiz

split-screen mode.

To return to the Horiz split screen from a full screen when

in Horiz mode, press any- key or key combination that

displays the graph, home screen, Y= editor, stat list editor,

window editor, or table editor.

9-4 Split Screen

G-T (Graph-Table) Split Screen

G-T Mode

Moving from Half

to Half in G-T

Mode

Using _in

G-T Mode

Full Screens in

G-T Mode

In G-T (graph-table) split-screen mode, a vertical line splits

tile screen into left and right halves.

X Y1

,2: X=Bgq.

The left half displays the graph.

The right half displays the table.

To use the left half of the split screen:

• Press [g_ or _.

• Select a ZOOM or CALC operation.

To use tile right half of the split screen, press [:_ [TABLE].

As you lnove tile trace cursor along a graph in the split

screen's left half in G-T mode, the table on the right half

autolnatically scrolls to match tile current cursor values.

x_ X Vi

1.07 .B77_

1._7_7 ,97:'9

t,l_0g .999h

g=.B0ZtlTZ0h

Y=,7190761B

Note: When you trace in Par graphing mode, both components of an

equation (XnT and YnT) are displayed in the two columns of the table.

As you trace, the current value of the independent variable Tis

displayed on the graph.

All screens other than the graph and the table are

displayed as full screens in G-T split-screen mode.

To return to the G-T split screen from a full screen when in

G-T mode, press any key or key combination that displays

the graph or the table.

Split Screen 9-5

TI-83 Pixels in Horiz and G-T Modes

TI-SaPixelsin "i

Horiz and G-T (o,0.', l .(°._.h.)?l

Modes €,30,0) 1 o0,9_)_,

"*. _ X

I=o

Note: Each set of numbers in parentheses above represents the row

and column of a corner pixeI, which is turned on.

DRAW POINTS

Menu Pixel

Instructions

For PxI-On(, PxI-Off(, Pxl-Change(, and pxI-Test(:

• In Horiz mode, row nmst be _<30; column nmst be _<94.

• In G-T mode, row nmst be _<50; column nmst be _<46.

Pxl-On(row,column)

DRAW Menu

Text( Instruction

For the Text( instruction:

• In Horiz mode, row nmst be _<25; column must be _<94.

• In G-T mode, row nmst be _<45; column nmst be _<46.

Text(row,column,"text")

PRGM I/O Menu

Output(

Instruction

For the Output( instruction:

• In Horiz mode, row nmst be _<4; column nmst be _<16.

• In G-T mode, row nmst be _<8; column nmst be _<16.

Output(row,column, "text")

Setting a

Split-Screen

Mode from the

Home Screen or

a Program

To set Horiz or G-T from a program, follow these steps.

1. Press [M0_] while the cursor is on a blank line in the

program editor.

2, Select Horiz or G-T,

The instruction is pasted to the cursor location. The mode

is set when the instruction is eneountered during program

execution. It remains in effect after execution.

Note: You also can paste Horiz or G-T to the home screen or

program editor from the CATALOG (Chapter 15).

9-6 Split Screen

10 Matrices

Contents Getting Started: Systems of Linear Equations ............ 10-2

Defining a Matrix ........................................ 10-2

Viewing and Editing Matrix Elements .................... 10-4

Using Matrices with Expressions ........................ 10-7

Displaying and Copying Matrices ........................ 10-8

Using Math Functions with Matrices ..................... 10-9

Using the MATRX MATH Operations ..................... 10-12

'_ TEXAS iNSTRUMENTS T1=83

MRTRIX[R] 8 x4

r_-_.:l.h_: 1:_

E"1 _:.1h11_ 0

ro 0 0

r 0 0 BB

E1.B 0 0

r 0 .8571h 0

[0 0 2

i, i=3.141592653

STATPLOT TBLSET FORMAT CALC TABLE

Matrices 10-1

Getting Started: Systems of Linear Equations

Getting Started is a fast-paced introduction. Read the chapter for details.

Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83, you

can solve a system of linear equations by entering the coefficients as elements

in a matrix, and then using rref( to obtain the reduced row-echelon form.

1. Press [_. Press [] [] to display- the

MATRX EDIT menu. Press 1to select 1: [A],

2. Press 2[_ 4[_ to define a 2x4

matrix. The rectangular cursor indicates

the current element. Ellipses (...) indicate

additional eolunms beyond the screen.

3. Press 1[_ to enter the first element.

The rectangular cursor nloves to the

second colunm of the first row.

Press 2[g_ 3[g_ 3[g_ to complete

the first mw for X + 2Y + 3Z = 3.

Press 2[_ 3[_ 4 [_ 3[_ to

enter the second row for 2X + 3Y+ 4Z = 3,

Press [_ [QUIT] to return to the home

screen. If necessary, press @ to clear

the home screen. Press _ [] to

display the MATRX MATH menu. Press [] to

wrap to the end of the menu. Select B:rref(

to copy rref( to the home screen.

Press [_ 1to select 1: [A] from the

MATRX NAMES menu. Press [] FENTERI.The

reduced row-echelon form of the matrix is

displayed and stored in Ans.

iX- 1Z=-3 so X=-3+Z

1Y+2Z=3 so Y=3-2Z

MATRIX[R] 2x4

[0 0

1_1=0

MATRIX[R] 2 x4

[0 0 0

I_Z=0

IMRTRIX[A] 2 x4

rre?(|

rref'([Al )-31

[[1 18 213 ]l

10-2 Matrices

Defining a Matrix

What Is a Matrix? A matrix is a two-dimensional alTay. You can display',

define, or edit a matrix in the matrix editor. Tile TI-83 h_s

10 matrix variables, [A] through [J]. You can define a

matrix directly in an expression. A matrix, depending on

available nlelnolT, may have up to 99 rows or colunms.

You can store only real numbers in TI-83 matrices.

Selecting a

Matrix

Accepting or

Changing Matrix

Dimensions

Before you can define or display a matrix in the editor, you

first nmst select the matrix name. To do so, follow these

steps.

1. Press _ [] to display the MATRX EDIT menu. The

dimensions of any previously defined lnatrices are

displayed.

MATH

[el

[D]

[El

[F]

[G]

2, Select the matrix you want to define. The MATRX EDIT

screen is displayed.

MATRIX[B] I xl

ro I

The dimensions of the matrix (row xcolumn) are

displayed on the top line. The dimensions of a new matrix

are 1 xl, You nmst accept or change the dimensions each

time you edit a matrix, When you select a matrix to define,

the cursor highlighLs the row dimension.

• To accept the row dimension, press [_.

• To change the row dimension, enter the number of rows

(up to 99), and then press [_.

The cursor moves to the eolunm dimension, which you

must accept or change the same way you accepted or

changed the row dimension. When you press [_, the

rectangular cursor moves to the first matrix element.

Matrices 10-3

Viewing and Editing Matrix Elements

Displaying Matrix

Elements After you have set the dimensions of the matrix, you can

view the matrix and enter values for the matrix elements.

In a new matrix, 'all values are zero.

Select the matrix from the MATRXEDIT menu and enter or

accept the dimensions. The center portion of the matrix

editor displays up to seven rows and three eolunms of a

matrix, showing the values of the elements in abbreviated

form if necessary. The full vMue of the current element,

which is indicated by the t_ctangular cursor, is displayed

on the bottonl line.

MRTRIX[R] 8 x4 i

"t _:.tht6 0

i,i=3. 141592653

This is an 8 x 4 matrix. Ellipses in the left or right colunm

indicate additional columns, i' or _ in the right column

indicate additional rows.

Deleting a Matrix To delete matrices fronl nlenlory, use the MEMORY DELETE

FROM seconding- menu ((;hapter 18).

10-4 Matrices

Viewing a Matrix

Viewing-Context

Keys

The matrix editor has two contexts, viewing and editing, In

viewing context, you can use the cursor keys to move

quickly from one matrix element to the next. The full value

of the highlighted element is displayed on the bottom line,

Select the inatrix fl'oin the MATRX EDIT menu, and then

enter or accept the dimensions.

MRTRIX[R] 8 x4 1

":1, }.:DI:I.I_ 0

I,I=3. 141592653

Key Function

[] or [] Moves the rectangular cursor within the

current row.

[] or [] Moves the rectangular cursor within the

current coluinn; on the top row, [] moves

the cursor to the colunm dimension; on the

coluinn dimension, [] moves the cursor to

the row dimension.

[gNT_ Switches to editing context; activates the

edit cursor on the bottom line.

@ Switches to editing context; clears the

value on the bottoin line.

Any entry Switches to editing context; clears the

character value on the bottoln line; copies the

character to the bottom line.

[_ [INS] Nothing

[ggn Nothing

Matrices 10-5

Editing aMatrix

Element

Editing-Context

Keys

In editing context, an edit cursor is active on the bottom

line. To edit a lnatrix element value, follow these steps.

1. Select the matrix from the MATRX EDiT menu, and then

enter or accept the dimensions.

2. Press [], [], [], and [] to nlove the cursor to the lnatrix

element you want to change.

3. Switch to editing context by pressing [ggT_, @, or

an entw key-.

4. Change the value of the tnatrix element using the

editing-context keys described below. You nlay enter an

expression, which is evaluated when you leave editing

context.

Note: You can press @ _ to restore the value at the

rectangular cursor if you make a mistake.

5. Press IgOr, [], or [] to Inove to another element.

MRTRIX[RI 8 ×4

r :Ll_ntG ":kl_ 13

[ 0 0 BII

[:t.B 0 0

[0.BgT:th 0

[0 0

3, i=2Xz+3|

MRTRIX[R] 8 x4 i

3.1_I_ ").1ill 1_

Key Function

[] or [] Moves the edit cursor within the value,

[] or [] Stores the value displayed on the bottom

line to the nlatrix element; switches to

xqewing context and nloves the rectangular

cut.or within the colunm.

[g_Tgm Stores the value displayed on the bottom

line to the nlatrix element; switches to

viewing context and moves the rectangular

cm'sor to the next row element.

@ Clears the value on the bottom line.

Any entry- Copies the character to the location of the

character edit cursor on the bottom line.

[_ [INS] Activates the insert cursor.

[DE[] Deletes the character under the edit cursor

on the bottonl line.

10-6 Matrices

Using Matrices with Expressions

Using a Matrix in

an Expression

Entering a Matrix

in an Expression

To use a matrix in an expression, you can do any of the

following.

• Copy the name from the MATRX NAMES menu.

• Recall the contents of the lnatrix into the expression

with [_ [RCL] (Chapter 1).

• Enter the matrix directly (see below).

You can enter, edit, and store a matrix in the nlatlJx editor.

You also can enter a nlatrix directly in an expression.

To enter a nlatrix in an expression, follow these steps.

1. Press [2_] [ [ ] to indicate the beginning of the nlatrix.

2. Press [2_] [ [ ] to indicate the beginning of a row.

3. Enter a value, which can be an expression, for each

element in the row. Sepm'ate the values with conlnlas.

4. Press [2_] [] ] to indicate the end of a row.

5. Repeat steps 2 through 4 to enter all of the rows.

6. Press [2_] [] ] to indicate the end of the nlatrix.

Note: The closing ]] are not necessary at the end of an expression

or preceding -'>.

The resulting matrix is displayed in the form:

[[elementl,l,._,elementl,_l,...,[element.,,_,l,...,element,,_,_]]

Any expressions are evaluated when the enttsz is

executed.

2.[11[1,2,31[[_418"1014'5'161211

Note: The commas that you must enter to separate elements are

not displayed on output.

Matrices 10-7

Displaying and Copying Matrices

Displaying a

Matrix

Copying One

Matrix to Another

Accessing a

Matrix Element

To display- the contents of a matrix on the home screen,

select the nmtrix from tile MATRX NAMES menu, and then

press [_.

lEA, El; 711

Ellipses in the left or fight eolunm indicate additional

colunms. I' or 4 in the right colunm indicate additional

rows. Press [_, [], [], and [] to scroll the lnatrix.

46.0000 I

...116. 0000

...49. 0000 --62. (_iiiI

-96.8...I

%88oo

65.00...I

i::47'. 0000 -69.04,

...3, 0000 136,0...

To copy a matrix, follow these steps.

1. Press [_ to display the MATRXNAMES menu.

2. Select the name of the lnatrix you want to copy.

3. Press _.

4. Press _ again and select the name of the new

nmtrix to which you want to copy the existing matrix.

5. Press [_ to copy the lnatrix to the new lnatrix nalne.

On the home screen or fronl within a program, you can

store a vMue to, or recM1 a value from, a matrix element.

The element nmst be within the currently defined matrix

dimensions. Select matrix from the MATRX NAMES menu.

[matrixl(row,column)

0-:* [BI (2, 3)-" [BI

[[7 891

[B1(2,3)[3 20110

10-8 Matrices

Using Math Functions with Matrices

Using Math

Functions with

Matrices

+ (Add), -

(Subtract), *

(Multiply)

-(Negation)

You can use many of the math functions on the TI-83

keybom'd, tile MATH menu, tile MATH HUM menu, and tile

MATH TEST menu with matrices. However, the dimensions

nmst be appropriate. Each of the functions below creates a

new matrix; the original matrL, c remains the same.

To add ([_) or subtract ([_) matrices, the dimensions must

be the same, The answer is a matrix in which the elements

are the sum or difference of the individual corresponding

elements.

matrixA +matrixB

matrixA -mat)_ixB

To nmltiply ([_) two matrices together, the colunm

dimension of matrixA nlust match the row dimension of

matrixB.

matrixA *mat_qxB

Multiplying a matrix by a value or a value by a matrix

returns a matrix in which each element of matrix is

nmltiplied by value,

matrix*value

value*matrix

Negating a matrix (D) returns a matrix in which the sign

of evetN element is changed (reversed),

-matrix

[RI [[212; 41-211]

-ira -41

Matrices 10-9

abs(

round(

-I (Inverse)

Powers

abs( (absolute value, MATH NUM menu) returns a matrix

containing the absolute value of each element of matrix.

abs(mat_qx)

[°] 14,69'

abs([Cl_[2512369]14]

round( (MATH NUM menu) returns a matrix. It rounds every

element in matrix to #decimals (<_9), If #decimals is

olnitted, the elements are rounded to 10 digits,

rou nd(mat)qx[ ,#decimals ])

MAT IX[m2 ×2 1

[3,662 I,'15_ Pound([A],2) ]

[[1.26 2.331

[3.66 4.121

[Jse the -1 function ([_ ) to invert a matrix ("-1 is not

valid), matrix nmst be square. The determinant cannot

equal zero.

matrix-1

MRTRIX[R] 2 x2 ] l[m-, ]

El z[[-2 1 ]E_ _ [1.5 -.51

To raise a lnatrix to a power, matrix lnust be square. You

can use 2 (_), 3 (MATH menu), or ^power (D) for integer

power between 0 and 2S&

matrix 2

matrix 3

matrix^power

MRTRIX[R]__ 2 x2 ] [R]_ i

[[37 54 ]

[81 1181

[R]_,5

[[1069 15581

[2337 34061

10-10 Matrices

Relational

Operations

iPart(, fPart(, int(

To compare two matrices using the relational operations =

and _ (TEST menu), they must have the sanle dimensions, =

and _ compare mat_ixA and mat_ixB on an element-by-

element basis. The other relational operations are not valid

with matrices.

matri._'A=matrixB returns 1if eveFy" comparison is true; it

t_tums 0 if any comparison is false.

matrixA_matrixB t_tums 1if at least one comparison is

false; it returns 0 if no comparison is false,

[R]=[B]

[RI#[B]

iPart( (integer part), fPart( (fractional part), and int(

(greatest integer) are on the MATH NUM menu,

iPart( returns a matrix containing the integer part of each

element of matrix,

fPart( returns a matrix containing the fractional part of

each element of matrix.

int( returns a matrix containing the greatest integer of each

element of matrix,

iPart(matrix)

fPart(matrix)

int(matrix)

100.5 47. 151

iPaPt([D1) i

[[1 31

[100 471

¢PaPt([D])

[[.25 .3331

[.5 .15 ]

Matrices 10-11

Using the MATRX MATH Operations

MATRX MATH

det(

T(Transpose)

Accessing Matrix

Dimensions with

dim(

To display the MATRX MATH menu, press _ [_,

NAMES MATH

i: det(

2: T

3: dim(

4: Fill(

5:identity(

6: randM(

7:augment(

8: Matr*list(

9: List*matr(

O: cumSum(

A: ref(

B: rref(

C: rowSwap(

D: row+(

E: *row(

F: *row+(

EDIT

Calculates the determinant.

Transposes the matrix,

Returns the matrix dimensions.

Fills all elements with a constant.

Returns the identity matrix.

Returns a random matrix.

Appends two matrices.

Stores a matrix to a list.

Stores a list to a matrix.

Returns the eunmlative sums of a matrix.

Returns the row-echelon form of a matrix.

Returns the reduced row-echelon form.

Swaps two rows of a matrix.

Adds two rows; stores in the second row.

Multiplies the row by a number.

Multiplies the row, adds to the second row.

det((determinant) returns the determinant (a real number)

of a squm'e matrix.

det(matrix)

T(transpose) returns a matrix in which each element (row,

colunm) is swapped with the corresponding element

(colunm, row) of matrix.

matrix T

[R]

[[1 2 311

[32 11

[R]T

[3 11

dim((dimension) returns a list containing the dimensions

({rows columns} ) of mat_qz.

dim(matrix)

Note: dim(mat'rix)->Ln:Ln(1) returns the number of rows.

dim(mat'rix)->Ln:Ln(2) returns the number of columns.

dim( [_2,7,11[ -8, dim([l>+Li:L1

3,111 {2 3} 3,111

10-12 Matrices

Creating a Matrix

with dim(

Redimensioning a

Matrix with dim(

Fill(

identity(

randM(

Use dim( with _ to create a new matrixname of

dimensions rows x columns with 0_Lseach element.

{rows,columns}_dim(mat_xname)

{2,2}+di_([E]) I

[0 01

[E] [ [0 011

Use dim( with _ to redimension an existing

matrixname to dimensions rows xcolumns, The elements

in the old matrixname that m_ within the new dimensions

are not changed. Additional created elements are zeros.

Matrix elements that m'e outside the new dimensions are

deleted.

{rows,columns}-> dim(matrixname)

Fill(storesv_uetoeve_ elementin mat_xname.

Fill(v_ue,mat_xname)

FilI(5,[E]) Done

[El [[5 5]

[5 51]

identity( returns the identity matrix of dimension rows x

dimension colunms.

identity(dimension)

randM( (create random matrix) returns a rows xcolumns

random matrix of integers _>-9 and _<9, The seed value

stored to the rand function controls the values (Chapter 2),

randM(rows,eolumns)

I÷r-and: PahdM(2,2 I

[[0 -71

[88 1]

Matrices 10-13

augment(

Mats,list(

augment( appends matrixA to matrixB as new colunms.

matrixA and mahqxB both nlust have tile sanle number of

[_)WS.

augment(mat) qxA,matrixB)

[1,21 [3,41 ]+JR] ]

[ [5,61 [7,811+[BI

_a,.,gr,,ent([Rl,[B[

[[1 256]

[3 47811

MatrHist( (lnatrix stored to list) fills each listname with

elements from each colunm in mahqx. MatrHist( ignores

extra listname arguments. Likewise, MatrHist( ignores

extra matrix colunms.

MatrHist(matrix,listnomeA,._,listname n)

[[R] [[1 2 31It( i_ {I ii

MatP_lis[4 5 611 "* Lz

,Li,LI) [Rl,LiDone {3{25}

MatrHist( also fills alistname with elements fronl a specified

column# in matrix. To fill a list vdth a specific colunm from

matrix, you lnust enter column# _ffter matrix.

Mat_list(matrix,column#,listnome)

[R] It1 2 31 ILt {3 6}

[a 56111 "*

Matr_list(

Lt )JR] ,3,

Done

Listymatr( List)matr( (lists stored to matrL, c) fills matrixna,me colunm by

colunm with the elements fronl each list. If dimensions (ffMI

lists are not equal, Cist_matr(fills each extra matrixna,r_w

row with O.Conlplex lists are not valid.

List_matr(listA,._,list n,mah_xname)

List.*matP( IX, L_", I

{1'2'3}+L_I 2 3} LB,[CI) O°nel'

{4'5'6]'+L_4 5 _ ... [C] [[1 _ _ll]l

10-14 Matrices

cumSum(

Row Operations

ref(, rref(

cumSum( returns cumulative sums of the elements in

mat_'ix, starting with tlle first element. Each element is the

cumulative sum of the colunm from top to bottom.

cumSum(mat,_ix)

[0] [[1151361412]] °ur_Su'_([Dl_[9[46212]]]]

MATRX MATH menu items A th['ough F m'e row operations.

You can use a row operation in an expression, Row

operations do not change matrix in nlenloi_yL You can

enter all row numbers and values as expressions. You can

select the matrix fronl the MATRX NAMES menu,

ref( 0"ow-echelon fornl) returns the row-echelon if)rill of a

real mat'_i:c. The number of columns must be greater than

or equal to the number of _'ows.

ref(mat,_ix)

rref( (reduced row-echelon ff)rm) ret, umls the reduced row-

echelon form of a _al matrix', The number of colunms must

be greater than or equal to the number of rows,

rref(mat,_ix)

[B] [ [4 5 6] ]

[7 89]

re?([B])

[[1 1.142857143_3

[0 1 ...

rre?([B])

[[1 0 -1]

[0 1 2 ]]

Matrices 10-15

rowSwap(

row+(

* row(

* row+(

rowSwap( returns a matrix, It swaps rowA and rowB of

matrix,

rowSwap(matrix, rowA,rowB)

[F] [[2 _ 46 791]

[2 5 1 O]

[6 3 8 51

PowSwaP ( [F] ,2,4>[I

row+( (row addition) returns a lnatnx. It adds rowA and

rowB of matrix and stores the results in rowB.

row+(mat_x,rowA,rowB)

[[2,5,7118,9,411

+[O] [[2 5 71

[8 9 41 row+{[D],l,2)[1012514711111

*row( (row nmltiplieation) returns a matrix. It nmltiplies

row of matrix by value and stores the results in row.

*row(value,matrix,row)

*row+( (row nmltiplication and addition) returns a nlatdx,

It nmltiplies rowA of matrix by value, adds it to rowB, and

stores the results in rowB.

*row+(value,matrix,rowA,rowB)

*Pow+(3, [E], 1,2) I

[[1 21 3511

10-16 Matrices

11 Lists

Contents Getting Started: Generating a Sequence .................. I I-2

Naming Lists ............................................. 11-3

Storing and Displaying Lists ............................. 11-4

Entering List Names ..................................... 11-6

Attaching Fornmlas to List Names ....................... 11-7

Using Lists in Expressions ............................... 11-9

LIST ©PS Menu .......................................... 11-10

LIST MATH Menu ........................................ 11-17

'_ TEXAS iNSTRUMENTS T1=83

cunSu_,( {1,2, 3, 4,

5} ){1 6 18 15}

STATPLOT TBLSET FORMAT CALC TABLE

Lists 11-1

Getting Started: Generating a Sequence

Getting Started is a fast-paced introduction. Read the chapter for details.

Calculate the first eight terms of the sequence i/k-'. Store the results to a use>

created list. Then display the results in fraction form. Begin this example on a

blank line on the home screen.

1, Press [gfi_ [LIST] [] to display the LIST OPS

nlenu,

2. Press 6to select 6:seq(, which pastes seq( to

the current cursor location.

3. Press l[] @ [A][] [] @ [A][] l

[] 8[] 1[] to enter the sequence.

4. Press F_, and then press [_ @ to

turn on alpha-lock. Press [s] [E] [Q], and

then press @ to turn off alpha-lock.

Press 1to complete the list name.

5. Press F_ to generate the list and store it

in SEQ1. The list is displayed on the home

screen. An ellipsis (...) indicates that the list

continues beyond the viewing window.

Press [] repeatedly- (or press and hold [_)

to scroll the list and view all the list

elements.

Press [gfi_ [LIST] to display the LIST NAMES

menu. Press FENTEmto p_Bte LSEQ1to the

current cursor location. (If SEQ1 is not item

1 on your LIST NAMES menu, move the

cursor to SEQ1 before you press F_.)

7. Press [_ to display the MATH menu.

Press 1to select 1:*Frac, which pastes *Frac

to the current cursor location.

8. Press F_ to show the sequence in

fraction form. Press [] repeatedly (or press

and hold [_) to scroll the list and view all

the list elements.

MRTH

3:dim(

4:Fill(

5:se_(

8:cumSu_(

7$_List(

se_(I/RZ,R,1,8,1

i;S_ .1111111...

_IOPS MRTH

Ise_(i/Ri,R,1,8,1

)+SEQI

{i .25 .1111111._

LSEQI*Frac

_I 1/4 1,'9 Ix16_.

11-2 Lists

Naming Lists

Using TI-83 List

Names L1

through L6

Creating a List

Name on the

Home Screen

The TI-83 has six list names in nlenlol_-: L1, L2, L3, L4, L5,

and L6. The list names L1 through L6 are on the keyboard

above the numeric keys [] through [_. To paste one of

these names to a valid screen, press E_], and then press

the appropriate key. L1 through L6 are stored in stat list

editor colunms 1through 6when you reset nlenlory,

To create a list name on the home screen, follow these steps.

1. Press [_] [ { ], enter one or more list elements, and then

press [_ [ }]. Separate list elements with conunas. List

elements can be real nulnbe_\s, complex numbers, or

expressions.

I<1'2'3'4> I

2. Press _.

3. Press @ [letter from A to Z or 0] to enter the first

letter of the name.

4. Enter zero to four letters, 0, or numbers to complete the

nanle.

[<10203,4}+TEST I

5, Press [E_, The list is displayed on the next line. The

list name and its elements are stored in memory. The

list name becomes an item on the LIST NAMES menu.

_:I,2,3,4]'+TEST{I2 3 4} 21TEI2_""_OPS MRTH I

Note: if you want to view a user-created list in the stat list editor,

you must store it in the stat list editor (Chapter 12).

You also call create a list nalne ill these four places,

• At the blame= prompt in the stat list editor

• At an Xlist:, Ylist:, or Data List: Dxnnpt in the stat plot

editor

• At a List:, List1:, List2:, Freq:, Freql:, Freq2:, XList:, or

YList: prompt in the inferential stat editors

• On the home screen using SetUpEditor

You can create as many list names as your TI-83 memo[3z

has space to store.

Lists 11-3

Storing and Displaying Lists

Storing Elements

to a List

Displaying a List

on the Home

Screen

You can store list elements in either of two ways.

• Use braces and _ on the home screen.

{4+2t, 5-3t } _k G

{4+2t _,-3t }

• Use the stat list editor (Chapter 12).

The maxinmm dimension of a list is 999 elements.

Tip: When you store a complex number to a list, the entire list is

converted to a list of complex numbers. To convert the list to a list of

real numbers, display the home screen, and then enter

real(listname)->listname.

To display" the elements of a list on the home selden, enter

the name of the list (preceded by L if neeessa_77; see page

11-16), and then press FEET'. An ellipsis indicates that the

list continues beyond the viewing window. Press []

repeatedly (or press and hold []) to scroll the list and view

all the list elements.

_IDRTR {2 5 _0}

{2. 154 50,47 ....

11-4 Lists

Copying One List

to Another

Accessing aList

Element

Deleting a List

from Memory

To copy a list, store it to another list.

LTEST {123:}}

LTEST÷TEST2

{123

You can store a value to or recall a value fronl a specific

list element. You can store to any element within the

current list dimension or one element beyond.

listname(element)

{1'2'3}÷L_I 23}

4÷L_(4){L_234

L:_(z.) }2

To delete lists fronl nlenlol_, including L1through L6,use the

MEMORY DELETE FROM secondatF- menu (Chapter 18).

Resetting nlenlory restores L1through L6. Removing a list

from the stat list editor does not delete it from nlenlol_L

Using Lists in

Graphing

You can use lists to graph a family of creates (Chapter 3).

Lists 11-5

Entering List Names

Using the

LIST NAMES

Entering a User-

Created List

Name Directly

To display- the LIST NAMES menu, press [_ [LIST]. Each

item is a user-created list name. LIST NAMES menu items m'e

sorted automatically in alphanumerieal order. Only the first

10 items are labeled, using 1 through 9, then 0. To jump to

the first list name that begins with a particulm" alpha

character or 0, press @ [letter from A to Z or 0].

_ IOF'S MRTH

Tip: From the top of a menu, press [] to move to the bottom. From the

bottom, press [] to move to the top.

Note: The LIST NAMES menu omits list names I_1through 1.6. Enter

L1through L6 directly from the keyboard (page 11-3).

When you select a list name from the LIST NAMES menu,

the list name is pasted to the cmTent cursor location.

• The list name symbol, precedes a list nmne when the

name is pasted where non-list name data also is valid,

such as the home screen.

LTEST (I 2 34}

• The Lsymbol does not precede a list name when the

name is pasted where a list name is the only valid input,

such as the stat list editor's Name-- p_x)mpt or the stat

plot editor's XList: and YList: prompts.

To enter an existing list nmne directly-, follow these steps.

1. Press [_ [LIST] [] to display" the LIST OPS menu.

Select B:L, which pastes Lto the current cursor location.

L is not always necessary (page 11-16).

NRMES [_]_R MRTH Note: You also can paste L to the

61"CMFISL, Ir'l (current cursor location from the

7: _List( CATALOG (Chapter I5).

8: Selec.t(

9: augrqent(

81List*F, ate(

R: Mate* 1ist(

=11,

3. Enter the characters that conlprise the list name.

ILT123I I

11-6 Lists

Attaching Formulas to List Names

Attaching a

Formula to a List

Name

You call attach a formula to a list name so that each list

element is a result of the fornmla. When executed, the

attached formula nmst resolve to a list.

V_llen anything in the attached formula changes, the list to

which the fornmla is attached is updated automatically.

• When you edit an element of a list that is referenced in

the fornmla, the corresponding element in the list to

which the fornmla is attached is updated.

• When you edit the fonnula itself, all elements in the list

to which the fornmla is attached are updated.

For example, the fit\st screen below shows that elements

are stored to L3, and the fornmla L3+10 is attached to the

list name LADD10, The quotation lnarks designate the

formula to be attached to LADD10. Each element of LADD10

is the sum of an element in L3 and 10.

{I°2'3}÷L_I 2 3}[

"L_+IO"+ LADD10

La+IB I

LRDD10

{11 12 13}

The next screen shows another list, L4.The elements of L4

are the sum of the same formula that is attached to L3.

However, quotation marks are not entered, so the fornmla

is not attached to L4,

On the next line, -6->L3(1):L3 changes the first element in L3

to -6, and then redisplays L3.

W+IO+L4 I

{II 12 13}I

-6÷Li(1):Li

{-6 2 3}

Tile last screen shows that editing L3updated LADD10, but

did not change L4. This is because the formula L3+10 is

attached to LADDIO,but it is not attached to L4.

LRDDIO {4 12 13}

L4 {Ii 12 13}

Note: To view a formula that is attached to a list name, use the stat list

editor (Chapter12).

Lists 11-7

Attaching a

Formula to a List

on the Home

Screen or in a

Program

Detaching a

Formula from a

List

To attach a ff)rnmla to a list name from a blank line on the

home screen or from a program, follow these steps.

1. Press @ [.], enter the formula (which must resolve to

a list), and press @ [-] again.

Note: When you include more than one list name in a formula,

each list must have the same dimension.

Press _.

Enter the name of the list to which you want to attach

the fornmla.

• Press [_, and then enter a TI-83 list name kl

through ks.

• Press [_ [LIST] and select a usm_created list name

from the LIST NAMES menu.

• Enter a use_created list name directly- using t (page

11-16).

Press ITNt_RI.

{4, 8, 9}÷L_4 8 9}

"5*LI '% tLIST

5.LI

LLIST {28 40 45}

Note: The stat list editor displays a formula-lock symbol next to

each list name that has an attached formula. Chapter 12 describes

how to use the stat list editor to attach formulas to lists, edit

attached formulas, and detach formulas from lists.

You can detach (cleat') an attached fornmla fron] a list in

any- of tht_e ways.

• Enter ""Olistname on the home screen.

• Edit any element of a list to which a fornmla is

attached.

• Use the stat list editor (Chapter 12).

Note: You also can use ClrList or ClrAIIList to detach a formula

from a list (Chapter 18).

11-8 Lists

Using Lists in Expressions

Using a List in an

Expression

You can use lists in an expression in any- of three ways.

When you press [NY_, any expression is evaluated for

each list element, and a list is displayed.

• Use L1-Ls or any user-created list name in an expression.

5 16}

20/L1 {10 4 2}

• Enter the list elements directly (step 1 on page 11-3).

20/{2, 5, 10}{10 4 2}

• Use [_ [RCL] to recall the contents of the list into an

expression at the cursor location (Chapter 1).

Rcl Lt "* {2,5,10}I{425 i00}

Note: You must paste user-created list names to the Rcl prompt by

selecting them from the LIST NAMES menu. You cannot enter them

directly using L.

Using Lists with

Math Functions You can use a list to input several values ff)r some math

functions. Other chapters and Appendix A specify whether

a list is valid. The function is evaluated for each list

element, and a list is displayed.

When you use a list with a function, the function lnust

be valid for every element in the list, In graphing, an

invalid element, such as -1 in _({1,0,-1}), is ignored,

14"({1,O,-1}) I This returns an error.

F'loti Plot_: F'lot3 ) This graphsX*_(1) and X*_(O),

\VIBx,r( {1, O, -I} but skips X*_(-1).

When you use two lists with a two-argulnent function,

the dimension of each list must be the same, The

function is evaluated for corresponding elements.

{i, 2, 3}+{4, 5, 6}

{5 79}

When you use a list and a value with a two-argument

function, the value is used with each element in the list.

{1'2'3}+4{5 67}

Lists 11-9

LIST OPS Menu

SortA(, SortD(

To display the LIST OPS menu, press [_ [LIST] [_.

NAMES OPS MATH

1:SortA(

2:SortD(

3:dim(

4:Fill(

5:seq(

6:cumSum(

7:aList(

8:Select(

9:augment(

O:List_matr(

A:Matr_list(

B:L

Sorts lists in _Lscending order.

Sorts lists in descending order.

Sets the list dimension,

Fills 'all elements with a constant.

Creates a sequence,

Returns a list of cunmlative sums,

Returns difference of successive elements,

Selects specific data points,

Concatenates two lists,

Stores a list to a nlatrix.

Stores a lnatrix to a list.

Designates the list-name data type,

SortA( (sort ascending) sorts list elements fron] low to high

values, SortD( (sort descending) sorts list elements from

high to low values. Complex lists are sorted based on

magnitude (modulus).

With one list, SortA( and SortD( sort the elements of

listnome and update the list in nlenloi_.

SortA(listname) SortD(listname)

Sor.tR(L_ ) Done {6

L_ {4 5 6}

With two or more lists, SortA( and SortD( sort keylistname,

and then sort each dependlist by placing its elements in the

same order as the corresponding elements in keylistname.

All lists nmst have the same dimension,

SortA(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist n])

SortD(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist n])

{5'6'4}÷L_5 64} S°rtR(k_'L_>Done

{1,2,3},L_I 2 _ {4 5 6}

3} {3 1 2}

Note: In the example, 5is the first element in L4, and 1 is the first

element in L5. After SortA(L4,Ls), 5becomes the second element of

L4, and likewise, 1becomes the second element of L5.

Note: SortA( and SortD( are the same as $ortA( and SortD( on the

STAT EDIT menu (Chapter 12).

11-10 Lists

Using dim( to

Find List

Dimensions

Using dim( to

Create a List

Using dim( to

Redimension a

List

Fill(

dim((dimension) returns the length (number of elements)

of list.

dim(list)

diM({1,3,5,7}) 4

You can use dim( with _ to create a new listname with

dimension length from 1 to 999. The elements are zeros.

length_ dim(listname)

3÷diFKLz ) 0_

Lz {0 0

You can use dim with [gg_] to redimension an existing

listnome to dimension length from 1 to 999.

• The elements in the old listname that are within the

new dimension are not changed.

• Extra list elements are filled by 0.

• Elements in the old list that are outside the new

dimension are deleted.

length_ dim(listname)

{4'8'6}÷L_4 8 6

4÷dim(L1 )

LI {4 8 6 0} 3÷diM(L1 ) 6_

L1 {4 8

Fill( replaces each element in listnome with value.

Fill(value,listname)

{3'4'5}÷L_3 4 5}

FilI(8,L_) Done

L_ {8 8 8}

Fill(4+3t,Li_one

{4+or 4+3t 4+3t}

Note: dim( and Fill( are the same as dim( and Fill( on the MATRX

MATH menu (Chapter 10).

Lists 11-11

seq(

cumSum(

AList(

Select(

seq((sequence) returns a list in which each element is the

result of the evaluation of expression with regard to

variable for the values ranging from begin to end at steps

of increment, variable need not be defined in memory.

increment can be negative; the default value for increment

is 1. seq( is not valid within expression.

seq(expression,variable,begin,e_l[,increment])

se_(AZ, R, 1,11,3)

{I 16 49 100}

cumSum( (cunmlative sunl) returns the cunmlative sunls of

the elements in list, starting with the first element, list

elements can be real or complex numbers.

cumSum(list)

c.umSum( {i,2, 3,4,

5}){I 3 610 15}

aList( returns a list containing the differences between

consecutive elements in list. AList subtracts the first

element in list from the second element, subtracts the

second element from the third, and so on. The list of

differences is always one element shorter than the original

list. list elements can be a real or complex numbers.

AList(list)

{20,30, 45., 70}÷ LD

IST I

{20 30 45 70}

aList(LDIST)

{10 15 25}

Select( selects one or more specific data points fronl a

scatter plot or xyLine plot (only), and then stores the

selected data points to two new lists, xlistname and

ylistname. For example, you can use Select( to select and

then analyze a portion of plotted CBL 2/CBL or CBR data.

Select(xlistname,ylistname)

Note: Before you use Select(, you must have selected (turned on) a

scatter plot or xyLine plot. Also, the plot must be displayed in the

current viewing window (page 11-13).

11-12 Lists

Before Using

Select(

Using Select( to

Select Data

Points from a

Plot

Before using Select(, follow these steps.

1. Create two list names and enter the data.

2. Turn on a stat plot, select Le: (scatter plot) or [_- (xyLine),

and enter the two list names for Xlist: and Ylist: (Chapter

12).

3. Use ZoomStat to plot the data (Chapter 3).

{1,2, 3, 4, 5,6,7,8]

,9,9.5,10}+DIST I _DOnO_z _1*t_

el. . °o

I{i 2 3 45 6 7...I TgPe: I If"_ ".

1{15, 15, 15, 13, ll,I _ i_ _ .

IEg,?,5,3,2,2)÷TIM I Xlist.:oIsm °

YlisL:TIME °

I{15 15 15 13 11...I Mark: [] ÷• %.

t J

To select data points fronl a scatter plot or xyLine plot,

follow these steps.

1. Press [2_] [LIST][] 8 to select 8:Select( from the LIST

OPS menu. Select( is pasted to the home screen.

2. Enter xlistname, press [], enter ylistname, and then

press [] to designate list names into which you want

the selected data to be stored.

ISeleot(L1,Cz)l I

3. Press [g_-gm. The graph screen is displayed with

Left Bound? in the bottom-left corner.

au iI

LeFtBound? 000

Press [] or [] (if more than one stat plot is selected) to

move the cursor onto the stat plot from which you want

to select data points.

Press [] and [] to move the cursor to the stat plot data

)oint that you want as the left bound.

keFt BOLIhd? _ua

Lists 11-13

6. Press [NER]. A _indicator on the graph screen shows

the left bound. Right Bound? is displayed in the bottonl-

left corner.

Pi:BIST.,TIH{

oa a _

RiZlht _OUnd? uua

Press [] or [] to nlove tile cursor to the stat plot point

that you want for the ri ht bound, and then press [ENY_.

PI:DIST_TIHE

:a aa_

iamu a o

Ri_htBound? " u u"_ u " [] u

The x-values and y-values of the selected points are

stored in xlistname and ylistname. A new stat plot of

._:listname and ylistname replaces the stat plot from

which you selected data points. The list names are

updated in the stat plot editor.

119 7 s 3

]91ist:Lz

Mark: [] ÷ .

Note: The two new lists (xlistnanw and ylistname) willinclude the

points you select as left bound and right bound. Also, left-bonnd

x-volne < "l_ight-bound x-value must be true.

11-14 Lists

augment(

List_matr(

augment(concatenates the elements of listA and listB. The

list elements can be real or complex numbers.

augment(listA,listB)

{1,17,21}+L_

{1 1721}

augment.(L_o{a5,3

8,41}) -,

{1 17 21 25 o0 ...

List*matr( (lists stored to matrix) fills matrixname colunm

by colunm with the elements from each list. If the

dimensions of all lists are not equal, then List_matr{ fills

each extra matrixname row with O. Complex lists are not

valid.

List*matr(listl,list2, ...,list n,mat_xname)

3} List*matt( LX, L'_J, I

{l'2'3}+LX1 2 LB, 1C1) Oone[

Lists 11-15

MatrHist( MatrHist( (matrix stored to lists) fills each listname with

elements from each colunm in mahqx. If the number of

listname argulnents exceeds the number of colunms in

matrix, then MatrHist( ignores extra listr_ame arguments.

Likewise, if the number of colunms in matrix exceeds the

number of listr_ame arguments, then MatrHist( ignores

extra matrix colunms.

Mat_list(mat_x,listnamel,listname2 .... ,listnamen)

[4 5 6111 -- Lz

Matr_li_t( {2 5}

,Lz,L_) [RI,L1

Done {3

Math.list(also fills a listname with elements fronl a

specified column# in matrix. To fill a list with a specific

colunm from matrix, you nmst enter a column# after

matrix.

Mat_list(matrix,column#,listnome)

IN] [[1 2 31 [ L1 {3 6}

5 6111 --

Matt*list(

LI) [R1,3,

Done

t preceding one to five characters identifies those

characters _ts a use>created listname, listname may

comprise letter\% 0, and numbers, but it nmst begin with a

letter fi'onl A to Z or 0.

Llistname

Generally, L must precede a user-created list name when

you enter a use>created list name where other input is

valid, for example, on the home screen. Without the t, the

TI-83 may misinterpret a use>created list name as implied

nmltiplication of two or more characters.

t need not precede a use>created list name where a list

name is the only valid input, for example, at the Name=

prompt in the stat list editor or the Xlist: and Ylist: prompts

in the stat plot editor. If you enter • where it is not

necessary, the TI-83 will ignore the enttT.

11-16 Lists

LIST MATH Menu

LIST MATH Menu To display the LIST MATH menu, press [_ [LIST] E],

NAMES OPS MATH

i: min(

2: max(

3: mean(

4: median(

5: sum(

6: prod(

7:stdDev(

8: variance(

Returns nnninmm element of a list.

Returns nl_ximum element of a list.

Returns mean of a list,

Returns median of a list,

Returns sum of elements in a list.

Returns product of elements in list,

Returns standard deviation of a list,

Returns the variance of a list,

min(, max(

mean(, median(

min((nlininlunl) and max((nlaxinlunl) retul]l the smallest or

largest element of listA. If two lists are compared, it returns

a list of the snmller or larger of each pair of elements in listA

and listB. For a complex list, the element with snmllest or

largest magnitude (modulus) is returned.

min(listA [,listB ])

max(listA[,listB])

mir,({lo2,3},{3,21

,i}> {I 2 I}II

max({l,2,3},

,i}> {3 2{3'23}

Note: min( and max( are the same as min( and max( on the MATH

NUM menu.

mean( returns the mean value of list. median( returns the

median value of list. The default value forfreqlist is 1.

Eachfreqlist element counts the number of consecutive

occurrences of the corresponding element in list. Complex

lists are not valid.

mean(list[ #¢reqlist])

median(list[ dreqlist ])

mean( {1,2,3}, {3,

2, I} >I. 666666667

_'_edian ({i, 2, 3} )2

Lists 11-17

sum(, prod(

Sums and

Products of

Numeric

Sequences

stdDev(,

variance(

sum((sununation) returns the sunl of the elements in list,

start and end are optional; they specify a range of

elements, list elements can be real or complex numbers.

prod( _tma_s the product of all elements of list. start and

end elements are optional; they specify- a range of list

elements, list elements can be real or complex nmnbers.

sum(list[,start,ef_l]) prod(list[,start,ef_l])

L_ {I 2 5 8 10} k_ {I 2 5 8 10}

sur_(L_ ) 26 Prod(L1 )

su_KLI,3,5) 23 Prod(Li,3,5) 400800

You can colnbine sum( or prod( with seq( to obtain:

upper

expression(x)

x=lower

upper

x=lower

To evaluate Z 2 (N 1)fl'Oln N=I to 4:

sur_(se_ (2" (N- I ),

N, 1,4, I)) 15

stdDev( retrains the standard deviation of the element._ in list.

The default value forfreqlist is 1, Eachfreqlist element

counts the number of consecutive occurrences of the

con'esponding element in list. Complex lists m'e not valid.

variance( returns the variance of the elements in list, The

default value forfreqlist is 1, Eachfreqlist element counts

the number of consecutive occmTences of the corresponding

element in list. Complex list.s are not valid.

stdDev(list[freqlist]) vadance(list[freqlist])

stdOev( {i, 2, 5, -6 variance( {i,

,3, -2}) -6,3, -2}) 2,5,

3.937003937 15.5

11-18 Lists

2Statistics

Contents Getting Started: Pendulum Lengihs and Periods ......... 12-2

Setting Up Statistical Analyses ........................... 12-10

Using the Stat List Editor ................................ 12-11

Attaching Fornmlas to List Names ....................... 12-14

Detaching Formulas from List Names .................... 12-1(;

Switching Stat List Editor Contexts ...................... 12-17

Stat List Editor Contexts ................................. 12-18

STAT EDITMenu ........................................ 12-20

Regression Model Features .............................. 12-22

STAT CALC Menu ........................................ 12-24

Statistical Variables ...................................... 12-2(.)

Statistical Analysis in a Program ......................... 12-30

Statistical Plotting ....................................... 12-31

Statistical Plotting in a Program ......................... 12-37

TEXAS INSTRUMENTS TI-83

p Z:LI_RE:VIn D

M M

0 0 0

g=Nl.g Y='.OZ7001

STAT PLOT TBLSET FORMAT CALC TABLE

Statistics 12-1

Getting Started: Pendulum Lengths and Periods

Getting Started is a fast-paced introduction. Read the chapter for details.

A group of students is attempting to determine the lnathelnatical relationship

between the length of a pendulum and its period (one complete swing of a

pendulum). The group makes a simple pendulum froln string and washers and

then suspends it from tile ceiling. They record the pendulum's period for each

of 12 string lengths.*

Length (cm) Time (sec)

6.5 0.51

11.0 0.68

13.2 0.73

15.0 0.79

18.0 0.88

23.1 0.99

24.4 1.01

26.6 1.08

30.5 1.13

34.3 1.26

37.6 1.28

41.5 1.32

1. Press [_DE] [] [] [] [g_gg] to set Func

graphing mode.

2. Press [g_g] 5 to select 5:SetUpEditor.

SetUpEditor is pasted to the honm

screen.

Press [gfff_. This relnoves lists fronl stat

list editor colunms 1through 20, and

then stores lists L1through L6 in

eolunms 1through 6.

Note: Removinglistsfromthe stat list editordoesnot

deletethem frommemory.

3. Press [gf_] 1to select 1:Edit fronl the

STAT EDIT menu. The stat list editor is

displayed. If elements are stored in 1-1

and I_2,press [] to move the cursor onto

1_1,and then press @ [gNT_ [] []

@ [gg7_ to clear both lists. Press []

to move the rectangular cut\sor back to

the first row in 1_1.

SetUeEditof Done[

L1(1)=

*This example is quoted and adapted from Contempo'_mT P'recal(vdns Th'mugh Applications,

by the North Carolina School of Science and Mathematics, by permission of Janson

12-2 Statistics

4. Press6[] 6_ to store the first

pendulum string length (6.5 cm) in 1.1.

The _ctangular cursor nloves to the

next row. Repeat this step to enter each

of the 12 string length values in the table

on page 12-2.

Press [] to inove the rectangular cursor

to the first row in 1.2.

Press [] 61 _ to store the first time

measurement (.51 sec) in 1.2. The

rectangulm" cursor moves to the next

row, Repeat this step to enter each of

the 12 time wdues in the table on

page 12-2.

6. Press [] to display- the Y= editor.

If necessm'y, press @ to clem" the

fm_ction Y1. As necessmy, press [], [E_,

and [] to turn off Plot1, Plot2, and Plot3

from the top line of the Y= editor

(Chapter 3). As necessmy, press [], [_,

and [_ to deselect functions.

Press [_ [STAT PLOT] 1to select 1:Plot1

fi'om the STAT PLOTS menu. The stat

plot editor is displayed for plot 1.

Press _ to select On, which turns on

plot 1. Press [] _ to select ,,'."

(scatter plot). Press [] _ [L1] to

specify- ×list:1.1 for plot 1. Press []

[L2] to specify- Ylist:1.2 for plot 1.

Press [] [] _ to select + _ksthe Mark

for each data point on the scatter plot.

Press _ 9 to select 9:ZoomStat fronl

the ZOOM menu. The window variables

are adjusted automatically, and plot 1 is

displayed. This is a scatter plot of the

time-versus-length data.

LI .Z L_: 1

26,6

37.ti

L1(1_) =

Lt .Z L_: Z

26.6 t.0B

3LI.:_ t.Ztl

3?.tl J..ZB

Plot1 PloLZ Plot:_

\V1 =11

".Yz=

_.y_=

xy_=

"_y_=

xY_;=

\Y?=

_peO Plo_2 P1o_:_

+-,._

liar-k: .[] •

÷ + ÷

+÷+

Statistics 12-3

Sincethescatterplotoftime-versus-lengthdataappearstobeapproxhnately

linear, fit a line to the data.

10. Press _ [] 4 to select 4:LinReg(ax+b) LinReg(ax+b) |

(linear regression nlodel) fronl the STAT

CALC menu, kinReg(ax+b) is pasted to

tile home screen.

11. Press [_ [L1] [] _ [L2] [_. Press

[] 1to display the VARS Y-VARS

FUNCTION secondmT menu, and then

D_ss 1to select 1:Y1. Lt L2, and Y1 are

pasted to the home screen as arguments

to LinReg(ax+b).

12. Press [_ to execute LinReg(ax+b). The

lineal" regression for the data in L1 and L2

is calculated. Values for a and b are

displayed on the home screen. The linear

regression equation is stored in Y1,

Residuals are calculated and stored

automatically in the list name RESID,

which becomes an item on the LIST

NAMES menu,

13. Press _. The regression line and the

scatter plot are displayed.

LinReg

9=_x+b

a=.0230877122

b=.4296826236

12-4 Statistics

Theregressionlineappearstofitthecentralportionofthescatterplotwell.

However,aresidualplotmayprovidemoreinformationaboutthisfit.

14.Press[g_g] 1to select 1:Edit. The stat

list editor is displayed.

Press [] and [] to lnove the cursor onto

L3.

Press [_ [INS]. An unnamed colunm is

displayed in colunm 3; 1.3, k4, L5, and 1_6

shift right one colunm. The Name=

prompt is displayed in the entry line, and

alpha-lock is on.

15. Press [2_ [LIST] to display the LIST

NAMES menu.

If necessatT, press [] to inove the cursor

onto the list name RESID.

16. Press _ to select RESID and paste it

to the stat list editor's Name= pt_mlpt.

E2; 2;1

11 ._8

1_; ,79

18 ,8B

;:3.1 .99

2h.h 1,01

NaMe=_

Lt .2 _

&5 ,B1

11 ,l_B

13.2 .73

1_: .79

1B .EB

.2_:.1 .99

2h.h 1.01

I_.B ,51 ".06911

11 .6B ".0036

13.2 ,73 ".OOhh

1_: .79 .01h

1E .BE .03h?h

?._:.1 .99 .0Z699

2h._ 1.=31 .0lEgit

eCSZD=£-. 0697527...

17. Press IgOr. RESID is stored in colunm 3

of the stat list editor.

Press [] repeatedly to examine the

residuals.

Notice that the first three residuals are negative. They cotTespond to the

shortest pendulum string lengths in L1. The next five residuals are positive, and

three of the last four are negative. The latter correspond to the longer string

lengths in L1. Plotting the residuals will show this pattern more clearly.

Statistics 12-5

18. Press [2_] [STAT PLOT] 2to select 2:Plot2

from the STAT PLOTS menu. The stat

plot editor is displayed for plot 2.

19. Press [_T@] to select On, which turns on

plot 2.

Press [] FEffEENto select _ (scatter plot).

Press [] [2_] [L1] to specify Xlist:L1 ff)r

plot 2. Press [] [R] [E] [S] [I] [D]

(alpha-lock is on) to specify Ylist:RESID

for plot 2. Press [] FEflT_]to select [] as

the mark for each data point on the

scatter plot.

20. Press [] to display the Y= editor.

Press [] to nlove the cursor onto the

= sign, and then press [g_ to deselect

Y1. Press [] [g_ to turn offplot 1.

21. Press _ 9to select 9:ZoomStat fl'oln

the ZOOM menu. The window variables

are adjusted automatically, and plot 2 is

displayed. This is a scatter plot of the

residuals.

Pl*t:[O_ P10t?

_uPe: m k:2 dt_

Xlist:L1

YI ist: RESIO

Mark: [] * .

PI*L1 _Pl*t_

xY1 =. 02308771216

587X+. 4296826135

7287

xYz=

xY?=

xY_=

\Y_=

Eli=

Notice the pattern of the residuals: a group of negative residuals, then a group

of positive residuals, and then another group of negative residuals.

12-6 Statistics

Theresidualpatternindicatesacm5Tatureassociatedwiththisdatasetfor

whichthelinearmodeldidnotaccount.Theresidualplotemphasizesa

downwardcurvature,soamodelthatcm_'esdownwiththedatawouldbe

moreaccurate.Perhapsafunctionsuchassquarerootwouldfit.TFFapower

regression to fit a function of the form y = a * xt'.

22. Press [] to display the Y=editor,

Press @ to clear tile linear regression

equation from Y1,Press [] [ggY_ to turn

on plot 1,Press [] [g_gO to turn off plot

23. Press _ 9to select 9:ZoomStat froin

the ZOOM menu. The window variables

are adjusted automatically, and the

original scatter plot of time-versus-

length data (plot 1) is displayed.

",Yz=

,.Y_=

_.y_=

-,y_=

_.y_=

\y;_=

÷ + ÷

÷÷÷

PuPReg L1,Lz,Yi|

24. Press Fgg_ [] @ [A] to select

A:PwrReg from the STAT CALC menu.

PwrReg is pasted to the home screen.

Press [g_ [L1][] [g_ [L2][]. Press

[] 1to display the VARS Y-VAR$

FUNCTION secondmT menu, and then

press 1to select 1:Y1.1.1, 1_2,and Y1 are

pasted to the home screen as arguments

to PwrReg.

25. Press [g_gm to calculate the power

regression. Values for a and b are

displayed on the home screen. The

power regression equation is stored in

Y1. Residuals are calculated and stored

automatically in the list name RESID,

PwrReg

_=a*x^b

a=.1922828621

b=.5224982852

26. Press _. The regression line and the

scatter plot are displayed.

Statistics 12-7

The new function y=.192x _"- appears t( fit the data well. To get nlore

information, examine a residual plot.

27. Press [] to display the Y= editor.

Press [] _ to deselect Y1.

Press [] [NY_ to turn offplot 1. Press

[] [ggY_ to turn on plot 2.

Note: Step 19 defined plot 2 to plot residuals (RESID)

versus string length (11).

Pl*tl _Pl*t3

".,Y 1----.19228286213

552X% 5224982852

\y_=

\Y_=

28. Press _ 9 to select 9:ZoomStat froln

the ZOOM menu. The window variables

are adjusted automaticMly, and plot 2 is

displayed. This is a scatter plot of the

residuMs.

[]

The new residual plot shows that the residuals are random in sign, with the

residuals increasing in magnitude as the string length increases.

To see the magnitudes of the residuals, continue with these steps.

29. Press _.

Press [] and [] to trace the data.

Observe the values for Y at each point.

With this model, the largest positive

residual is about 0.041 and the smallest

negative residual is about -0.027. All

other residuals are less than 0.02 in

magnitude.

P;':LI_F;E$'r B []

II/:_1.5 Y:'.OZ?OOJ.

12-8 Statistics

Nowthatyouhaveagoodmodelfortherelationshipbetweenlengthand

period,youcanusethemodeltopredicttheperiodforagivenstringlength.

Toprediettheperiodsforapendulumwithstringlengthsof20cmand50cm,

continuewiththesesteps.

30.Press[_ [] 1todisplay-theVARS

Y-VARSFUNCTIONseconda[wmenu,and

thenpress1toselect1:Y1.Y1ispasted

tothehomescreen.

31.Press[] 20 [] to enter a string length of

20 enl,

Press _ to calculate the predicted

time of about 0.92 seconds.

Based on the residual anMysis, we would

expect the prediction of about 0.92

seconds to be within about 0.02 seconds

of the actual value.

_1 II

32. Press _ [ENTRY] to recall the Last EnbTy'.

Press [] [] [] 6to change the string

length to 51) enL

33. Press _ to calculate the predicted

time of about 1.48 seconds.

Since a string length of 50 cnl exceeds

the lengths in the data set, and since

residuals appear to be increasing _

string length increases, we would expect

more etTor with this estimate.

_11(50)(28!9198781364

I. 484736865

Note: You also can make predictions using the table

with the TABLE SETUP settings Indpnt:Ask and

Depend:Auto (Chapter 7).

Statistics 12-9

Setting Up Statistical Analyses

Using Lists to

Store Data

Setting Up a

Statistical

Analysis

Displaying the

Stat List Editor

Data for statistieM analyses is stored in lists, which you

can create and edit using the stat list editor. The TI-83 h_ks

six list vadal_les in lnelnory, L1 through L6, to which you

can store data ff_r statistical calculations. Also, you call

store data to list names that you create (Chapter 11).

To set up a statistical analysis, follow these steps. Read the

chapter for details.

1. Enter the statistical data into one or more lists.

2. Plot the data.

3. Calculate the statistical vm'iables or fit a model to the data

4. Graph the regression equation for the plotted data.

5. Graph the residuals list ff)r the given regression model.

The stat list editor is a table where you can store, edit, and

xqew up to 20 lists that are in nlenlol_yL Also, you Call create

list nalnes fronl the stat list editor.

To display- the stat list editor, press [g_T], and then select

1:Edit fronl the STAT EDIT menu,

CRLC TESTS

SortO(

ClrList

SetUeEditor

L1 L_: ._ 1

mmm

LI(I)=

The top line displays list names. L1 through L6 are stored in

colunms 1through 6 after a lnelnolT reset. The number of

the current colunm is displayed in the top-right corner.

The bottom line is the entry line. All data entry occurs on

this line. The characteristics of this line change according

to the current context (page 12-17).

The center area displays up to seven elements of up to

tht_e lists; it abbreviates wdues when neeessalT. The enttT

line displays the full value of the curt_nt element.

12-10 Statistics

Using the Stat List Editor

Entering a List

Name in the Stat

List Editor

To enter a list name in tile stat list editor, follow these steps.

1. Display the Name= prompt in the entt T line in either of

two ways.

• Move the cursor onto the list name in the colunm

whet_ you want to insert a list, and then press

[_ [iNS]. Nil unnamed colunm is displayed and the

remaining lists shift right one colunm.

• Press [] until the cut\sor is on the top line, and then

press [] until you reach the unnamed colunm.

Note: If list namesare storedto all20 columns,you mustremove

a listnameto makeroomfor an unnamedcolumn.

The Name= prompt is displayed and alpha-lock is on.

LI L:;" 1

qame=_

2. Enter a valid list name in any of four ways.

• Select a name fl'onl file LIST NAMES menu (Chapter 11).

• Enter Cl, C2, Ca, L4, ks, or C6fronl the keyboard.

• Enter an existing user-created list name directly from

the key! Joard.

• Enter a new user-created list name (page 12-12).

I I I

I,Iamo=RBC I

3. Press [ggtgN or [] to store the list name and its

elements, if any-, in the cutTent colunm of the stat list

editor.

Lt k:;" t

To begin entering, scrolling, or editing list elements, press

[]. The rectangular cursor is displayed.

Note: If the list name you entered in step 2 already was stored in

another stat list editor column, then the list and its elements, if any,

move to the current column from the previous column. Remaining list

names shift accordingly.

Statistics 12-11

Creating a Name

in the Stat List

Editor

Removing a List

from the Stat List

Editor

Removing All

Lists and

Restoring L1

through L6

Clearing All

Elements from a

List

To create a name in the stat list editor, ff)llow these steps,

Follow step 1 on page 12-11 to display- the Name=

prompt.

Press [letter from A to Z or 0] to enter the first letter of

the name. The first character cannot be a number.

Enter zero to four letters, O, or numbers to conlplete the

new user-created list name. List names can be one to

five characters long.

Press [g_ or [] to store the list name in the current

colunm of the stat list editor. The list name becomes an

item on the [_[ST NAMES menu (Chapter 11).

To remove a list from the stat list editor, move the cursor

onto the list name and then press [DTn. The list is not deleted

from memory; it is only removed from the stat list editor.

Note: To delete a list name from memory, use the MEMORY

DELETE:List selection screen (Chapter 18).

You can remove all user-created lists from the stat list

editor and restore list names L1 through L6 to colunms 1

through 6 in either of two ways.

• Use SetUpEdRor with no arguments (page 12-21).

• Reset all memotT (Chapter 18).

You can clear all elements from a list in any- of five ways.

• Use ClrList to clear specified lists (page 12-20).

• In the stat list editor, press [] to move the cursor onto a

list name, and then press @ [ggg_.

• In the stat list editor, move the cursor onto each

element, and then press [g_ one by one.

• On the home screen or in the program editor, enter

O->dim(listname) to set the dimension of listname to 0

(Chapter 11).

• Use ClrAIILists to cleat' all lists in memory (Chapter 18).

12-12 Statistics

Editing aList

Element To edit a list element, follow these steps.

1. Move the rectangular cursor onto the element you want

to edit.

2. Press [_ to move the cursor to the entry line.

Note: If you want to replace the current value, you can enter a new

value without first pressing _. When you enter the first

character, the current value is cleared automatically.

3, Edit tile element in tile entity- line,

• Press one or lnore keys to enter the new value. When

you enter the ill,st character, the current value is

cleared automatically.

• Press [] to move the cta'sor to the character before

which you want to insert, D_ess [_ [_NS], and then

enter one or more charactegs,

• Press [] to move the cta'sor to a chm'acter you want to

delete, and then press [ff_] to delete the character.

To cancel any editing and restore the original element at

the rectangular cursor, press @ [_.

ABe Lt L2 t

_co)=25-1000|

Note: You can enter expressions and variables for elements.

4. Press [gNYE_, [], or [] to update the list. If you entered

all expression, it is evaluated. If you entered only a

variable, the stored value is displayed as a list element.

ttl_C L1 L_: 1

:LO

_C(_)=20

When you edit a list element ill the stat list editor, the list is

updated in nlenloFy inunediately.

Statistics 12-13

Attaching Formulas to List Names

Attaching a

Formula to a List

Name in Stat List

Editor

You can attach a fornmla to a list name in the stat list

editor, and then display- and edit the calculated list

elements. VCl_enexecuted, the attached fommla nmst

resolve to a list. Chapter 11 describes in detail the concept

of attaching fornmlas to list names.

To attach a fonnula to a list name that is stored in the stat

list editor, follow these steps.

1. Press [Kf_T]_ to display the stat list editor.

2. Press [] to move the cursor to the top line.

3. Press [] or [_, if necessm% to move the cm_sor onto the

list name to which you want to attach the fornmla.

Note: If a formula in quotation marks is displayed on the entry line,

then a formula is already attached to the list name. To edit the

formula,press_, andthen edit theformula.

4. Press @ [,,], enter the fornmla, and press @ [,,].

Note: If youdo notuse quotationmarks,the T1-83calculatesand

displays thesame initiallist of answers,butdoes notattach the

formula forfuture calculations.

I i:i_¢ "II] L;_ ;;

tO ....

L20__ul_5__.LFIEIC+IO"11

Note: Any user-created list name referenced in a formula must be

preceded by an L symbol (Chapter 11 ).

5. Press IENTERI.The TI-S3 calculates each list element and

stores it to the list name to which the fornmla is

attached. A lock symbol is displayed in the stat list

editor, next to the list name to which the fornmla is

attached.

lock symboI

I=I_C Lt $j L> _:

tO _:0

;;_:O00 _O::!.0

u_1_=15

12-14 Statistics

Using the Stat

List Editor When

Formula-

Generated Lists

Are Displayed

Handling Errors

Resulting from

Attached

Formulas

When you edit an element of a list referenced in an

attached fommla, the TI-83 updates the co_Tesponding

element in the list to which the fornmla is attached

(Chapter 11).

ABC LI $._: 1

I(, _:0

2_:000 _:_:0i0

Z$ ._0

ItI_C LI $ .2 1

2_:000 ;:_:0i0

_c_z_=1e

When a list with a formula attached is displayed in the stat

list editor and you edit or enter elements of another

displayed list, then the TI-83 takes slightly- longer to accept

each edit or ent_3; than when no lists with formulas

attached are in view.

Tip: To speed editing time, scroll horizontally until no lists with

formulas are displayed, or rearrange the stat list editor so that no lists

with formulas are displayed.

On the home screen, you can attach to a list a formula that

t_ferences another list with dimension 0 (Chapter 11).

However, you cannot display the fornmla-generated list in

the star list editor or on the home screen until you enter at

least one element to the list that the formula references.

All elements of a list t_ferenced by an attached fornmla

nmst be valid for the attached fornmla, For example, if

Real number mode is set and the attached formula is

log(l_1), then each element of 1.1 nmst be greater than O,

since the logarithm of a negative number returns a

complex result,

Tip: If an error menu is returned when you attempt to display a

formula-generated list in the stat list editor, you can select 2:Goto,

write down the formula that is attached to the list, and then press

_ to detach (clear) the formula. You then can use the stat

list editor to find the source of the error. After making the appropriate

changes, you can reattach the formula to a list.

If you do not want to clear the formula, you can select 1:Quit, display

the referenced list on the home screen, and find and edit the source of

the error. To edit an element of a list on the home screen, store the

new value to list'name(element#) (Chapter 11).

Statistics 12-15

Detaching Formulas from List Names

Detaching a

Formula from a

List Name

You can detach (clear) a formula fronl a list name in any of

four ways,

• In the stat list editor, nlove the cursor onto the name of

the list to which a fornmla is attached. Press [gflT_

@ [Ni_. All list elements remain, but the fommla

is detached and the lock symbol disappeat\s.

• In the stat list editor, nlove the cursor onto an element

of the list to which a fornmla is attached. Press [gflT_,

edit the element, and then press [ggT_. The element

changes, the fornmla is detached, and the lock symbol

disappears. All other list elements remain.

• Use CIrList (page 12-20). All elements of one or more

specified lists are cleared, each formula is detached, and

each lock symbol disappears. All list names remain.

• Use ClrAIILists (Chapter 18). All elements of 'all lists in

nlenlory are cleared, M1fornml_ts m'e detached from 'all

list names, and all lock symbols disappear. All list

nanles renlain.

Editing an

Element of a

Formula-

Generated List

As described above, one way to detach a fornmla fronl a

list name is to edit an element of the list to which the

formula is attached. The TI-83 protects against

inadvertently detaching the fornmla from the list name by

editing an element of the fornmla-generated list.

Because of the protection feature, you lnust press [gflT_

before you can edit an element of a formula-generated list.

The protection feature does not allow you to delete an

element of a list to which a formula is attached. To delete

an element of a list to which a formula is attached, you

nmst first detach the fornmla in any- of the ways described

above.

12-16 Statistics

Switching Stat List Editor Contexts

Stat List Editor

Contexts

Lt _L_ 1

Z,SE7 2,55?

2_ 30

Z5 35

_c ={5, 10,25000...

LI $L2 i

5 i _5 ......

I_5._ii_5,

_5 i 35

Asc :|5_10,25000...

_5C LI $L&

2_5E?

_ i 3_

_5 i 35

LIc3)=25000010

AI_5 LI $ L2

5 i _,5 ......

2_5E7

25 i 35

LI(3)=|5000010

5 _5

:i._ 20

2,557 2.557

20 3_

25 35

fist _'1 _ L2 2

5 i 15 ......

2.5E7 _.5£?

_ i 30

25 i 35

Li =" LR_C+10"

_5C LI $ L2 2.

5 im ......

:L_ i 20

2.5E7 i 2,557

2_ i 30

25 i 35

LI(I)=15

The stat list editor has four contexts,

• View-elements context • Edit-elements context

• View-nanles context • Enter-name context

The star list editor is first displayed in view-elements

context. To switch through the four contexts, select 1:Edit

from the STAT EDIT menu and follow these steps,

1, Press [] to move the cursor onto a list name. You are

now in view-names context, Press [] and [] to xqew list

names stored in other stat list editor columns,

Press [_, You are now in edit-elements context, You

may edit any element in a list, All elements of the

cmTent list are displayed in braces ( { } )in the enhzy-

line, Press [] and [] to view more list elements.

Press [gNY_ again. You are now in view-elements

context. Press [], [_, [], and [] to view other list

elements. The current element's full value is displayed

in the entt3z line.

Press fNY_ again. You are now in edit-elements

context. You may edit the current element in the entl3z

line,

5, Press [] until the cursor is on a list name, then press

[_ [INs]. You are now in enter-name context,

6, Press @, You are now in view-naines context.

7, Press [], You are now back in _dew-elements context.

Statistics 12-17

Stat List Editor Contexts

View-Elements

Context In view-elements context, the enttT line displays the list

name, the cmTent element's place in that list, and the full

value of the current element, up to 12 chm'acters at a time.

An ellipsis (...) indicates that the element continues beyond

12 characte_\s.

hBC Lt $._ 2

5t5

2._:E7

;'0 _0

tu_)=25000010

To page down the list six elements, press @ []. To

page up six elements, press @ []. To delete a list

element, press [DT0.Remaining elements shift up one row.

To insert a new element, press [g_ [INS]. 0 is the default

value for a new element.

Edit-Elements

Context In edit-elements context, the data displayed in the enttT

line depends on the previous context.

When you switch to edit-elements context from xqew-

elements context, the full value of the cmTent element

is displayed. You can edit the value of this element, and

then press [] and [] to edit other list elements.

R_(: LI $L_:

_0 _0

_g 3E:

_co)=25000

ABe LI $

2g010

2g 25

A_co_=|5000

When you switch to edit-elements context fronl view-

names context, the full vMues of 'allelements in the list

are displayed. An ellipsis indicates that list elements

continue beyond the screen. You can press [] and [] to

edit any element in the list.

L1 $k:;" 1

g1_; -,

t0 Z0

_000 Zg0t0

IA_c:£5, 10, 25000._ _c =I5, 10, 25000...

L1 $.2 1

I0 ZO

Z_:000 7_010

Note: In edit-elements context, you can attach a formula to a list

name only if you switched to it from view-names context.

12-18 Statistics

View-Names

Context

Enter-Name

Context

In view-names context, the entry line displays the list name

and the list elements,

LI € .2 I

515

10 _O

25 _O

25 _5

,Pc =15,10,25000_.

To remove a list from the stat list editor, press [3_],

Remaining lists shift to the left one colunm. The list is not

deleted from memow.

To insert a name in the eutTent colunm, press [_ [_NS],

Remaining eolunms shift to the right one colunm,

In enter-name context, the Name= prompt is displayed in

the entw line, and alpha-lock is on.

At the Name= prompt, you can create a new list name,

Dkste a list nalne fronl L1 to L6 fronl tile keyboard, or paste

an existing list nalne froln the LIST NAMES menu

(Chapter 11). The • s3qnbol is not required at the Name=

prompt.

_BC .1 ') i

r. 1_r

10 _0

_OOO -_SOiO

_O 30

Name=_

To leave enter-name context without entering a list name,

press @. The stat list editor switches to xqew-names

context.

Statistics 12-19

STAT EDIT Menu

SortA(, SortD(

CIrList

To display the STAT EDIT menu, press [_,

EDIT CALC TESTS

i: Edit..,

2: SortA(

3: SortD(

4: ClrList

5: SetUpEditor

Displays the stat list editor.

Sorts a list in ascending order.

Sorts a list in descending order.

Deletes all elements of a list.

Stores lists in the stat list editor.

Note: Chapter 13: Inferential Statistics describes the STAT TESTS

menu items.

SortA( (sort ascending) sorts list elements fl'om low to high

values, SortD( (sort descending) sorts list elements fl'om

high to low values, Complex lists are sorted based on

magnitude (modulus). SortA( and SortD( each can sort in

either of two ways.

With one listname, SortA( and SortD( sort the elements

in listname and update the list in memory.

With two or more lists, SortA( and SortD( sort

keylistname, and then sort each dependlist by placing

its elements in the same order as the corresponding

elements in keylistname, This lets you sort two-variable

data on X and keep the data pairs together, All lists

nmst have the same dimension.

The sorted lists are updated in nlen]ot_yL

SortA(listname)

SortD(listname)

SortA(k¢ylistname,depe_MJistl[,depezwllist2,...,depezMlist n])

SortD(k_ylistname,depe_Mlistl[,depe_wllist2,...,depe_Mlist n])

{5, 4,33 +L _ IL_ I}

{5 4 3}I {3 4 5}

{1,2,3}+L4 I _

,- {i 2 3} {3 2

_ortR (L_, L4 >Done

Note: SortA( and SortD( are the same as SortA( and SortD( on the

LIST OPS menu.

ClrList clears (deletes) from memotT the elements of one

or more listnames. Clrkist also detaches any fornmla

attached to a listname.

ClrList listname l ,listname2,...,listname n

Note: To clear from memory al! elements of all list names, use

OIrAIILists (Chapter 18).

12-20 Statistics

SetUpEditor With SetUpEditor you can set up the stat list editor to

display- one or more listnames in the order that you

specify-. You can specify zero to 20 listnames.

SetUpEditor [listnamel,listname2,...,listname n]

SetUpEditor with one to 20 listnames removes all list

names fron] the stat list editor and then stores listnames in

the stat list editor colunms in the specified order,

beginningincoluinnl.

SetUPEditor RESI

D,L_,L_,TIME,LOH

G,RI23 Done

_E_ID L_ ._ _t

.00692 2 12

".001_ h t_

.OOBh _ I_

",OOIB 6 16

",0106

RESZD<V=-. 0013125_.

TIME Lgn6 _123 h

s6 Is

120 B2 It0

30 ?h I1_

...... _6 I_

98 130

TIHE(!) =_

If you enter a listname that is not stored in lnelnory

already, then listname is created and stored in memory; it

becoines an item on the LIST NAMES menu,

Restoring L1

through L6 to the

Stat List Editor

SetUpEditor with no listnames removes all list names fronl

the stat list editor and restores list names kl through ks in

the stat list editor columns 1through 6.

SetUPEditor Done

Lt L2 ._ t

._1 1

11 ,6B _"

13.2 ,7_

1_; ,79 h

1B .BB 5

2_.1 ,99 6

:*h,h 1,01

L1(I:_=6,5

Lh L5 [L6 $ h

1LI

[i6

Lh(1)=

Statistics 12-21

Regression Model Features

Regression

Model Features

Automatic

Residual List

Automatic

Regression

Equation

STAT CALC menu items 3through Care regression models

(page 12-24). The automatic residual list and automatic

_gression equation features apply to all regression

models, Diagnostics display mode applies to some

regression models.

Vclmn you execute a regression model, the automatic

residual list feature computes and stores the residuals to

the list name RESID. RESID becomes an item on the

LIST NAMES menu (Chapter 11).

OPS MRTH

The TI-83 uses the fommla below to compute RESID list

elements. The next section describes the variable RegEQ.

RESID =Ylistname -RegEQ(Xlistname)

Each regression nlodel has an optional argulnent, regequ, for

which you can specify- a Y= variable such as Y1. Upon

execution, the regression equation is stored automatically to

the specified Y= variable and the Y= function is selected.

2, -5_÷t_l -2

LinReg(ax+b)

Lz,Y_I

Lir_Re9 I nou _ no_

[ ,,,1=

b=I.333333333 B-2X+l. 333333

13333333 I

Regardless of whether you specify- a Y= variable for regequ,

the regression equation always is stored to the TI-83

variable RegEQ, which is item 1on the VARS Statistics EQ

secondmT menu.

XY E L_ TEST PTS

3-'b

Note: For the regression equation, you can use the fixed-decimal

mode setting to control the number of digits stored after the decimal

point (Chapter I ). However, limiting the number of digits to a small

number could affect the accuracy of the fit.

12-22 Statistics

Diagnostics

Display Mode

When you execute sonle t_gression nlodels, the TI-83

computes and stores diagnostics values for r (correlation

coefficient) and r2(coefficient of determination) or for N2

(coefficient of determination).

r and r2 are computed and stored for these regression

models.

LinReg(ax+b) LnReg PwrReg

LinReg(a+bx) ExpReg

R2 is computed and stored for these t_gression models.

QuadReg CubicReg QuartReg

The r and r2that are computed for LnReg, ExpReg, and

PwrReg are based on the linearly transformed data. For

example, for ExpReg (y=ab^x), r and r2 are computed on

In y=ln a+x(ln b).

By- default, these values are not displayed with the results

of a regression model when you execute it. However, you

can set the diagnostics display mode by executing the

DiagnosticOn or DiagnosticOff instruction. Each instruction

is in the CATALOG (Chapter 15).

CATALOG

det(

DiagnostioO_

vDiagnostioOn

diM(

Note: To set DiagnosticOn or DiagnosticOff from the home

screen, press _ [CATALOG], and then select the instruction for the

mode you want. The instruction is pasted to the home screen. Press

to set the mode.

When DiagnosticOn is set, di_nostics m'e displayed with

the results when you execute a regression model.

OiagnostioOnoone LinReg

_=_x+b

L_Reg(a×+b) L,, a=-2

b=1.333333333

ni=.9230769231

n=-.9607689228

When DiagnosticOff is set, di_nostics are not displayed

with the results when you execute a regression model.

Diagno_tioO¢_one LinReg

_=ax+b

L_Reg(ax+b) LI, a=-2

b=1.333333333

Statistics 12-23

STAT CALC Menu

STAT CALC

Frequency of

Occurrence for

Data Points

To display the STAT CALC menu, press [KY_] [_.

EDIT CALC TESTS

1:1 Var Stats

2:2 Var Stats

3:Med Med

4: LinReg(ax+b)

5:QuadReg

6: CubicReg

7: QuartReg

8: LinReg(a+bx)

9: LnReg

O: ExpReg

A: PwrReg

B: Logistic

C: SinReg

Calculates 1-vmiable statistics,

Calculates 2-vmiable statistics.

Calculates a lnedian-lnedian line,

Fits a linear model to data.

Fits a quadratic model to data,

Fits a cubic model to data.

Fits a quartic model to data,

Fits a linear model to data.

Fits a logarithmic model to data,

Fits an exponential model to data,

Fits a power model to data,

Fits a logistic model to data,

Fits a sinusoidal model to data,

For each STAT CALC menu item, if neither Xlistname nor

Ylistname is specified, then the default list names m'e kl

and k2. If you do not specifyfreqlist, then the default is 1

occurrence of each list element.

For most STAT CALC nlenu itenls, you can specify a list of

data occurrences, or frequencies (freqlist).

Each element infreqlist indicates how many times the

corresponding data point or data pair occurs in the data set

you are analyzing.

For example, if 1_1={15,12,9,14} and LFRlaQ={1,4,1,3}, then

the TI-83 interprets the instruction 1-Vat Stats 1.1, LFREO to

mean that 16 occurs once, 12 occurs four times, 9occurs

once, and 14 occurs three times.

Each element infreqlist nmst be _>0, and at least one

element nmst be > 0.

Nonintegerfreqlist elements m'e valid. This is useful when

entering frequencies expressed as percentages or parts

that add up to 1. However, iffreqlist contains noninteger

frequencies, Sx and Sy are undefined; wdues m'e not

displayed for Sx and $y in the statistical results,

12-24 Statistics

1-Var Stats

2-Var Stats

Med-Med

(ax+b)

LinReg

(ax+b)

QuadReg

(axZ+bx+c)

1-Var Stats (one-variable statistics) analyzes data with one

measm'ed variable. Each element infreqlist is the

frequency of occurrence for each corresponding data point

in Xlistname. freqlist elements nmst be real numbers > 0.

1-Var Stats [Xlistnamefreqlist]

_iVaP Stats LI,L

2-Var Stats (two-variable statistics) analyzes paired data.

Xlistname is the independent variable. Ylistname is the

dependent variable. Each element infreqlist is the

frequency of occutTence for each data pair

(Xlistname, Ylistname),

2-Var Stats [Xlistname,_Tistnome_freqlist]

Med-Med (nmdian-n]edian) fits the model equation y=ax+b

to the data using the median-nmdim_ line (resistmlt line)

technique, calculating the sunul]aYy points xl, yl, x2, y2, x3,

and y3. Med-Med displays values for a (slope) and

b (y-intercept).

Med-Med[Xlis_ame,_is_ame_v_ist,regequ]

_ed-Med L_,L_,Yz Med-Med

_=ax+b

a=.875

b=1.541666667 I

LinReg(ax+b) (linear regression) fits the model equation

y=ax+b to the data using a least-squares fit. It displays values

for a(slope) and b(y-intercept); when DiagnosticOn is set, it

also displays values for r2and r,

LinReg(ax+b) [Xlistname,Ylistname_freqlist,regequ]

QuadReg (quadratic regression) fits the second-degree

polynomial y=ax2+bx+c to the data. It displays values for a,

b, and c; when DiagnosticOn is set, it also displays a value

for R2. For three data points, the equation is a polynomial

fit; for four or more, it is a polynomial regression. At least

three data points are required.

QuadReg [Xlistname,Ylistname_freqlist,regequ]

Statistics 12-25

CubicReg

(ax3+bx2+cx+d)

CubicReg (cubic regression) fits the third-degree

polynomial y=ax:_+bx2+ex+d to the data. It displays wdues

for a, b, c, and d; when DiagnosticOn is set, it also displays

a wdue for R2. For four points, the equation is a polynomial

fit; for five or more, it is a polynomial regression. At least

four points are requil_d.

CubicReg [Xlistname,_istnamedCreqlist,regequ ]

Qua_Reg

(ax4+bx3+cx2+

dx+e)

LinReg

(a+bx)

LnReg

(a+b In(x))

ExpReg

(abx)

QuartReg (quartic regression) fits tile fourth-degree

polynomial y=ax4+bx:%cx2+dx+e to the data. It displays

values for a, b, c, d, and e; when DiagnosticOn is set, it also

displays a wdue for R2. For five points, the equation is a

polynomial fit; for six or more, it is a polynomial

regression. At least five points are required.

OuartReg [Xlistname,YlistnamedCreqlist,regequ]

LinReg(a+bx) (linear regression) ills the model equation

y=a+bx to the data using a least-squalls fit. It displays values

for a (y-intercept) and b(slope); when DiagnosticOn is set, it

also displays values for r2and r.

LinReg(a+bx) [Xlistname,_istnamedCreqlist,regequ ]

LnReg (logarithmic regression) fits the model equation

y=a+b ln(x) to the data using a least-squares fit and

transformed values ln(x) and y. It displays values for aand

b; when DiagnosticOn is set, it also displays values for r2

and r.

LnReg [Xlistname,YlistnamedCreqlist,regequ]

ExpReg (exponential regression) fits the model equation

y=ab _ to the data using a least-squares fit and transformed

values x and ln(y). It displays values for aand b; when

DiagnosticOn is set, it also displays values for r2 and r.

ExpReg [Xlistname,YlistnamedCreqlist,regequ]

12-26 Statistics

PwrReg

(axb)

Logistic

c/(l+a*e -bx)

SinReg

a sin(bx+c)+d

PwrReg (power l_gression) fits the model equation y=ax bto

the data using a least-squares fit and transformed values

ln(x) and ln(y). It displays wdues for a and b; when

DiagnosticOn is set, it 'also displays values for r2 and r.

PwrReg [Xlistname,Ylistname_freqlist,regequ]

Logistic fits the model equation y=c/(l+a*e -bx) to tile data

using an iterative least-squares fit. It displays values for a, b,

and c.

Logistic [Xlistname,Ylistname_reqlist,regequ]

SinReg (sinusoidal regression) fits the model equation

y=a sin(bx+e)+d to the data using an iterative least-squares

fit. It displays values for a, b, c, and d. At least fore" data

points m'e required. At least two data points per cycle m'e

required in order to avoid aliased frequency estimates.

SinReg [iterations,Xlistname,I_istname,period,regequ]

iterations is the nlaxinlonl number of times the algorithm

will iterate to find a solution. The value for iterations can

be an integer _>1 and _<16; if not specified, the default is 3.

The algorithm nlay find a solution before iterations is

l_a('hed. Typically, lm'ger values for iterations result in

longer execution times and better accuracy for SinReg, and

vice versa.

Aperiod guess is optional. If you do not specify-period, the

difference between time values in Xlistname must be equal

and the time values nmst be ordered in ascending

sequential order. If you specify-period, the algorithm nlay

find a solution nlore quickly, or it nlay find a solution when

it would not have found one if you had omitted a value for

period. If you specify period, the differences between time

values in Xlistname can be unequal.

Note: The output of SinReg is always in radians, regardless of the

Radian/Degree mode setting.

ASinReg example is shown on tile next page.

Statistics 12-27

SinReg Example:

Daylight Hours in

Alaska for One

Year

Compute the regression model for the number of hours of

daylight in Alaska durin

se_(X, X, 1,361,30

)+LI : {5.5,8, ii, 1

3.5, 16.5, 19, 19.5

,17, 14.5, 12.5,8.

5_6.5,5.5}+Lz

{5.5 8 Ii 13.5

one year.

[liar Notz _lotx

orr

IT_Pe:_I.._ _

-_ li<,listiE1-

6Jlist:Lz

Mark: ° [] .

SinReg LI,Li,VI1

SinReg

_=a*sin(bx+c)+d

a=6.770292445

b=.8162697853

o=-1.215498579

d=12.18138372

With noisy data, you will achieve better convergence

results when you specify- an accurate estimate for period.

You can obtain aperiod guess in either of two ways.

• Plot the data and trace to determine the x-distance

between the beginning and end of one complete period,

or cycle. The illustration above and to the right

graphically depicts a complete period, or cycle.

• Plot the data and trace to determine the x-distance

between the beginning and end of N complete periods,

or cycles. Then divide the total distance by N.

M'ter your fit_t attempt to use SinReg and the default value

for iterations to fit the data, you may find the fit to be

approximately correct, but not optimal. For an optimal fit,

execute SinReg 16,Xlistname,I_istfzame,2_ I b where bis

the value obtained froln the prexqous SinReg execution.

12-28 Statistics

Statistical Variables

The statistical variables are calculated and stored as indicated below, To

access these variables ff)r use in expressions, press _, and select

5:Statistics. Then select the VARS menu shown in the colunm below under

VARS menu. If you edit a list or change the type of analysis, all statistical

vm'iables m'e clem'ed.

Variables 1-Var 2-Var Other VARS

Stats Stats menu

mean of xvalues _ _ XY

SUnl of xvalues Ex Ex E

sunl of X2values Yx2Yx2E

sample standard deviation of xSx Sx XY

population standard deviation of x _x Gx XY

nulnber of data points n n XY

mean of yvalues _ XY

sunl of yvalues 2y 1;

sunl of y2 values 'Fy2 y

sample standard dexqation of y Sy XY

population standard deviation of y_y XY

sunl of X * y Zxy Z

lninimuln of xvalues minX minX XY

lnaxilnuln of xvalues maxX max)( XY

lninimuln of yvalues minY XY

lnaxilnum of yvalues maxY XY

1st quartile Q1 PTS

median Med PTS

3rd quartile Q3 PTS

regression/fit coefficients a, bEQ

polynomial, Logistic, and SinReg a, b, c, EQ

coefficients d, e

correlation coefficient rEQ

coefficient of determination r2, R2 EQ

regression equation RegEQ EQ

sulnl:laI T points (Med-Med only) xl, yl, x2, PTS

y2, x3, y3

Q1 and Q3 The first quartile (Q1) is the median of points between

minX and Meal (median). The third quartile (Q3) is the

median of points between Med and maxX.

Statistics 12-29

Statistical Analysis in a Program

Entering Stat

Data

Statistical

Calculations

You can enter statisticM data, calculate statistical results,

and fit models to data from a program. You can enter

statistical data into lists directly within the program

(Chapter 11),

PROGRRM: STRTS ]

: {1,2,3}÷LI

: {-I, -2, -5}÷Lz

To perform a statistical calculatkm from a program, follow

these steps,

1, On a blank line in the progrmn editor, select the type of

calculation from the $TAT CALC menu.

2, Enter the names of the lists to use in the calculation.

Separate the list names with a conlnla,

3, Enter a conulla and then the name of a Y= variable, if you

want to store the regression equation to a Y= variable.

PROGRRM:STRT5

:{1,2,3}÷LI

:{-I,-2,-5}÷L1

:LinReg(ax+b) LI

12-30 Statistics

Statistical Plotting

Steps for Plotting

Statistical Data in

Lists

(Scatter)

(xyLine)

You call plot statistical data that is stored in lists. The six

types of plots available m'e scatter plot, xyLine, histogram,

modified box plot, regulm" box plot, and normal probability

plot. You can define up to three plots.

To plot statistical data in lists, follow these steps.

1, Store the stat data in one or more lists.

2, Select or deselect ¥= functions as appropriate.

3, Define the stat plot.

4. Turn on the plots you want to display.

5, Define the v_ewing window.

6, Display and explore the graph.

Scatter plots plot the data points fronl Xlist and Ylist as

coordinate pairs, showing each point as a box ( o ), cross

(+), or dot ( • ). Xlist and Ylist nmst be the sanle length.

You can use the same list for Xlist and Ylist,

"t]';i'Off

T'_Pe:_m_,._ k____

Xlist.;_t--

Vli__L:Lz

Mark: [] []

+÷

:+_ .........

xyLine is a scatter plot in which the data points are plotted

and connected in order of appearance in Xlist and Ylist.

You nlay want to use SortA( or SortD( to sort the lists

beffwe you plot them (page 12-20).

_Pe: -L_ _ J_

Y,IisL:LI_

Vlist:Lz

Mark: [] *.

Statistics 12-31

(Histogram)

(ModBoxplot)

Histogram plots one-variable data. The Xscl window variable

value determines the width of each bar, beginning at Xmin.

ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all

values, and 'also adjusts Xscl. The inequality

(Xmax - Xmin) /Xscl _<47 must be true. A value that occurs

on the edge of a bar is counted in the bar to the right.

m 0f'€

Xlist,;"Ct

Fr.e_: I

i ;

Ip_in=_B.4Bt30B

ModBoxplot (modified box plot) plots one-variable data,

like the regular box plot, except points that are 1.5 *

Interquartile Range beyond the quartiles. (The Interquartile

Range is defined _s the difference between the third

quartile Q3 and the first quartile Q1.) These points are

plotted individually beyond the whisker, using the Mark

(5 or + or ,) you select. You can trace these points, which

are called outliers.

The prompt ff)r outlier points is x=, except when the outlier

is the maximunl point (maxX) or the minimunl point

(minX). When outliers exist, the end of each whisker will

display x=. When no outliers exist, minX and maxX are the

prompts for the end of each whisker. O1, Med (median),

and Q3 define the box (page 12-29).

Box plots are plotted with respect to Xmin and Xmax, but

ignore Ymin and Ymax. When two box plots are plotted, the

first one plots at the top of the screen and the second plots

in the middle. When three a_ plotted, the first one plots at

the top, the second in the middle, and the third at the

bottonL

Lt 1 +

2:Plot2...On

,'D,-L2 1 +

3: P 1 ot3...O_f

L1 LZ

4.&P lotsO_

12-32 Statistics

(Boxplot)

(NormProbPIot)

Boxplot (regular box plot) plots one-variable data. The

whiskers on the plot extend fronl tile nlininlunl data point

in the set (minX) to the first quartile (Q1) and from the third

quartile (Q3) to the nlaxinmln point (maxX). The box is

defined by Q1, Med (median), and Q3 (page 12-29).

Box plots are plotted with respect to Xmin and Xmax, but

ignore Ymin and Ymax. When two box plots are plotted, the

first one plots at the top of the screen and the second plots

in the middle. When three ale plotted, the first one plots at

tile top, tile second in tile middle, and the third at the

bottonl.

L,t li q le

2: Plot2...0n

3:Plot3...Of'f"

44,P 1otsOtPt" ,a ....

NormProbPIot (normal probability plot) plots each

observation X in Data List vel\sus the corresponding

quantile zof the standard nonnM distribution, If the plotted

points lie close to a straight line, then the plot indicates

that the data are normal.

Enter a valid list nalne in the Data List field. Select Xor Y

for the Data Axis setting.

• If you select X, tile TI-83 plots tile data on tile x-axis and

the z-values on the y-axis.

• If you select Y, the TI-83 plots the data on the y-axis and

the z-values on the x-axis.

[PandHorp_(35, 2,90

)÷L_ 7 36

Plot1 p1OI:;_

m 0f'f"

T_Pe: -L_ b-_ 31_

_.- a]b I

Data Crst.--: L _

Data Axis:@ Y

Mar'k: =*II

P3:Lh

N=')E.E:1321E ?=.?hEIBB19

Statistics 12-33

Defining the

Plots To define a plot, follow these steps.

1, Press [_ [STAT PLOT]. The STAT PLOTS menu is

displayed with the current plot definitions,

2, Select the plot you want to use, The stat plot editor is

displayed for the plot you selected,

3, Press _ to select On if you want to plot the

statistical data imnlediately. The definition is stored

whether you select On or Off,

4, Select the type of plot. Each type prompts for the

options checked in this table.

Plot Type XList YList Mark Freq Data Data

List Axis

_L_ Scatter _ _i _ rl [] []

xyLine _ 121 _ [] [] []

Zn_ Histogram _ [] [] _ [] []

o,. ModBoxplot _ [] _ _ [] []

_:_> Boxplot _ [] [] _ [] []

[__ NormProbPIot [] [] _ [] _ lTI

Enter list names or select options for the plot type,

• Xlist (list name containing independent data)

• Ylist (list name containing dependent data)

•Mark (aor +or.)

• Freq (frequency list for Xlist elements; default is 1")

•Data List (list nanle for NormProbPIot)

•Data Axis (axis on which to plot Data List)

12-34 Statistics

Displaying Other

Stat Plot Editors Each stat plot has a unique stat plot editor. The name of

the current stat plot (Plot1, Plot2, or Plot3) is highlighted in

the top line of the stat plot editor. To display the stat plot

editor for a different plot, press [], [], and [] to lnove the

cursor onto the name in the top line, and then press [_.

The stat plot editor for the selected plot is displayed, and

the selected name remains highlighted.

_" _ L_

Xlist:L1

Vlist:Lz

Mark: [] *

Turning On and

Turning Off Stat

Plots

PlotsOn and PlotsOff allow you to turn on or turn off stat

plots from the home screen or a program. With no plot

number, PlotsOn turns on M1plots and PlotsOff turns off 'all

plots. With one or more plot numbers (1, 2, and 3), PlotsOn

turns on specified plots, and PlotsOff turns off specified

plots.

PlotsOff [1,2,3]

PlotsOn [1,2,3]

PlotsOf'f"

Note: You also can turn on and turn off stat plots in the top line of the

Y= editor (Chapter 3).

Statistics 12-35

Defining the

Viewing Window

Tracing a Stat

Plot

Stat plots are displayed on the current graph. To define the

xqewing window, press _ and enter values for the

window variables. ZoomStat redefines the xqewing window

to display all statistical data points.

When you trace a scatter plot or xyLine, tracing begins at

the first element in the lists.

VClmnyou trace a histogram, the cursor nloves fronl the

top center of one colunm to tile top center of tile next,

starting at the first colunm.

When you trace a box plot, tracing begins at Med (the

median). Press [] to trace to Ol and minX. Press [] to trace

to O3 and maxX.

When you press [] or [] to move to another plot or to

another Y= function, tracing moves to the current or

beginning point on that plot (not the nearest pixel).

The ExprOn/ExprOff format setting applies to stat plots

(Chapter 3).When ExprOn is selected, the plot number and

plotted data lists are displayed in the top-left corner.

12-36 Statistics

Statistical Plotting in a Program

Defining a Stat

Plot in aProgram

To display a stat plot fronl a program, define the plot, and

then display the graph.

To define a star plot from a program, begin on a blank line

in the program editor and enter data into one or more lists;

then, follow these steps.

1. Press [g_ [STATPLOT]to displw tile STAT PLOTS menu.

T"tPE MARK

i3:Plot3(

i4.PlotsOgg

5:Plot.sOn

Select the plot to define, which pastes Plot1(, Plot2(, or

Plot3( to the cursor location.

PROGRAM:PLOT

:{I,2,3,4}+LI

:{5,6,7,8}+Lz

:Plot2(I

Press[_[STATPLOT][_todisplaytheSTATTYPE

nlenu,

PLOTS _ MARK

._Soatter

z: x_Line

5:Bo>,'gIot

S:HorMProbPlot

Select the type of plot, which pastes the name of the

plot type to the cm'sor location.

PROGRAM:PLOT

:{1,2,3,4}+LI

:{5,6,7,8}+Lz

:Plot2(SoatterI

Statistics 12-37

Displaying a Stat

Plot from a

Program

Press []. Enter the list names, separated by eonunas.

Press [] [_ [STAT PLOT] [] to display the

STAT PLOT MARK menu. (This step is not necessaqy- if

you selected 3:Histogram or 6:Boxplot in step 4.)

Select the type of nlark (D or + or °) for each data point.

The selected mm'k symbol is pasted to the cursor

location.

Press [] _ to complete the command line,

PROGRAM: PLOT L

: {I02,3,4}÷LI

: {5, 6, 7,8}÷Lz

:Plot2(Soattet-,

To display- a plot from a program, use the DispGraph

instruction (Chapter 16) or any of the ZOOM instructions

(Chapter 3),

PROGRR_I: PLOT

: {1,2,3,4}÷LI

:,.5,6, _, 8}+Lz

: Plot2(ScatteP, L

I,Lz,=)

::DisParaF-h

PROGRRM:PLOT

:{1,2,3,4}÷Lt

:_506,7,8}÷Lz

:Plot2(ScatteP,L

I,Lz,.)

::_°°MStat

12-38 Statistics

3InferentialStatisticsand Distributions

Contents Getting Started: Mean Height of a Population ............ 13-2

Inferential Star Editors ................................... 13-6

STAT TESTS Menu ...................................... 13-9

Inferential Statistics Input I)eseriptions .................. 13-26

Test and Interval Output Variables ....................... 13-28

Distribution Functions ................................... 13-29

Distribution Shading ..................................... 13-35

'_ TEXAS iNSTRUMENTS T1=83

z=.ee:l. I_=._?e:_

STATPLOT TBLSET FORMAT CALC TABLE

Inferential Statistics and Distributions 13-1

Getting Started: Mean Height of a Population

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to estimate the mean height of a population of women given

tile random sample below. Because heights among a biological population tend

to be normally distributed, a tdistribution confidence interval can be used

when estimating the mean. The l0 height wdues below are the first l0 of 90

wdues, randonfly generated from a normally distributed population with an

assumed mean of 165.1 cm. and a standard dexqation of 6.35 cm.

(randNorm(165.1,6.36,90) with a seed of 789).

Height (in cm.) of Each of 10 Women

169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.64 167.15 159.53

Press [gTKg][gNT_ to display the stat list

editor.

Press [] to nlove the cursor onto L1, and

then press [_] [,NS]. The Name= prompt is

displayed on the bottom line. The [] cursor

indicates that alpha-lock is on. The

existing list name eolunms shift to the

right.

Note: Your stat editor may not look like the one

pictured here, depending on the lists you have

already stored.

Enter [H] [G] [H] [T] at the Name= prompt,

and then press [gNT_. The list to which

you will store the women's height data is

created.

Press [] to move the cursor onto the first

row of the list. HGHT(1)=is displayed on the

bottom line.

Press 169 [] 43 to enter the first height

value. As you enter it, it is displayed on the

bottom line.

Press [gNT_. The value is displayed in the

first row, and the rectangular cursor

nloves to the next row.

Enter the other nine height values the

sanle way,

1.I L_ I

HaMe==

HGHT .1 L;' 1

mmm

H6HT(1) =

HGHT .1 L_ 3

1_9.7B

171.17

16Y.tg

H6HT(11)=

13-2 hfferential Statistics and Distributions

4. Press [gY_ [] to display the STAT TESTS

menu, and then press [] until 8:Tlnterval is

highlighted.

5. Press _ to select 8:Tlnterval. The

inferential stat editor for Tlnterval is

displayed. If Data is not selected for Inpt:,

press [] [ggY_ to select Data.

Press [] and [H] [G] [a] [T] at the List:

prompt (alpha-lock is on).

Press [] [] [] g@to enter a 99 percent

confidence level at the C-Level: prompt.

6. Press [] to move the cursor onto Calculate,

and then press IgOr. The confidence

intet¢TM is calculated, and the Tlnterval

results are displayed on the home screen.

Interpret the results.

EDIT CRLCIII_

2ST-Test,,

3:2-SamPZTest

4:2-Sar4eTTest_

7:ZIntervM,.,"-

[_tlTInterval...

TlntervM

InPt:_ Stats

List:HGHT

Fre_:1

C-Level:.99

Calculate

Tlnterval

(159.74,173.94)

R=166.838

Sx=6.907879237

n=lO

The first line, (159.74,173.94), shows that the 99 percent confidence inte_xal for

the population mean is between about 159.74 cm. and 173.94 cm. This is about

a 14.2 cm. spread.

The .99 confidence level indicates that in a vet3z lm'ge number of samples, we

expect 99 percent of the intervals calculated to contain the population mean.

The actual mean of the population sampled is 165.1 cm. (introduction; page

13-2), which is in the calculated interval.

The second line gives the mean height of the sample N used to compute this

intet_'al. The third line gives the sample standard deviation Sx. The bottom line

gives the sample size n.

Inferential Statistics and Distributions 13-3

To obtain a more precise bound on the population mean _tof women's heights,

increase the sample size to 96. Use a sample mean ._ of 163.8 and sample

standard deviation Sx of 7.1 calculated from the larger random sample

(introduction; page 13-2). This time, use the Stats (sunullal_y statistics) input

option.

Press [g_g] [] 8to display" the inferential

star editor for Tlnterval.

Press [] [g_N to select Inpt:Stats. The

editor changes so that you can enter

sunullal_ statistics as input.

TInterual

InPt:Data I¢_

5:166.838

Sx:G.90787923Z_

n:10

C-Leuel:.99

Calculate

TInterual

InPt:Data _

R:IG3.8

Sx:7.1

n:90

C-Leuel:.99

Calculate

8. Press [] 163 [] 8 [N?_ to store 163.8 to _.

Press 7[] 1[ggY_ to store 7.1 to Sx.

Press 90 [NTgN to store 96 to n.

Press [] to move the cursor onto Calculate,

and then press [g_N to calculate the new

99 percent confidence interval. The results

are displayed on the home screen.

TInterual

(161.83,165.77)

R=163.8

Sx=7.1

n=90

If the height distribution among a population of women is normally distributed

with a nlean [J of 165.1 cm. and a standard deviation _ of 6.35 cm., what height

is exceeded by only 5 percent of the women (the 95th percentile)?

10. Press @ to clear the home screen.

Press [2_] [DISTR] to display the DISTR

(distributions) menu.

DRAW

normalcd?(

3:invNorm(

4:tPd?(

5:tod¢(

6:XZpd?(

74XZod¢(

13-4 hfferential Statistics and Distributions

11.Press3to paste invNorm( to the home invHorr_(. 95,165.

screen. 1_6.35)

Press_ 95_ lS5_ 1_ 6_ 35_ I175.5448285

.95 is the area, 1G5.1 is p, and 6.35 is o.

The result is displayed on the home screen; it shows that five percent of the

women are taller than 175.5 cm.

Now graph and shade the top 5 percent of the population.

Xres=l

12. Press [_ and set the window

variables to these values.

Xmin=145 Ymin=-.02

Xmax=185 Ymax=.08

Xscl=5 Yscl=0

gINDOg

XMin=145

Xmax=185

Xsol=5

YMin=-.82

YMax=.88

Yscl=O

XPes=1

13. Press [_ [DISTR] [] to display the DISTR

DRAW menu. STR Llli'_l_

ShadeNoPm (

3: ShadeX z (

4: ShadeF (

invHor.M(. 95,165.

1,6.35)

175. 5448285

ShadeNoPFKRns, 1E

99, 165. 1,6.35)I

firca=.OB

low='l 7_:._:LI_: up,=:LEBB

14. Press _ to paste ShadeNorm( to the

home screen.

Press [_ [ANS] [] 1 _ [EEl 99_ 165[_ 1

D6[]asD.

Ans (175.5448205 from step 11) is the

lower bound. 1E99 is the upper bound. The

normal curve is defined by a mean p of

165.1 and a standm'd deviation o of 6.35.

15. Press [gfff_ to plot and shade the normal

eui%re.

Area is the area above the 95th percentile.

low is the lower bound, up is the upper

bound.

Inferential Statistics and Distributions 13-5

Inferential Stat Editors

Displaying the

Inferential Stat

Editors

When you select a hypothesis test or confidence intetsTal

instruction from the home screen, the appropriate

inferential statistics editor is displayed. The editors yaw

according to each test or interval's input requirements.

Below is the inferential stat editor for T-Test.

T-Test

InPt:_ Stats

List:L1

Fne_:l

_:_ <_ >_n

Calculate Orau

Using an

Inferential Stat

Editor

Note: When you select the ANOVA( instruction, it is pasted to the

home screen. ANOVA( does not have an editor screen.

To use an inferential stat editor, follow these steps.

1. Select a hypothesis test (Jr confidence intet_'al from the

STAT TESTS menu. The appropriate editor is displayed.

2. Select Data or Stats input, if the selection is available.

The appropriate editor is displayed.

3. Enter real numbers, list names, (Jr expressions for each

argument in the editor.

4. Select the alternative hypothesis (€, <, or >) against

which to test, if the selection is available.

5. Select No or Yes for the Pooled option, if the selection is

available.

6. Select Calculate (Jr Draw (when Draw is available) to

execute the instruction.

• When you select Calculate, the results are displayed

on the honle screen.

• When you select Draw, the t_sults are displayed in a

graph.

This chapter describes the selections in the above steps for

each hypothesis test and confidence intetwal instruction.

13-6 hfferential Statistics and Distributions

Select Data or

Stats input

Enter values for

arguments

Selecting Data or

Stats

Entering the

Values for

Arguments

Selecting an

Alternative

Hypothesis

(_ < >)

Stats

Calculate Omau

Sete_ an alternative

hypothesis

Select Calculate

or Draw output

Most inferential stat editors prompt you to select one of

two types of input. (1-PropZlnt and 2-PropZTest, 1-PropZlnt

and 2-PropZlnt, x2-Test, and LinRegTTest do not,)

• Select Data to enter the data lists _s input.

• Select Stats to enter sunmm_ statistics, such as 2, Sx,

and n, as input.

To select Data or Stats, move the cursor to either Data or

Stats, and then press [ggY_.

Inferential stat editors require a value for ever7 argument.

If you do not know what a pm'ticulm" argument symbol

represents, see the tables on pages 13-26 and 13-27.

When you enter values in any inferential stat editor, the

TI-83 stores them in nlenlory so that you can run many

tests or intetnT'als without having to reenter evet3z vMue.

Most of the inferential stat editors for the hypothesis tests

prompt you to select one of three alternative hypotheses.

• The first is a _ Mternative hypothesis, such as p¢p0 for

the Z-Test.

• The second is a <alternative hypothesis, such as pl<_t2

for tile 2-SampTTest.

• The third is a >alternative hypothesis, such as pl>p2 for

the 2-PropZTest.

To select an alternative hypothesis, nlove the cursor to the

appropriate alternative, and then press [ggY_.

Inferential Statistics and Distributions 13-7

Selecting the

Pooled Option

Selecting

Calculate or Draw

for a Hypothesis

Test

Selecting

Calculate for a

Confidence

Interval

Bypassing the

Inferential Stat

Editors

Pooled (2-SampTTest and 2-SampTInt only) specifies

whether the vmiances m'e to be pooled for the calculation,

• Select No if you do not want the vmiances pooled.

Population vm'iances can be unequal.

• Select Yes if you want the wu'iances pooled. Population

wu'iances m'e assumed to be equal.

To select the Pooled option, move the cursor to Yes, and

then press [_T_].

Alter you have entered all arguments in an inferential star

editor for a hypothesis test, you nmst select whether you

want to see the calculated results on the home screen

(Calculate) or on the graph screen (Draw).

• Calculate c_dculates the test results and displays the

outputs on the home screen.

• Draw draws a graph of the test results and displays the

test statistic and p-value with the graph. The window

variables m'e adjusted automatically to fit the graph.

To select Calculate or Draw, nlove the cursor to either

Calculate or Draw, and then press IgOr. The instruction is

inunediately executed.

Alter you have entered all arguments in an inferential star

editor for a confidence inte_'al, select Calculate to display

the results. The Draw option is not available.

When you press [g_EN, Calculate calculates the confidence

inte_w'M results and displays the outputs on the home

screen.

To paste a 1wpothesis test or confidence inte_-'al

instruction to the home screen without displaying the

corresponding inferential stat editor, select the instruction

you want from the CATALOG menu. Appendix A describes

the input syntm, c for each hypothesis test and confidence

inte_nTal instruction.

12-Sar,_PZTest(I

Note:You can pastea hypothesistestorconfidenceinterval

instruction to a command line in a program. From within the program

editor, select the instruction from either the CATALOG (Chapter I5)

or the STAT TESTS menu.

13-8 hfferential Statistics and Distributions

STAT TESTS Menu

STAT TESTS

Inferential Stat

Editors for the

STAT TESTS

Instructions

To display the STAT TESTS menu, press [gT_] [_. When you

select an inferential statistics instruction, the appropriate

inferential stat editor is displayed.

Most STAT TESTS instructions store some output varial_les

to memory. Most of these output variables are in the TEST

secondmT menu (VARS menu; 5:Statistics). For a list of

these varial)les, see page 13-28.

EDIT CALC TESTS

1:Z Test,..

2:T Test,.,

3:2 SampZTest...

4:2 SampTTest,..

5:1 PropZTest...

6:2 PropZTest,..

7:Zlnterval,.,

8:Tlnterval,.,

9:2 SampZlnt.,.

0:2 SampTlnt.,.

A:I PropZlnt.,.

B:2 PropZlnt.,.

C:X2 Test,,.

D:2 SampFTest...

E: LinRegTTest,..

F: ANOVA(

Test for 1 p, known

Test for i p, unknown

Test compming 2 #'s, known _'s

Test compming 2 #'s, unknown _'s

Test for 1 proportion

Test compming 2proportions

Confidence intmwal for 1 #, known

Confidence intmwal for 1 #, unknown

Conf. int. for diff. of 2 p's, known o's

Conf. int. for diff. of 2 #'s, unknown o's

Confidence int. for 1 proportion

Confidence int. for diff. of 2 props

Chi-squm'e test for 2-way tables

Test compming 2 o's

ttest for regression slope and p

One-way analysis of variance

Note: When a new test or interval is computed, all previous output

variables are invalidated.

In this chapter, the description of each STAT TESTS

instruction shows the unique inferential stat editor for that

instruction with example arguments.

• Descriptions of instructions that offer the Data/Stats

input choice show both types of input screens.

• Descriptions of instructions that do not ofl_r the

Data/Stats input choice show only one input screen.

The description then shows the unique output screen for

that instruction with the example results.

• Descriptions of instructions that offer the

Calculate/Draw output choice show both types of

screens: calculated and graphic results.

• Descriptions of instructions that offer only the Calculate

output choice show the calculated results on the home

screen.

Inferential Statistics and Distributions 13-9

Z-Test

Input:

Calculated results:

Z-Test (one-sample ztest; item 1) performs a hypothesis

test for a single unknown population mean _ when the

population standard deviation cris known. It tests the null

hypothesis H0: g= P0 against one of the alternatives below.

• H_,:_!¢P0 (vt:_to)

• H_,:_<_00a:<_to)

• H_,:_>_0 (_t:>_to)

In tile example:

L1={299,4 297.7 301 298.9 300.2 297}

Data

Z-Test

Inet:_ Stats

0.:3

List:L1

Fre_:l

_:#_ _ >_o

Calculate Draw

Z-Test

v.<300. 0000

z= -. 7893

P=. 2150

_=299. 0333

mx= 1. 5029

ir,=6. 0000

:=-.7B9_ _=._I_

Stats

Z-Test

InPt:Oata

v.n : 300

0:3

_: 299. 0333

n:6

v.:#v.n_ >_n

Calculate Draw

Z-Test

u<300.0000

z=-.7893

e=.2150

R=299.0333

I n=6.0000

Drawn results:

Note: All examples on pages13-10 through t3-25 assume a fixed-

decimal mode setting of 4 (Chapter 1). If you set the decimal mode to

Float or a different fixed-decimal setting, your output may differ from

the output in the examples.

13-10 Inferential Statistics and Distributions

T-Test

Input:

Calculated results:

T-Test (one-sample ttest; item 2) performs a hypothesis

test for a single unknown population mean p when the

population standard deviation _ is unknown. It tests the

null hypothesis H0:P=P0 against one of the alternatives

below.

•H_,:PCPo (p:¢po)

• H_,:P<Po (p:<po)

• H_,:P>Po (,u:>_.to)

In the example:

TEST={91.9 97.8 111.4 122.3 105.4 95}

Data

T-Test

InPt:_ Stats

_n:105

List:TEST

FPe_:l

_:_ <_n >_n

Calculate DPau

T-Test

,,lo5.00oo

t=-.,_20_

P=. 8340

2= 100 •9667

Sx= 1 I. 4669

in=6. 0000

t= -,i:_:07 _=,g3h

Stats

T-Test

InPt:Oata

p0:105

7,:103. 9667

Sx: 11.4669

n:6

Calculate OPau

T-Test

_#105.0000

t=-.2207

P=.8340

R=103.9667

Sx=II.4669

in=6.0000

Drawn results:

Inferential Statistics and Distributions 13-11

2-SampZTest

Input:

Calculated results:

Drawn resutts:

2-SampZTest (two-sample ztest; item 3) tests the equality

of the means of two populations (Pl and #2) based on

independent samples when both population standard

deviations (_1 and a_,) are known. The null hypothesis

H0:#1=p2 is tested against one of the alternatives below.

• H_,: _[l<_t2 (pl:<p2)

• H_,: #1>P2 (pl:>p2)

In the example:

LISTA={154 109 137 116 140}

LISTB={108 115 126 92 146}

Data

2-SamPZTest

InPt =I_ Stats

¢I: 15.5

¢2:13.5

ListI:LISTR

List2:LISTB

FPe_l:l

_Fre_2:l

_I:#_2 <_2 _

Calculate Drau

2-SaMmZTest

P:. 695

_1=131.0000

2z=I17.4000

1_Sx,=18.6145

S×z=20.1941

ni=5.0000

inz=5.0000

z=l.h795 _=.Ofigg

Stats

2-SaMPZTest

InPt:Data

¢I: 15.5

¢2:13.5

RI: 131

hi:5

R2:117.4

_n2:5

=-LI:#p.2 <p.2 I_

Calculate Dr-a,,J

2-SaMPZTest

z= I. 4795

P=. 0695

RI=131. 0000

Rz=117.4000

l.n i =5. 0000

r,z=5.0000

13-12 Inferential Statistics and Distributions

2-SampTTest

Input:

Calculated results:

2-SampTTest (two-sample ttest; item 4) tests the equality

of the lneans of two populations (_l 1 and g2) based on

independent samples when neither population standard

deviation ((_1or (_2)is known, The null hypothesis

n0:_11=_12 is tested against one of the alternatives below.

• H_,:_11<_l2(_1:<_2)

• H_,:_11>_12(_1:>_2)

In the example:

8AMPl={12.207 16.869 25,05 22,429 8,456 10,589}

SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}

Data

2-SamPTTest

InPt:liI_11_Stats

ListI:SRMPI

List2:SRMP2

Fre_l:l

Fre_2:l

SPooled:l_ 9es

I Calc.ulate Draw I

Stats

2-SaMPTTesL

Inet: Data !i_rul_lEl

1 : 15. 9333

SxI :6. 7014

nl:6

_2:9.4998

Sx2: I. 9501

i.n2:6

_LI:_ <_2 >_2

PooI_:[_ Yes

Calculate Draw

2-SamPTTest

t=2.2579

P=.0659

d_=5.8408

RI=15.9333

$_z=9.4998

m =6. 00e

I r,z=6. 0000

2-SamPTTest

t=2.2579

P=.0659

d€=5.8408

RI=15.9333

_2z=9.4998

I SXI=6"7014

Sxz=1.9501

ni=6.0000

nz=6.0000

Drawn resutts:

Inferential Statistics and Distributions 13-13

1-PropZTest

Input:

Calculated results:

1-PropZTest (one-proportion ztest; item B) computes a test

for an unknown proportion of successes (prop). It takes as

input the count of successes in the sample xand the count

of observations in the sample n. 1-PropZTest tests the null

hypothesis H0:prop=p0 against one of the alternatives

below.

• H_,:prop€p0 (prop:¢p0)

• H_,:prop<p0 (prop:<po)

• H_,:prop>p0 (prop:>po)

1-ProPZTest I

pill .5 I

x: 2848 I

n: 4848 I

eroI=Ei1"_,'1<ell >Pal

Caloulate Draw

l-ProeZTest

ProP#. 5000

z=. 8810

P=. o783

_=. 5069

in=4e4e. 0088

Drawn results:

13-14 Inferential Statistics and Distributions

2-PropZTest

Input:

2-PropZTest (two-proportion ztest; item 6) computes a test

to compare the proportion of successes (Pl and P2) fronl

two populations. It takes _ksinput the count of successes in

each sample (x 1and x2) and the count of observations in

each sample (nl and n2). 2-PropZTest tests the null

hypothesis H0:pl=p2 (using the pooled sample proportion

_) against one of the alternatives below.

• H_,:pl;eP2 (pl:_p2)

• H_,:pl<P2 (pl:<p2)

• H_,:pl>P2 (pl:>p2)

2-PPoeZTest

xi:45

hi:61

x2:38

n2:62

el:I <e2 >e2

Calculate Draw

Calculated results:

B-

2-ProeZTest

e1#ez

z=1.4773

P=.1396

@i=.7377

@z=.6129

4#=.6748

nI=61.0000

nl=62.0000

-I

Drawn results:

Inferential Statistics and Distributions 13-15

Zlnterval

Input:

Zlnterval (one-sample zconfidence intetsTal; item 7)

computes a confidence interval for an unknown population

mean p when the population standard deflation cris

known. The computed confidence intet_-'al depends on the

user-specified confidence level,

In the example:

L1={299.4 297.7 301 298.9 300.2 297}

Data

ZInterval

In_t:l_ellI_Stats

List:L1

Fre_:l

C-Level:.9

Calculate

Stats

ZInterval

Inet:Data

_:3

R: 299. 0333

n:6

C-Legel :. 9

Calculate

Calculated results:

-B-

ZInterval

(297.02,301.85)

R=299.0333

Sx=1.5029

|n=6.0000

Zlnterval

(297.02,301.05)

13-16 Inferential Statistics and Distributions

Tlnterval

Input:

Tlnterval (one-sample tconfidence inte_nTal; item 8)

computes a confidence interval for an unknown population

mean p when the population standard deviation _ is

unknown. The computed confidence inte_wTal depends on

the user-specified confidence level.

In the example:

L6={1.6 1.7 1.8 1.9}

Data

Tlnterval

InPt:llL_u1_Stats

List:L_

Fre_:l

C-Level:.95

Calculate

Stats

TInterva I

InF.t:Data

_: 1.75

Sx:. 1291

n:4

C-Level: .95

Caloulate

Calculated results:

-B-

TInterval

(1.5446,1.9554)

R=1.7500

Sx=.1291

|n=4.0000

TInterval

(1.5446, i.9554)

R=1.7500

Sx=.1291

|n=4.0000

Inferential Statistics and Distributions 13-17

2-SampZlnt

Input:

Calculated results:

2-SampZInt (two-sample z confidence inte_wTal;item 9)

c()mputes a confidence inte[wTal for the difference between

two population means ({11-_12) when both population

standard deviations (or1and a_) are known. The computed

confidence inte_'al depends on the user-specified

confidence level.

In the example:

LISTC={154 109 137 116 140}

LISTD={108 115 126 92 146}

Data

2-SamPZlnt

InPt:[._Z Stats

_i:15.5

_2:13.5

ListI:LISTC

List2:LISTD

Fre_l:l

SFre_2:l

C-Level:.99

Calculate

2-SamPZInt

(-10.08,37.278)

21=131.0000

2z=117.4000

Sxi=18.6145

Sxz=20.1941

$ni=5.0000

n2=5.0000

Stats

2-SamPZ Int

InPt:Data

_I: 15.5

¢2:13.5

21:131

ni:5

22:117.4

_n2:5

C-Level:.99

Calculate

2-SamPZlnt

(-10.08,37.278)

21=131.0000

2_=117.4000

m=5.0000

inz=5.0000

13-18 Inferential Statistics and Distributions

2-SampTInt

Input:

Calculated results:

2-SampTInt (two-sample tconfidence inte[wTal; item O)

c()mputes a confidence inte[wTal for the difference between

two population means (Pl-P2) when both population

standard deviations (a 1 and _) are unknown. The

computed confidence interval depends on the user-

specified confidence level.

In the example:

SAMP1={12.207 16.869 25.05 22,429 8.456 10.589}

SAMP2={11.074 9.686 12.064 9.351 8,182 6.642}

Data

2-SamPTlnt

InPt:_ Stats

ListI:SRMPI

List2:SRMP2

Fne_l:1

Fne_2:l

C-Level:.95

$Pooled:l:_ Yes

Calculate

2-SamPTlnt

(%5848,13.452)

d¢=5.8408

Ri=15.9333

Rz=9.4998

SxI=6.7014

$Sxz=1.9501

ni=6.8000

nz=6.0000

Stats

2-SaP/PT I r=t

Sxl :6. 7014

nl:6

R2:9.4998

Sx2:1.9581

_n2:6

C-Level :. 95

Pooled:l:_ Yes

Calculate

2-SamPT Int

( -.5849, 13. 452)

df=5.8408

_i =15. 9333

R1=9.4998

SxI=6. 7014

_Sx1=1.9501

ni=6.0000

nz=6.0000

Inferential Statistics and Distributions 13-19

1-PropZlnt 1-PropZInt (one-proportion zconfidence inte_'al; item A)

computes a confidence interval for an unknown proportion

of successes. It takes as input the count of successes in the

sample xand the count of obse_'ations in the sample n.

The computed confidence intetnTal depends on the user-

specified confidence level.

1-PPoeZlnt

x: 2848

n: 4848

C-Leve I :.99

input: Caicuiate

Calculated results:

-B-

l-ProeZlnt

(.4867,.5272)

A=.5069

|n=4040.0000

13-20 Inferential Statistics and Distributions

2-PropZlnt 2-PropZInt (two-proportion zconfidence inte_'al; item B)

computes a confidence intet_'al for the difference between

the proportion of successes in two populations (Pl-P2)- It

takes a_ninput the count of successes in each sample

(Xl and x2) and the count of observations in eaeh sample

(n 1 and n2), The computed confidence intetnTal depends on

the user-specified confidence level.

2-Pt-oPZ Int

xi:49

nl:61

x2:38

Input: n2: 62

C-Leve I :.95

Calculate

Calculated results:

-I

2-PPoeZInt

(.0334,.3474)

#I=.8033

#z=.6129

ni=61.0000

|nz=62.0000

Inferential Statistics and Distributions 13-21

z2-Test

Matrix editor:

Input:

z2-Test (chi-squm'e test; item C) computes a chi-squm'e test

for association on the two-way table of counts in the

specified Observed lnatrix. The null hypothesis H 0 for a

two-way table is: no association exists between row

variables and colunm variables. The Mternative hypothesis

is: the vm'iables are related.

Before computing a zZ-Test, enter the obsetnTed counts in a

matrix. Enter that matrix variable name at the Observed:

prompt in the z2-Test editor; default=[A]. At the Expected:

prompt, enter the matrix variable name to which you want

the computed expected counts to be stored; default=[B].

MATRIX[R] 3 x2 ]

[5.0000 19.000

[ i0. o000t,.000

J.3.000

Xi-Test

Observed:[R]

Exeected:[B]

Calculate Draw

XZ-Test

XZ=3.3750

P=.1850

d€=2.0000

Note: Press _ [] [] 1to

select 1:[A] from the MATRX

EDIT menu.

Calculated results:

Note: Press_ [B]_ to

display matrix [B].

[B]

[[8.0000 16.000.

[ :8888

16.000...i

Drawn results:

13-22 Inferential Statistics and Distributions

2-SampVTest

Input:

Calculated results:

2-SampFTest (two-sample V-test; item D) computes an

V-test to compare two normal population standard

deviations ((31 and (32). The population means and standard

deflations are all unknown. 2-$ampFTest, which uses the

ratio of sample variances Sxl_/Sx2 _, tests the null

hypothesis H0:(31=(32 against one of the alternatives below.

• H_,: (315(32 (G1:_(52)

•H_,:(31<(32 ((51 :<(52)

•H_,:(31>(32 ((51 :>(52)

In the example:

SAMP4={ 7-4 18 17 -3 -5 1 10 11-2}

SAMPS={ -1 12 -1 -3 3-5 5 2-11 -1-3}

Data

2-SamPFTest

InPt:_ SLats

ListI:SRMP4

List2:SRMP5

FPe_l:l

FPe_2:l

_i:_ <z2 >z2

Caloulate OPaw

Stats

2-Sar/PFTest

InPt: Data_

Sx i :8. 7433

hi: 10

Sx2: 5. 9007

n2: II

zl:_ <_2 >z2

Calculate Dra_,J

2-SameFTest

zl#zz

F=2. 1956

P=. 2364

S× _=8. 7433

Sxz=5. 9007

_nl =10. 0000

nz=l I.0000

2-SaMPFTest

zl #zz

F=2. 1955

P=. 2365

Sxl =8. 7433

Sx z=5. 9007

_i =5. 0000

2z=-.2727

n_=lO. 0000

in _= 1 I. 0000

Drawn results:

Inferential Statistics and Distributions 13-23

LinRegTTest

Input:

LinRegTTest (linear regressk)n ttest; item E) computes a

linear regression on the given data and a ttest on the value

of slope _ and the correlation coefficient p for the equation

y=(x +_x. It tests the null hypothesis H0:_=0 (equivalently,

p=O) against one of the alternatives below.

• Hr,: _€0 and pC0 ([3 & p:_0)

• H_,: _<0 and p<0 (9 & p:<0)

• H_,: _>0 and p>0 (9 & P:>0)

The regression equation is automatically stored to RegEQ

(MARS Statistics EQ secondary menu). If you enter a Y=

variable name at the RegEO: prompt, the eMeulated

regression equation is automatically stored to the specified

Y= equation. In the example below, the regression equation

is stored to Y1, which is then selected (turned on).

In the example:

L3={38 56 59 64 74}

L4={41 63 70 72 84}

LinRegTTest

Xlist:L_

91ist:L4

Fre_:l

B & P:_ <0 >0

RegEQ:_

Calculate

Calculated results:

lJ-

LinRegTTest

_=a+bx

B_O and p_O

t=15.9405

P=5.3684E-4

d€=3.8888

4a=-3.6596

$b=i.1969

s_1.9820

P_=.9883

P=,9941

PloLt PloI:Z PloL3 19

",371B-3. 6596+i.

69X

xYz=

xY4=

xVs=

xY_=

When LinRegTTest is executed, the list of residuals is

created and stored to the list name RESID automatically.

RESID is placed on the LIST NAMES menu.

Note: For the regression equation, you can use the fix-decimal mode

setting to control the number of digits stored after the decimal point

(Chapter I). However, limiting the number of digits to a small number

could affect the accuracy of the fit.

13-24 Inferential Statistics and Distributions

ANOVA(

Input:

ANOVA( (one-way analysis of variance; item F) computes a

one-way analysis of variance for COlnparing the means of

two to 20 populations. The ANOVA procedure for

COlnparing these means involves analysis of the variation

in the sample data. The null hypothesis H0:#1=#2 ..... #k is

tested against the alternative H_,: not all p 1---#l_are equal.

ANOVA(listl,list2[,...,list20])

In the example:

L1={7 4665}

L2={6 5 5 8 7}

L3={4 7 6 7 6}

RNOVR(LI,Lz,L_)I

Calculated results:

ll-

One-_au RNOVR

F=.olll

P=.7384

Factor

d_=2.0000

SS=.9333

_MS=.4667

Error

d_=12.0000

SS=18.0000

MS=1.5000

I_xP=1.2247

Note: SS is sum of squares and MS is mean square.

Inferential Statistics and Distributions 13-25

Inferential Statistics Input Descriptions

The tables in this section describe the inferential statistics inputs discussed in

this chapter. You enter values for these inputs in the inferentiM stat editors.

The tables present the inputs in the same order that they appear in this

chapter.

Input Description

_0 Hypothesized value of the population mean that you are

testing.

G The known population standard deviation; must be a real

number > 0.

List The name of the list containing the data you are testing.

Freq The name of the list containing the frequency values for the

data in List. Default=l. All elements must be integers ->0.

Calculate/Draw Determines the type of output to generate for tests and

intervals. Calculate displays the output on the home screen.

In tests, Draw draws a graph of the results.

_, Sx, n Sumlnary statistics (mean, standard deviation, and sample

size) for the one-sample tests and intervals.

_1 The known population standard deviation fronl the first

population for the two-sample tests and intervals. Must be

a real number > 0.

_2 The known population standard deviation fronl the second

population for the two-sample tests and intervals. Must be

a real number > 0.

List1, List2 The names of the lists containing the data you are testing

for the two-salnple tests and intervals. Defaults are L1 and

L2,respectively.

Freql, Freq2 The names of the lists containing the frequencies for the

data in List1 and List2 for the two-salnple tests and

intervals. Defaufis=l. All elements must be integers _>0.

_1, Sxl, nl, _2, Sununary statistics (mean, standard deviation, and sample

Sx2, n2 size) for sample one and sample two in the two-salnple

tests and intervals.

Pooled Specifies whether variances are to be pooled for

2-SampTTest and 2-SampTInt. No instructs the TI-83 not to

pool the variances. Yes instructs the TI-83 to pool the

variances.

13-26 Inferential Statistics and Distributions

Input Description

P0 The expected sample proportion for 1-PropZTest. Must be a

real nmnber, such that 0 < I90< 1.

x The count of successes in the sample for the 1-PropZTest

and 1-PropZlnt. Must be an integer _>0.

n Tile count of observations in the sample for the

1-PropZTest and 1-PropZlnt. Must be an integer > O.

xl The count of successes fronl sample one for the

2-PropZTest and 2-PropZlnt. Must be an integer _>0.

x2 The count of successes froln sample two for the

2-PropZTest and 2-PropZlnt. Must be an integer _>0.

nl The count of observations in sample one for the

2-PropZTest and 2-PropZlnt. Must be an integer > 0.

n2 The count of observations in sample two for the

2-PropZTest and 2-PropZlnt. Must be an integer > 0.

C-Level The confidence level for the inteP_-al instructions. Must be

>_0 and <100. If it is _>1, it is assumed to be given as a

percent and is divided by 100. Default=0.95.

Observed (Matrix) The matrix name that represents the colunms and rows for

the obseP_'ed values of a two-way table of counts for the

z2-Test. Observed nmst contain 'allintegers _>0. Matrix

dimensions nmst be at least 2x 2.

Expected (Matrix) The matrix name that specifies where the expected values

should be stored. Expected is created upon successful

completion of the z_Test.

Xlist, Ylist The names of the lists containing the data for LinRegTTest.

Defaults are L1 and L2, respectively. The dimensions of

Xlist and Ylist nmst be the same.

RegE(:l The prolnpt for the name of the Y= variable where the

cMculated regression equation is to be stored. If a

Y= variable is specified, that equation is automatically

selected (turned on). The default is to store the regression

equation to the RegEQ variable only.

Inferential Statistics and Distributions 13-27

Test and Interval Output Variables

The inferential statistics variables are calculated as indicated below. To access

these variables for use in expressions, press [_, 5(5:Statistics), and then

select the VARS menu listed in the last column below.

LinRegTTest, VARS

Variables Tests Intervals ANOVA Menu

p-value p p TEST

test statistics z, t, Z2_ F t, F TEST

degrees of freedom df df df TEST

sample mean of x values for 21,22 21, 22 TEST

sample 1 and sample 2

sample standard deviation of x Sxl, Sxl, TEST

for sample 1 and sample 2 Sx2 Sx2

nulnber of data points for sample nl, n2 nl, n2 TEST

1 and sample 2

pooled standm'd deviation SxP SxP SxP TEST

estimated sample proportion /3 /3 TEST

estimated sample proportion for /31 /31 TEST

population 1

estimated sample proportion for /32 /32 TEST

population 2

confidence interval pair lower, TEST

upper

mean of x values 2 _ XY

sample standm'd deviation of x Sx Sx XY

nulnber of data points n n XY

standard error about the line s TEST

regression/fit coefficients a, bEQ

correlation coefficient rEQ

coefficient of determination r2 EQ

regression equation RegEQ EQ

13-28 Inferential Statistics and Distributions

Distribution Functions

DISTR menu

normalpdf(

To display the DISTR menu, press [_ [DiSTR],

DISTR DRAW

i: normalpdf(

2: normalcdf(

3:invNorm(

4:tpdf(

5:tcdf(

6: z2pdf(

7: x2cdf

8: Fpdf(

9: Fcdf(

O: binompdf(

A: binomcdf(

B: poissonpdf(

C: poissoncdf(

D: geometpdf(

E: geometcdf(

Normal probability density-

Normal distribution probability

Inverse cunmlative normal distribution

Student-t probability density

Student-t distribution probability

Chi-square probability density-

Chi-square distribution probability

F probability density-

F distribution probability

Binomial probability

Binomial cunmlative density-

Poisson probability

Poisson cunmlative density

Geometric probability

Geometric cunmlative density-

Note: -1E99 and IE99 specify infinity. If you want to view the area left

of upp¢rbound, for example, specify lowerbound_1E99.

norwmalpdf( computes the probability density function

(pdf) for the normal distribution at a specified xvalue, The

defaults are mean p=O and standard deviation cr=l. To plot

the normal distribution, p_k_te normalpdf( to the Y= editor.

The probability density function (pdf) is:

1 - (x-")=

f(x)=_e 2_ ,_>0

4"z_c_

normalpdf(x[,p,o])

Pl,:,tl P10L2 Plot3

",V1 Bnor.r_alPdf" (X,

35,2>

Note: For this example,

Xmin = 28

Xmax = 42

Ymin = 0

Ymax = .25

Tip: For plotting the normal distribution, you can set window variables

Xmin and Xmax so that the mean p falls between them, and then

select 0:ZoomFit from the ZOOM menu.

Inferential Statistics and Distributions 13-29

normalcdf(

invNorm(

tpdf(

normalcdf( computes the normal distribution probability

between lowerbound and upperbound for the specified

nlean u and standard deviation or.The defaults are u=0

and 6= 1.

normalcdf(_werbound,upperbound[,p,_])

noPmalod_(-iE99,

36,35,2)

.6914624678

invNorm( computes the inverse cumulative normal

distribution function for a given area under the normal

distribution cut_'e specified by mean pand standard

de_iation cr. It calculates the xvalue associated with an

area to the left of the xvalue. 0 _<area _<1 must be true.

The defaults are p=0 and or=1.

invNorm(area[,p,_])

invNorr_(. 6914624

678,35, 2)

36. ee0000e4

tpdf( computes the probability density- function (pdf) %r

the Student-t distribution at a specified xvalue, df (degrees

of freedom) must be >0. To plot the Student-t distribution,

paste tpdf( to the Y= editor, The probability density-

function (pdf) is:

F [(df + 1)/2] (1 + x2/df) - (if + 1)/2

f(x) =F(df /2) x/_f

tpdf(x, dJ)

Pl_{:[ P1¢_: Plo{. _

",YI BtPd{'(X, 2) INote: For this example,

Xmin =-4.5

Xmax =4.5

Ymin = 0

Ymax = .4

13-30 Inferential Statistics and Distributions

tcdf(

x2pdf(

tcdf( computes the Student-t distribution probability

between lowo'bound and uppe_"bound for the specified df

(degrees of freedom), which nmst be > O.

tcdf(lowerbound,uppe'rbou.rwl,d]_

tc.d_" ( -2, 3, 18)

•9657465644

z2pdf( computes the probability density function (pdf) ff)r

the X2 (chi-square) distribution at a specified xvalue, df

(degrees of freedoln) nmst be an integer > 0, To plot the X2

distribution, paste x2pdf( to the Y= editor, The probability

density function (pdf) is:

f(x) = (1/2)df/2 x/f/:) -1e-x/:), x _>0

r(df /2)

:2pdf(x,dj)

P1,;,tl PloLZ Plot_

\YI B:KZPdf'(X, 9)

",VZ I_I;_Z Pdla (X _F)

xYs=

\Y_=

xY_=

\Y_=

Note: For this example,

Xmin = 0

Xmax = 30

Ymin = -.02

Ymax = .132

x2cdf( x2cdf( computes the Z z (chi-square) distribution probability

between lowerbound and upperbound for the specified df

(degrees of freedom), which nmst be an integer > O.

z2cdf(lowe'rbound,upperbound,dj)

_Zc.d_(O, 19. 023,9

.9750019601

Inferential Statistics and Distributions 13-31

Fpdf( Fpdf( computes the probability density- function (pdf) for

the F distribution at a specified xvalue, numerator df

(degrees of freedonl) and denominator dfnmst be integers

> O. To plot the F distribution, paste Fpdf( to the Y= editor.

The probability density function (pdf) is:

F[(n+d)/2] (d)n/2xn/2 l(l+,_a_./d)(n+d)/2,X> 0

f(X) = F(n/2)F(d/2)

where n= numerator degrees of freedom

d= denominator degrees of fi'eedom

F pdf(x,numero tor dr, denominator dJ_

Plot:l, plot:i: Plo_,3 Note: For this example,

_._1BFPdf (X, 24, 19 Xmin = 0

Xmax = 5

Ymin = 0

Ymax = 1

Fcdf( Fcdf( computes the F distribution probability between

lowerbound and uppe'rbound for the specified nume_-ator

df (degrees of freedon0 and denominator dr. numerator

dfand denominator df nmst be integers >0.

Fcdf(lowerbound,upperbound,numerator dr,

denominator dJ)

Fodf'(O, 2. 4523,24

,19) -,

• 9_ 49989576

13-32 Inferential Statistics and Distributions

binompdf(

binomcdf(

poissonpdf(

binompdf( computes a probability at xffw the discrete

binomial distribution with the specified numtrials and

probability of success (1)) on each trial, x can be an integer

or a list of integers. O_<p_<lnmst be true. numtrials nmst be

an integer > O. If you do not specify x, a list of probabilities

from 0 to numtrials is returned. The probability density

function (pdf) is:

X ( _7/, x n-x X

f( )=/xiP (l-p) , =O,1,...,n

where n=numtrials

binompdf(numtrials,p[,x ])

binomPd¢(5,. 6, {3

,4,5})

{. 3456 .2592 .0...

binomcdf( computes a cunmlative probability at xff)r the

discrete binomial distribution with the specified numtrials

and probability of success (p) on each trial, x can be a real

nmnber or a list of real nmnbers. O_<p_<1 nmst be true.

numtrials nmst be an integer > O. If you do not specify- x, a

list of cunmlative probabilities is returned.

binomcdf(numtrials,p[,x ])

binomcd¢(5,. 6, {3

,4,5})

{,66304 .92224 ...

poissonpdf( computes a probability at xff)r the discrete

Poisson distribution with the specified mean {l, which nmst

be a real nmnber > O. x can be an integer or a list of

integers. The probability density function (pdf) is:

f(x) =e- _ ,uX/x!, x= 0,1,2,...

poissonpdf(p,x)

PoissonPd¢(6,10)

.0413030934

Inferential Statistics and Distributions 13-33

poissoncdf(

geometpdf(

geometcdf(

poissoncdf( computes a eunmlative probability at xfor the

discrete Poisson distribution with the specified mean _l,

which nmst be a real number > O. xcan be a real number

or a list of real numbers.

poissoncdf(p,x)

eoissonod¢(.126,

{0,1,2,3})

{.8816148468 .9...

geometpdf( computes a probability at x, the number of tlle

trial on which the first success occurs, for the discrete

geometric distribution with the specified probability of

success p. 0_<p_<l nmst be true. xcan be an integer or a list

of integers. The probability density function (pdf) is:

f(x) =p(1 -p)X - 1, x= 1,2,...

geometpdf_,x)

geo_eted?(.4,6)

.031104

geometcdf( computes a cunmlative probability at x, the

number of the trial on which the first success occurs, for

the discrete geometric distribution with the specified

probability of success p. O_<p_<1 must be true. xcan be a

real number or a list of real numbers.

geometcdf_,x)

geo_etod¢(.5,{l,

2,3J)

{.5 .75 .875}

13-34 Inferential Statistics and Distributions

Distribution Shading

DISTR DRAW

ShadeNorm(

To display the DISTR DRAW menu, p_ss _ [DISTR] [].

DISTR DRAW instructions draw vmious types of density

functions, shade the area specified by lower'bound and

uppc'rbound, and display- the computed area vMue.

To clem" the drawings, select l:CIrDraw from the DRAW

menu (Chapter 8).

Note: Before you execute a DISTR DRAW instruction, you must set

the window variables so that the desired distribution fits the screen.

DISTR DRAW

i: ShadeNorm(

2:Shade t(

3:Shadez2(

4:ShadeF(

Shades normal distribution.

Shades Student-t distribution,

Shades )_ distribution.

Shades Fdistribution,

Note: -1E99 and IE99 specify infinity. If you want to view the area left

of upperbowad, for example, specify lowe'rbownd_1E99.

ShadeNorm( draws the normal density function specified

by mean uand standard deviation aand shades the m'ea

between lowc'rbound and upperbound. The defaults are

u=0 and a= 1.

ShadeNorm(lowerboural,uppc'rbound[,g,c_])

Note: For this example,

Xmin = 55

Xmax = 72

Ymin =-,05

Ymax = ,2

Inferential Statistics and Distributions 13-35

Shade_t(

Shadex2(

ShadeF(

Shade_t( draws the density function for the Student-t

distribution specified by df (degrees of freedom) and

shades the area between lowe_rbound and upperbound.

Shade_t(lowerbound,upperbound,dJ_

4)IShade-t(-l'IE99' Note: For this example,

Xmin =-3

Xmax = 3

Ymin = -,lS

Ymax = .S

Shadex2( draws the density function for the Z2(chi-square)

distribution specified by df (degrees of freedom) and shades

the area between lowerbou_l and uppe_rbound.

Shadex2(lowerbound,uppe_'bound,dj)

IShadeXZ (0, 4, 10)I I Note: For this example.

Xmin = 0

Xmax = 35

Ymin = -.025

Ymax = .1

ShadeF( draws the density function for the F distribution

specified by numerator df (degrees of freedom) and

denominator dfand shades the area between lowed'bound

and upperbour_l.

ShadeF (lowe'rbound,upperbound,numerator dr,

denominator d_

ShadeF()i 1,2, 10, 15 Note: For this example,

Xmin = 0

Xmax = S

Ymin = -.25

Ymax = .9

13-36 Inferential Statistics and Distributions

14 Financial

Functions

Contents Getting Started: Einaneing a Car. ........................ I4-2

Getting Started: Computing Compound Interest .......... 14-3

Using the TVM Solver .................................... 14-4

Using the Financial Functions ........................... 14-5

Calculating Time Value of Money (TVM) ................. 14-6

Calculating Cash Flows .................................. 14-8

Calculating Amortization ................................ 14-9

Calculating Interest Conversion .......................... I4-I2

Finding Days between Date_)efil_N Paynlent Method ..... 14-13

Using tile TVM Variables ................................. 14-14

TEXAS INSTRUMENTS T1=83

N=360.00

I_=IB.00

PV=100000.00

-PMT=-I507.09

FV=0.00

P/V=12.00

C/Y=12.00

PMT:L_ BEGIN

STAT PLOT TBLSET FORMAT CALC TABLE

Financial Functions 14-1

Getting Started: Financing a Car

Getting Started is a ftkst-paced introduction. Read the chapter for details.

You have found a cat" you would like to buy-. The car costs 9,1)00. You can

afford payments of 250 per month for four years. What annual percentage rate

(APR) will make it possible for you to afford the car?

Press[_[][][][][_to setthe

fixed-deeimalmode seging to 2. The TI-83

will display all numbers with two decimal

places.

2. Press [_ [FINANCE]to display" the

FINANCE CALC menu.

3. Press [_ to select I:TVM Solver. The

TVM Solver is displayed.

Press 48 [_ to store 48 months to N.

Press [] 9000 [gNT_ to store 9,000 to PV.

Press [] 2S0 [gNT_ to store -250 to PMT.

(Negation indicates cash outflow.) Press 0

[ggg_ to store 0 to FV. Press 12 F_tggl to

store 12 payments per year to P/Y and 12

compounding periods per year to O/Y.

Setting PlY to 12 will compute an annual

percentage rate (compounded monthly)

for I%.Press [] [gNT_ to select PMT:END,

which indicates that payments are due at

the end of each period.

4. Press [] [] [] [] [] [] to move the cursor

to the I%prompt. Press @ [SOLVE] to

solve for I%.What APR should you look

for?

Sci Ehg

_I_3456789

Degree

Pol Se_

Dog

Horiz G-T

VRRS

Solver...

gum_I%

gvm_PV

tvm_N

tvm_FV

,nev(

N=0.00

I%=0.00

PV=0.00

PMT=0.00

FV=0.00

P/Y=l.O0

C/V=l.00

PMT:L_ BEGIN

N=48.00

I%=0.00

PV=9000.00

PMT=-250.00

FV=0.00

P/Y=12.00

C/Y=12.00

PMT:[__[LL_BEGIN

N=48.00

"1%=14.90

PV=9000.00

PMT=-250.00

FV=0.00

P/Y=12.00

C/Y=12.00

PMT:L:[II_BEGIN

14-2 Financial Functions

Getting Started: Computing Compound Interest

At what annual interest rate, compounded monthly, will 1,250 accumulate to

2,000 in 7 years?

Note: Because there are no payments when you solve compound interest problems, PMT

must be set to 0 and PlY must be set to 1.

Press [_ [FINANCE] to display- the

FINANCE CALC menu.

Press [_ to select I:TVM Solver. Press 7

to enter the number of periods in years,

Press [] [] [] 12S0 to enter the present

value as a cash outflow (investment).

Press [] 0 to specify- no payments. Press

[] 2000 to enter the future value as a cash

inflow (return), Press [] 1to enter

payment periods per year, Press [] 12 to

set compounding periods per yea[" to 12.

Press [] [] [] [] [] to place the cursor on

the 1%prompt.

Press @ [SOLVE] to solve for I%, the

annual interest ['ate.

Z.._tvVRR5

M Solver

_,_PMt

3: tw,_l%

4: tvM_PV

5: tur,,_N

6: tvr.__FV

74nPv(

N=7

1%=0

PV=-1250

PMT=O

FV=2000

P/9=I

C/Y=12

PMT:L_IiE BEGIN

N=7

1%=|

PV=-1250

PMT=O

FV=2000

P/Y=1

C/Y=I2

PMT:I=_I_ BEGIN

.N=7.O0

1%=6.73

PV=-1250.00

PMT=0.00

FV=2000.00

P/Y=l.00

C/Y=12.00

PMT:_ BEGIN

Financial Functions 14-3

Using the TVM Solver

Using the TVM

Solver The TVM Solver displays the time-value-of-money (TVM)

variables. Given four variable wdues, tile TVM Solver solves

for the fifth variable.

The FINANCE VARS menu section (page 14-14) describes

the five TVM variables (N, I%, PV, PMT, and FV) and PlY and

C/Y,

PMT: END BEGIN in the TVM Solver corresponds to the

FINANCE CALC menu items Pmt_End (pa3qnent at the end

of each period) and Pmt_Bgn (payment at the beginning of

each period).

To solve for an unknown TVMvm'iable, follow these steps.

1, Press [2ffa][FINANCE] _ to display the TVM Solver. The

screen below shows the default values with the fixed-

decimal mode set to two decimal places,

N=0.00

Ia=0.00

PV=0.00

PMT=O,00

FV=0.00

P/V=I.00

C/V=I.O0

PMT:[__II_BEGIN

2. Enter the known vMues for four TVM variables.

Note: Enter cash inflows as positive numbers and cash

outflows as negative numbers.

Enter a value for P/Y, which automatically enters the

same wdue for C/Y; if PW €CIY, enter a unique value for

C/Y.

4. Select END or BEGIN to specify- the pa3qnent method.

5. Place the cursor on the TVM vm'iable for which you

want to solve.

Press @ [SOLVE].The answer is computed,

displayed in tile TVM Solver, and stored to the

appropriate TVM variable, An indicator square in the left

colunm designates the solution variable.

N=360.00

I%=1B.00

PV=100000.00

PMT=-I507.09

FV=0.00

P/Y=I2.00

CXY=12.00

PMT:I:IIIIBEGIN

14-4 Financial Functions

Using the Financial Functions

Entering Cash

Inflows and Cash

Outflows

FINANCE CALC

TVM Solver

When using the TI-83 financial functions, you lnust enter

cash inflows (cash received) as positive numbers and cash

outflows (cash paid) as negative numbel\_. The TI-S3

follows this convention when computing and displaying

answers.

To display the FINANCE CALC menu, press [_ [FINANCE].

CALC VARS

i : TVM Sol ver.,.

2 : tvm Pmt

3: tvm I%

4:tvm PV

5:tvm N

6:tvm FV

7:npv(

8:irr(

9: bal(

O:EPrn(

A:EInt(

B:_Nom(

C:_Eff(

D:dbd(

E: Pmt End

F: Pmt Bgn

Displays tile TVM Solver.

Conlputes the amount of each payment.

Conlputes the interest rate per year,

Computes the present value.

Colnputes the nulnber of paylnent periods,

Computes the future value,

Computes the net present value,

Computes the internal rate of l_tum.

Computes the amortization sched, balance,

Computes the amort, sched, principal sum,

Computes the amort, sched, interest sum.

Computes the nominal interest rate,

Computes the effective interest rate.

Calculates the days between two dates,

Selects ordinary annuity (end of period).

Selects annuity- due (beginning of period),

[ _se these functions to set up and perform financial

calculations on the home screen,

TVM Solver displays tile TVM Solver (page 14-4).

Financial Functions 14-5

Calculating Time Value of Money (TVM)

Calculating Time

Value of Money

tvm_Pmt

I_se tilne-value-of-lnoney (TVM) functions (menu items 2

through 6) to analyze financial instruments such as

annuities, loans, mortgages, leases, and sa_ings.

Each TVM function takes zero to six arguments, which

must be real numbers. The wdues that you specify as

arguments for these functions m'e not stored to the TVM

variables (page 14-14).

Note: To store a value to a TVM variable, use the TVM Solver (page

14-4) or use _ and any TVM variable on the FINANCE VARS

menu (page 14-14).

If you enter less than six arguments, the TI-83 substitutes a

previously stored TVM vm'iable value for each unspecified

argument.

If you enter any argunlents with a TVM function, you nlust

place the argmnent or arguments in parentheses,

tvm_Pmt computes the amount of each payment.

tvm_Pmt [(N,I %,PV,FV, P_, C/Y) ]

N=360

I%=8.5

Pg=IO0000

PMT=O

FV=O

P/?=I2

C/V=12

PMT:I_I[ BEGIN

tvm_Pmt -768 91 I

tvm_Pr_t (360, 9: 5) I

-840.85

Note: In the example above, the values are stored to the TVM

variables in the TVM Solver. Then the payment (tyro_Pint) is

computed on the home screen using the values in the TVM Solver.

Next, the interest rate is changed to 9.5 to illustrate the effect on the

payment amount.

14-6 Financial Functions

tvm_]%

tvm_PV

tvm_N

tvm_FV

tvm_I% computes the annual inte[_st rate.

tvm_1%[(N,PV,PMT, FV, P/Y, C/Y) ]

tvm_l%(48, 10000, I

-250,0, 12) 9 24

Rns÷l% 9124

tvm_PV computes the present vMue.

tvm_PV[(_I%,PMT, FV, P/Y,C/Y)]

360÷N:II÷I%:-100

÷PMT:O÷FV:12÷P/

tvm_PV 12.00

I 1o5oo6.351

tvm_N computes the number of paylnent periods.

tvm_N[(I%_V_MT, FV, P/Y,C/Y)]

6÷I%:9000÷PV:-351

O÷PMT:O+FV:3÷P/V l

tvm_N 3.00

36.47

tvm_FVcomputesthe _turevMue.

tvm_FV[(_I%,PV, PMT_X,C/Y)]

6÷N:8÷I%:-5500÷P

V:0÷PMT:l÷P/_.00

tvm_FV 8727.81

Financial Functions 14-7

Calculating Cash Flows

Calculating a

Cash Flow Use the cash flow functions (menu items 7 and 8) to

analyze the value of money over equal time periods. You

can enter unequal cash flows, which can be cash inflows or

outflows. The syntax descriptions for npv( and irr( use

these arguments.

•interest rate is the rate by which to discount the cash

flows (the cost of money) over one period.

• CFO is the initial cash flow at time 0; it nmst be a real

nunlber.

• CFList is a list of cash flow alnounts after the initial

c_sh flow CFO.

• CFFreq is a list in which each element specifies the

frequency of occurrence for a grouped (consecutive)

cash flow amount, which is the corresponding element

of CFList. The default is 1; if you enter values, they

nmst be positive integers < 10,000.

For example, express this uneven cash flow in lists.

2000 2000 2000 4000 4000

; I T I I

CFO = 2000

CFList = {2000,-3000,4000}

CFFreq = {2,1,2}

- 3000

npv(, irr( npv( (net present value) is the sunl of the present values

for the cash inflows and outflows. A positive result for npv

indicates a profitable investment.

npv(interest rate,CFO,CFList[,CFFreq])

irr( (internal rate of return) is the interest rate at which the

net present value of the cash flows is equal to zero,

irr(CFO,CFList[,CFFreq])

1000 0 5000 3000

1 1

2000 -2500

{1000,-2500,0,501

00,3000_+L1 I

<1000.00 -2500....

nPv(6,-2000,Lt)

2920.65

irP(-2000,L1) 27.88

14-8 Financial Functions

Calculating Amortization

Calculating an

Amortization

Schedule

bal(

EPrn(, Elnt(

Use the amortization functions (menu items 9, 0, and A) to

calculate balance, sum of principal, and sum of interest for

an amortization schedule.

bal( computes tile balance ff)r an amortization schedule

using stored wdues ff)r I%, PV, and PMT. npmt is the

number of the payment at which you want to calculate a

balance. It nmst be a positive integer < 10,000. roundvalue

specifies the internal precision the calculator uses to

calculate the balance; if you do not specify roundvalue,

then the TI-83 uses the cmTent Float/Fix decimal-mode

setting.

bal(npmt[,roundvalue])

IO0000÷PV: 8.5÷I% bal (12) 99244.07

I_.O0

EPrn( computes the sunl of the principal during a specified

period for an amortization schedule using stored values for

I%, PV, and PMT. pmtl is the starting paylnent, pmt2 is the

ending payment in the range, pmtl and pmt2 nmst be

positive integers < 10,000. roufwlvalue specifies the internal

precision the calculator uses to calculate the principal; if you

do not specify- _vu.rwlvalue, the TI-83 uses the current

Float/Fix deeinml-mode setting.

Note: You must enter values for 1%, PV, PMT, and before computing

the principal.

EPrn(pmtl,pmt2[,rou_wlvalue])

Elnt( computes the stun of the interest during a specified

period for an amortization schedule using stored values for

I%, PV, and PMT. pmtl is the starting paylnent, pmt2 is the

ending payment in the range, pmtl and pmt2 nmst be

positive integers < 10,000. roundvalue specifies the

internal precision the calculator uses to calculate the

interest; if you do not specify- roundvalue, the TI-83 uses

the emTent Float/Fix deeinml-mode setting.

Elnt(pmt l,pmt2[ ,roundvalue ])

360÷N: 100000÷PV: I EF'Po (I, 12)755._

8.5÷1%: -768.91÷P 93

MT:I2÷P/V 12.00 EInt(l,12)_8470.99

Financial Functions 14-9

Amortization

Example:

Calculating an

Outstanding

Loan Balance

You want to buy a home with a 30-year mortgage at S

percent APR. Monthly payments are 800, Calculate the

outstanding loan balance after each payment and display-

the results in a graph and in the table,

1, Press [_]. Press [] [] [] [] _ to set the

fixed-decimal mode setting to 2, Press [] [] [] _ to

select Par graphing mode,

Sci Eng I

II_34567891

Degree I

_Pol Se_

Dot I

SiMi I

hi, I e^8'

Horiz G-T

2, Press [_ [FINANCE] _ to display the TVM Solver.

3. Press 360 to enter number of payments. Press [] 8 to

enter the interest rate. Press [] [] [] 800 to enter the

paynmnt amount. Press [] 0 to enter the future value of

tile mortgage. Press [] 12 to enter the payments per

year, which also sets the compounding periods per year

to 12. Press [] [] _ to select PMT:END,

N=360.00

I%=8.00

PV=0.00

PMT=-800.00

FV=0.00

P/Y=12.00

C/Y=12.00

PMT:[_:IIL_BEGIN

4. Press [] [] [] [] [] to place the cul_or on tile PV prompt.

Press @ [SOLVE] to solve for the present value.

N=360.00

I%=8.00

PV=109026.80

PMT=-800.00

FV=0.00

PIV=I2.00

C/Y=12.00

PMT:I:I_I_BEGIN

5, Press [] to display tile parametric Y= editor. Turn off all

stat plots. Press _ to define X1T as T. Press [] [g_

[FINANCE] 9 _[_ to define Y1T as bal(T).

pI,:,I:I pl,:,l:._ plol:_

\X1 "r_T

YIT_baI(T)

14-10 Financial Functions

6. Press _ to display- the window variables. Enter

tile values below.

Tmin=0 Xmin=0 Ymin=0

Tmax=360 Xmax=360 Ymax=125000

Tstep=12 Xscl=50 Yscl=10000

7, Press _ to draw the graph and activate the trace

cursor. Press [] and [] to explore the graph of the

outstanding bahmce over time. Press a number and then

press [gNY_ to xqew the balance at a specific time T.

1T=T Y1T=b_I(T)

S, Press [g_ [TBLSET] and enter the vMues below.

TblStart=0

ATbI=12

9, Press [g_ [TABLE] to display the table of outstanding

balances (Y1T).

tZ.00 ,"4t-,a" YtT

Tim O,00 10907::7

IaL0O 10Bl11_

31L00 lO60E:I,

tlIEII00 rIB.00 1Oh9O_:

E0.O0 I;0,00 1031_g2

?_2{_00 72.00 10_:29g

T-

10.Press [g0_ [] [] [] [] [] [] [] [] [] [V_Y_ to select G-T

split-screen mode, in which the graph and table are

displayed sinmltaneously.

Press _ to display- XIT (time) and YIT (balance) in

the table.

_0.00 1.0Eg

72,00 1,0E5

.._.Eh.00 t.OEg

96.00 99_h

t0B,0 97510

T=132 _

X=132

?=93621.91

Financial Functions 14-11

Calculating Interest Conversion

Calculating an

Interest

Conversion

,Nom(

,Eft(

Use the interest conversion functions Onenu items Band

C) to convert interest rates from an annual effective rate to

a nominal rate (_Nom() or from a nominal rate to an annual

effective rate (_Eff().

_Nom( computes the nominal interest rate. effective rate

and compounding periods nmst be real numbers.

compounding periods nmst be >0.

_Nom(effective rate,compounding periods)

_Nor_( 15.87, 4)15.00

)Elf( computes the effective interest rate. nominal rate and

compounding periods must be real nulnbers.

compounding periods must be >0.

_Eff(nominal rate,compounding periods)

_E€€(8,12) 8.30

14-12 Financial Functions

Finding Days between Dates/Defining Payment Method

dbd(

Defining the

Payment Method

Pint_End

Pmt_Bgn

Use the date function dbd( (menu item D) to calculate the

number of days between two dates using the actual-day-

count method, datel and date2 can be numbers or lists of

numbers within the range of the dates on the standard

calendar.

Note: Dates must be between the years I950 through 2049.

dbd(date l,date2)

You can enter datel and date2 in either of two formats.

• MM.DDYY (United States)

• DDMM.YY (Europe)

The decimal placement differentiates the date formats,

dbd( 12. 3190, 12.3

192) 731.00

Pmt_End and Pmt_Bgn (menu items Eand F) specify- a

transaction _k_an ordinmy7 annuity or an annuity due. VC]mn

you execute either conunand, the TVM Solver is updated.

Pmt_End (payment end) specifies an ordinmTy- annuity-,

where payments occur at the end of eaeh payment period.

Most loans are in this catego[% Pint_End is the default.

Pmt_End

On the TVM Solver's PMT:END BEGIN line, select END to set

PMT to ordinmTy- annuity.

Pmt_Bgn (payment beginning) specifies an annuity due,

where payments occur at the beginning of each payment

period. Most leases are in this catego_7.

Pmt_Bgn

On the TVM Solver's PMT:END BEGIN line, select BEGIN to

set PMT to annuity due.

Financial Functions 14-13

Using the TVM Variables

FINANCE VARS

N, [%, PV, PMT,

PlY and C/Y

To display the FINANCE VARS menu, press _ [FINANCE]

[_. You can use TVM variables in TVM functions and store

values to them on the home screen,

CALC VARS

1: N

2:1%

3: PV

4: PMT

5: FV

6: P/Y

7: C/Y

Total number of payment periods

Annual interest rate

Present value

Payment amount

Future value

Number of payment periods per year

Number of compounding periods/year

N, I%, PV, PMT,and FV are the five TVM wu'iables. They

t_present the elements of eonunon financial transactions,

as described in the table above. I%is an annual interest rate

that is converted to a per-period rate based on the values

of P/Y and C/Y.

PW is the number of payment periods per year in a

financial transaction.

C/Yis the number of compounding periods per year in the

salne transaction.

When you store a value to P/Y, the value for C/Y

automatically changes to the same value. To store a unique

value to g/Y, you nmst store the value to C/Y after you have

stored a value to PlY.

14-14 Financial Functions

5CATALOG,Strings,

HyperbolicFunctions

Contents Browsing tile TI-83 CATALOG ........................... 15-2

Entering and Using Strings ............................... 15-3

Storing Strings to String Variables ....................... 15-4

String Functions and Instructions in the CATALOG ...... 15-6

Hyperbolic Functions in tile CATALOG .................. 15-10

TEXAS INSTRUMENTS T1=83

mCATALOG

_abs(

and

angle(

QNOUA(

Ans

augnenL(

AxesO_¢

STAT PLOT TBLSET FORMAT BALe TABLE

CATALOG, Strings, Hyperbolic Functions 15-1

Browsing the TI-83 CATALOG

What Is the

CATALOG?

Selecting an Item

from the

CATALOG

The CATALOG is an alphabetical list of all functions and

instructions on the TI-83. You also can access each

CATALOG item fronl a menu or the keyboard, except:

• The six string functions (page 15-6)

• The six hyperbolic functions (page 15-10)

• The solve( instruction without the equation solver editor

(Chapter 2)

• The inferential stat functions without the inferential stat

editors (Chapter 13)

Note:The only CATALOG programming commandsyoucan execute

from thehomescreenare GetCalc(, Get(, and Send(.

To select a CATALOG item, follow these steps.

1. Press F_a][CATALOG] to display the CATALOG.

iCRTRLOG

i*abs(

and

angle(

RNOVR(

Rn_

augment(

Axes0€€

The _ in the first colunm is the selection cursor.

2. Press [] or [] to scroll the CATALOG until the selection

cursor points to the item you want.

• To jump to the first item beginning with a particular

letter, press that letter; alpha-lock is on.

• Items that begin with a number are in alphabetical

order according to the first letter 'after the number.

For example, 2-PropZTest( is among the itenls that

begin with the letter P.

• Functions that appear as symbols, such as +, -1, <,

and g(, follow the last item that begins with Z. To

jump to the first s3qnbol, !, press [@

3. Press [ggY_ to paste the item to the current screen.

Iabs(1 I

Tip: From the top of the CATALOG menu, press [] to move to the

bottom. From the bottom, press [] to move to the top.

15-2 CATALOG, Strings, Hyperbolic Functions

Entering and Using Strings

What Is a String?

Entering a String

A string is a sequence of characters that you enclose within

quotation marks, On the TI-83, a string has two primaFy"

applications.

• It defines text to be displayed in a p_x)gram.

• It accepts input from the keyboard in a program,

Characters are the units that you combine to form a string.

• Count each number, letter, and space as one character,

• Count each instruction or function name, such as sin( or

cos(, as one character; the TI-83 interprets each

instruction or function name as one character.

To enter astring on ablank line on the home screen or in a

program, follow these steps.

1, Press @ [,] to indicate the beginning of the string.

2, Enter the characters that comprise the string.

• Use any combination of numbers, letters, function

names, or instruction names to create the string.

• To enter ablank space, press @ [_],

• To enter several alpha characters in a row, press [_

[A-LOCK] to activate alpha-lock.

3, Press @ [-] to indicate the end of the string.

"string"

4. Press [ENY_. On the home screen, the string is displayed

on the next line without quotations. An ellipsis (...)

indicates that the string continues beyond the screen,

To scroll the entire string, press [] and EO-

"RBC,D, 1234 EFGH

5678

RBCD 1234 EFGH ...

Note: Quotation marks do not count as string characters.

CATALOG, Strings, Hyperbolic Functions 15-3

Storing Strings to String Variables

String Variables The TI-83 has 10 variables to which you can store strings.

You can use string variables with string functions and

instructions.

To display the VARS STRING menu, follow these steps.

1, Press _ to display- the VARS menu, Move the cursor

to 7:String.

_ Y-VRRS

ndo_z..

2: Zoom.

3: GDB...

4: Picture...

5: Statistics_.

6: Table...

WString...

2, Press_ to displaytheSTRING secondarymenu,

5:Str3

Str4

Str5

Str6

,Str7

15-4 CATALOG, Strings, Hyperbolic Functions

Storing a String

to a String

Variable

Displaying the

Contents of a

String Variable

store a string to a string variable, follow these steps.

Press @ [,], enter the string, and press @ [-].

Press _.

Press _ 7 to display the VARS STRING menu.

Select the string variable (from $trl to $tr9, or $tr0) to

which you want to store the string.

4:Str.4

5:StP5

6:_tr6

74Str-7

The string variable is D_sted to the current cursor

location, next to the store symbol (-)).

Press _ to store the string to the string variable. On

the home screen, the stored string is displayed on the

next line without quotation marks.

"HELL0"eStP2

HELLO

To display the contents of a string variable on the home

screen, select the string variable from the VARS STRING

menu, and then press [gNT_. The string is displayed.

St.r2

HELLO I

CATALOG, Strings, Hyperbolic Functions 15-5

String Functions and Instructions in the CATALOG

Displaying String

Functions and

Instructions in

the CATALOG

+ (Concatenation)

Selecting a String

Function from

the CATALOG

String functions and instructions m'e available only fronl

the CATALOG. The table below lists the string functions

and instructions in the order in which they appem" among

the other CATALOG menu items. The ellipses in the table

indicate the presence of additional CATALOG items.

CATALOG

Equ)String(

expr(

inString(

length(

String)Equ(

sub(

Converts an equation to a string,

Converts a string to an expression.

Returns a chm'acter's place number.

Returns a string's chm'acter length.

Converts a string to an equation,

Returns a string subset as a string,

To concatenate two or more strings, follow these steps,

1, Enter stringl, which can be a string or string name.

2, Press [],

3, Enter string2, which can be a string or string name, If

necessmT, press [] and enter string3, and so on,

stringl +string2+string3, , ,

4, Press [_ to display- the strings as a single string.

"HIJK "+StPl :5tr

1+"LMHOP"

HIJK LMNOP

To select a string function or instruction and paste it to the

current screen, follow the steps on page 15-2.

15-6 CATALOG, Strings, Hyperbolic Functions

Equ*String(

expr(

inString(

Equ*String( converts to a string an equation that is stored

to any- VARS ¥-VARS variable. Yn contains the equation.

Strn (from Strl to Strg, or Str0) is the string variable to

which you want the equation to be stored as a string.

Equ*Stdng(Yn,Strn)

"3X"÷Y1 Done

E_u*String(gt, St

rl) Done

expr( converts the chm'acter string contained in string to

an expression and executes it. string can be a string or a

stringvariable.

expr(string)

l_X:"5X"+Strl 10 exPr(

x_r(Strl)÷R I0

,,l+2+XZ,,)

inString( returns the chm'acter position in string of the first

character of substring, string can be a string or a string

variable, start is an optional character position at which to

start the search; the default is 1.

inString(string,subst,ring[ ,start])

inStr ing ( "PQRSTU

V", "STU" ) 4

inStr ing ( "RBCRBC

,RBC ,4) 4

Note: If st:_ing does not contain snbst:Hng, or start is greater than the

lengthof string, inString( returns O.

CATALOG, Strings, Hyperbolic Functions 15-7

length(

String*Equ(

length( returns the number of chara('ters in st'ring, string

can be a string or string variable.

Note: An instruction or function name, such as sin( or cos(, counts as

one character.

length(string)

WXYz"WXYZ"eStrl 4

length(Strl)

String*Equ( converts st'ring into an equation and stores tlle

equation to Yn. st'ring can be a string or string vmiable,

String*Equ( is tlle inverse of Equ*String(.

String*Equ(st'ring,Yn)

String*E_u(Str2, I

'.?z) Done

Plot1 Plot;" Plot3 I

,,yl= I

",YzB2X

15-8 CATALOG, Strings, Hyperbolic Functions

sub(

Entering a

Function to

Graph during

Program

Execution

sub( returns a string that is a subset of an existing st'ring.

string can be a string or a string variable, begin is the

position number of the first character of the subset, length

is the number of characters in the subset.

sub(st_ng,b_in,length)

ABCDEFG"RBCDEFG"÷SLP5I

sub(StP5,4,2)

Inapmgram, youcanentera Nnctiontographdunng

programexecutionusin theseconunands.

PROGRRM:INPUT

:InPut "ENTRY ='' ,

StP3

:String*E_u(Str3

,Y_)

:DisPGraPh

PPYmINPUT

ENTRY=3XI

Note: When you execute this program, enter a function to store to Y3

at the ENTRY= prompt.

CATALOG, Strings, Hyperbolic Functions 15-9

Hyperbolic Functions in the CATALOG

Hyperbolic

Functions The hyperbolic functions are available only from the

CATALOG, The table below lists the hyperbolic functions in

the order in which they appear among the other CATALOG

menu items. The ellipses in the table indicate the presence

of additional CATALOG items.

CATALOG

c0 s h ( Hyperbolic cosine

c0 s h-1 ( Hyperbolic arccosine

s i nh ( Hyperbolic sine

si nh-1 ( Hyperbolic arcsine

t a nh ( Hyperbolic tangent

t a nh- 1( Hyperbolic arctangent

sinh(, cosh(,

tanh(

sinhd(, cosh-l(,

tanh-l(

sinh(, cosh(, and tanh( are the hyperbolic functions. Each is

valid for real numbers, expressions, and lists.

sinh(value)

cosh(value)

tanh(value)

sinh(.5)

.5210953055

cosh( {.25,. 5, I} )

{1.8314131 1.12

sinh-l( is the hyperbolic arcsine function, cosh-l( is the

hyperbolic arccosine function, tanh-l( is the hyperbolic

m'ctangent function. Each is valid for real nulnbers,

expressions, and lists.

sinh- l(value)

cosh- 1(value)

sinh -1(value)

sinh-1({O,l}) I

{0 .881373587}I

tanh-1(-.5)

-.5493061443

15-10 CATALOG, Strings, Hyperbolic Functions

6Programming

Contents Getting Started: Volume of a Cylinder .................... 16-2

Creating and Deleting Programs ......................... 16-4

Entering Colnmand Lines and Executing Programs ...... 16-5

Editing Programs ........................................ 16-6

Copying and Renaming Programs ........................ 16-7

PRGM CTL (Control) Instructions ....................... 16-8

PRGM I/O (Input/Output) Instructions ................... 16-16

('ailing Other Programs as Subroutines .................. 16-22

'_ TEXAS INSTRUMENTS T1=83

PROGRRM: CYL INDER

:PromPt R, H

:_R zH÷V

:Oise "VOLUME IS

.,.j

STATPLOT TBLSET FORMAT CALC TABLE

Programming 16-1

Getting Started: Volume of a Cylinder

Getting Started is a fast-paced introduction. Read the chapter for details.

A program is a set of connnands that the TI-83 executes sequentially, as if you

had entered them fl'om the keyboard. Create a program that prompts for the

radius R and the height H of a cylinder and then computes its volume.

Press [E_ [] [] to display the

PRGM NEW menu.

Press [_ to select 1:Create New. The

Name= prompt is displayed, and alpha-lock

is on. Press [c] [Y][L][I] [N][D] [E] [R], and

then press [g_-gm to name the prograin

CYLINDER.

You are now in the program editor. The

colon ( : ) in the first colunm of the second

line indicates the beginning of a command

line.

Press [E_ [] 2to select 2:Prompt from

the PRGM I/O menu. Prompt is copied to

the command line. Press @ [R] []

@ [H]to enter the variable names for

radius and height. Press [_.

Press [g_ Ix] @ [R] [] @ [H][g?_

@ [v] [_ to enter the expression

_R2H and store it to the variable V.

EXEC EDIT [{L_

BBCreate Flew

PIROGRRM:CYLINDER

PROGRRM: CYL INDER

16-2 Programming

Press J_ [] 3to select 3:Disp fronl the

PRGM I/O menu. Disp is p_ksted to the

conunand line. Press J_ [A-LOCK]["] [V]

[O] [L] [U] [M] [E][_] [I] [S] ["]@1_

@ [V]_ to set up the program to

display" the text VOLUMEIS on one line and

the calculated value of Von the next.

Press J_ [QUIT]to display tile home

screen.

Press [gff_ to display- the PRGM EXEC

menu. The items on this menu are the

names of stored programs.

Press [g_ to paste prgmCYLINBER to the

cmTent cursor location. (If CYLINDER is

not item 1 on your PRGM EXEC menu,

move the cursor to CYLINDERbefore you

press [ggT_. )

PROGRAM:CYLINBER

l:ProMPt R,H I

:=RZH+V

_DisP "VOLUME IS

:i v

_EOIT NEW

LINOER

Prg_CYLINOER|

Press [ggT_ to execute the prograln. Enter

1.8 if)r the radius, and then press [g_.

Enter a for the height, and then press

[g_. The text VOLUME iS, the value of V,

and Done are displayed.

Repeat steps 7 through 9 and enter

different values for R and H.

PPgMCYLINDER

R=?1.5

H=?3

VOLUME IS I

21.20575041

Bone

Programming 16-3

Creating and Deleting Programs

What Is a

Program.'?

Creating a New

Program

Managing

Memory and

Deleting a

Program

A prograln is a set of one or more connnand lines. Each

line contains one or more instructions. When you execute a

prograln, the TI-83 perk)tins each instruction on each

connnand line in the salne order in which you entered

them. The number and size of programs that the TI-83 can

store is limited only by available lnelnolT.

To create a new program, k)llow these steps.

1. Press _ [] to display tile PRGM NEW menu.

EXEC EDIT IIL=I_

HBCreate New

2. Press _ to select 1:Create New. The Name= proInpt

is displayed, and alpha-lock is on.

3. Press a letter fi'oln A to Z or 0 to enter tile first

character of tile new program nalne.

Note: A programname can beone to eight characterslong. The

first character must bea letter fromA to Z or e. The second

through eighth characters canbe letters,numbers, or e.

4. Enter zero to seven letters, numbers, or 0 to conlplete

the new prograln nalne.

5, Press ITNYERI,Tile prograin editor is displayed.

6. Enter one or more prograln commands (page 16-5).

7. Press [_ [QUIT]to leave the progranl editor and return

to the holne screen.

To check whether adequate nlenlol_y- is available for a

prograln you want to enter, press [_ [MEM], and then

select 1:Check RAM froln the MEMORY menu (Chapter 18).

To increase available nlenlolTy- ,press [_ [MEM], and then

select 2:Delete froln the MEMORY menu (Chapter 18).

To delete a specific prograln, press [_ [MEM], select

2:Delete froln the MEMORY menu, and then select 7:Prgm

froln the DELETE FROM seeondalT menu (Chapter 18).

16-4 Progranuning

Entering Command Lines and Executing Programs

Entering a

Program

Command Line

Executing a

Program

Breaking a

Program

You emn enter on a eonulland lille any instruction or

expression that you could execute from the home screen. In

the program editor, each new eonunand line begins with a

colon. To enter more than one instruction or expression on a

single eonunand line, separate each with a colon.

Note: A command line can be longer than the screen is wide; Iong

command lines wrap to the next screen line.

While ill the program editor, you call display and select

fronl menus. You can return to the prograln editor fronl a

menu in either of two ways.

• Select a menu item, which pastes the item to the

cmTent conunand line.

• Press @.

When you complete a eolnmand line, press [NY_. The

CUrSOr nloves to tile next eonulland lille,

Progralns can access variables, lists, lnatrices, and strings

saved in nlenlol_yL If a prograln stores a new wdue to a

variable, list, lnatrix, or string, the prograln changes the

value in nlenlory during execution.

You e an call another prograln as a subroutine (page 16-15

and page 16-22).

To execute a program, begin on a blank line on the home

screen and follow these steps.

1. Press [_ to display- the PRGM EXEC menu.

2. Select a pmgraln nalne froln the PRGM EXEC lnenu

(page 16-7). prgmname is pasted to the home screen

(for example, prgmCYUNDER).

3. Press [_ to execute the program. While the program

is executing, the busy indicator is on.

L_Bt Answer (Ans) is updated during prograln execution.

Last EntlT is not updated as each eonulland is executed

(Chapter 1).

The TI-83 checks for errors during prograln execution. It

does not check for errors msyou enter a progranL

To stop prograln execution, press [_. The ERR:BREAK

nlenu is displayed.

• To return to the honle screen, select 1:Quit.

• To go where the interruption occurred, select 2:Goto.

Programming 16-5

Editing Programs

Editing a

Program

Inserting and

Deleting

Command Lines

To edit a stored program, ff)llow these steps.

1. Press [V_ [] to display- the PRGM EDIT menu.

2. Select a program name froln the PRGM EDIT menu (page

16-7), Up to the first seven lines of the program are

displayed.

Note: The program editor does not display a ¢ to indicate that

a program continues beyond the screen.

3, Edit the program conlnland lines.

• Move tile cursor to the appropriate location, and

then delete, ove_wvrite, or insert.

• Press @ to clear all program eominands on the

eomnmnd line (the lending colon remains), and then

enter a new progrmn eonmmnd.

Tip: To move the cursor to the beginning of a command line, press

[_; to move to the end, press _ lB. To scroll the cursor down

seven command lines, press @ [_. To scroll the cursor up seven

command lines, press @ [_.

To insert a new eonnnand line anywhere in the progranl,

place the cursor where you want the new line, press [_

[tNs], and then press [_T_. A colon indicates a new line.

To delete a conlnland line, place the cursor on the line,

press @ to clear all instructions and expressions on

the line, and then press [ff_ to delete the eonlnland line,

including the colon.

16-6 Programming

Copying and Renaming Programs

Copying and

Renaming a

Program

Scrolling the

PRGM EXEC and

PRGM EDIT

Menus

To copy all conunand lines fronl one progranl into a new

program, follow steps 1 through 5 for Creating a New

Program (page 16-4), and then follow these steps.

1. Press [_ [RCL]. Rcl is displayed on the bottom line of

the prograln editor in the new program (Chapter 1).

2. Press _ [] to display- the PRGM EXEC menu.

3. Select a nalne fronl the menu. prgmname is pasted to

tile bottom line of the program editor.

4. Press [ENt_. All colnnland lines fl'om the selected

program are copied into the new program.

Copying programs h_s at least two convenient

applications.

• You can create a template for groups of instl_ctions

that you use Kequently.

• You can rename a program by copying its contents into

a new program.

Note: You also can copy all the command linesfrom one existing

program to another existing program using RCU

The TI-S3 sorts PRGM EXEC and PRGM EDIT menu items

automatically into alphanumerical order. Each menu only

labels the first 10 itenls using 1 through 9, then 0.

To jump to the first prograln name that begins with a

particular alpha character or O, press @ [letter from A

to Z or 0].

Tip: From the top of either the PRGM EXEC or PRGM EDIT menu,

press [] to move to the bottom. From the bottom, press [] to move to

the top. To scroll the cursor down the menu seven items, press @

[]. To scroll the cursor up the menu seven items, press @ [].

Programming 16-7

PRGM CTL (Control) Instructions

PRGM CTL Menu

Controlling

Program Flow

To display the PRGM CTL (program control) menu, press

[_ from the prograln editor only.

CTL I/0 EXEC

i: If

2: Then

3: Else

4: For(

5: While

6: Repeat

7: End

8: Pause

9: Lbl

O: Geto

A: IS>(

B: DS<(

C: Menu(

D: prgm

E: Return

F: Stop

G: DelVar

H: GraphStyle(

Creates a conditional test.

Executes conlnlands when If is true,

Executes eonnnands when If is false,

Creates an incrementing loop.

Creates a conditional loop.

Signifies the end of a block.

Pauses program execution,

Defnes a label.

Goes to a label.

Increments and skips if greater than.

Decrements and skips if less than.

Defines menu items and branches.

Executes a program as a subroutine.

Returns from a subroutine.

Stops execution.

Deletes a wuiable from within program.

Designates the graph style to be drawn.

These menu items direct the flow of an executing program.

They make it eaksy to repeat or skip a group of commands

during program execution. When you select an item from

the menu, the name is pasted to the cursor location on a

conlnland line in the program.

To return to the program editor without selecting an item,

press @.

Program control instructions tell the TI-83 which

command to execute next in a program, If, While, and

Repeat check a defined condition to determine which

command to execute next, Conditions frequently use

relational or Boolean tests (Chapter 2), as in:

IfA<7:A+I->A

If N=I and M:l:Goto Z

16-8 Programming

If-Then

[ _se If for testing and branching. If condition is false (zero),

then the command inunediately following If is skipped. If

condition is true (nonzero), then the next command is

executed. If instructions can be nested.

:If condition

:command (if true)

:command

Program

PROGRAM: COUNT

:O÷R _

:Lbl

:A+l÷A._ T_-,,

:OisP M i_ _,,,

: If' R_2

I: Stop

1:Goto Z

output

PrgmCOUNT

IR IS

R IS

Then following an If executes a group of commands if

condition is true (nonzero). End identifies the end of the

group of commands.

:If condition

:Then

:command (if true)

:End

:co_and

Program

PROGRRM:TEST

:I÷X:IO÷Y

:I_ X<IO

:Then

:2X+3÷X

:2Y-3÷Y

l:End

I:OisP X,Y

output

PPgmTEST O0_!

Programming 16-9

If-Then-Else Else following If-Then executes a group of commands if

condition is false (zero). End identifies the end of the

group of commands.

:If condition

:Then

:command (if true)

:Else

:command (if false)

:End

:command

Pro_lram

PROGRRM" TESTELSE

:InPut "X=",X

: Ii_X<B

:Then

:Xz÷y

:Else

: X÷Y

:End

:OisP {X,Y}

output

_:_TESTELSE

{5 5}

X=-5 Done

{-5 25}

Done

For( For( loops and inc[_ments. It increments variable fron]

begin to e_d by increme_t, increment is optional (default

is 1) and can be negative (end<begin). end is a nlmKinlunl

or lnininmnl value not to be exceeded. End identifies the

end of the loop. For( loops can be nested.

:For(variable,begin,end[,increme_t])

:command (while end not exceeded)

:command (while e_d not exceeded)

:End

:command

Pro_lram

PROGRRM: SQURRE

:For(R, 0, 8, 2)

::EDi,Ip RZ

output

PPgf_SQURRE Oon40e643616

16-10 Programming

While

Repeat

While performs a group of commands while condition is

true. condition is frequently a relational test (Chapter 2).

condition is tested when While is encountered. If

condition is true (nonzero), the program executes a group

of commands, End signifies the end of the group, When

condition is false (zero), the p_)gram executes each

command following End. While instructions can be nested.

:While condition

:command (while condition is true)

:End

:command

Program

PROGRAM: LOOP

:O÷l

:While _,.,_

:J+l÷J

: I+l÷I

:End

I:DisP J= ,J

Output

,_9mLOOP Done6

Repeat repeats a group of commands until condition is

true (nonzero). It is similar to While, but condition is tested

when End is encountered; therefore, the group of

commands is always executed at least once. Repeat

instructions can be nested.

:Repeat condition

:command (until condition is true)

:End

:command

Program

PROGRRM: RLOOP

I:0÷I

:O÷J >

:Repeat I_6

:J+l÷J

: I+l÷I

:End

FDisP .J= ,J

Output

,_r-cJrqRLOOP Done6

Programming 16-11

End

Pause

End identifies the end of a group of commands. You nmst

include an End instruction at the end of each For(, While, or

Repeat k)op. Also, you nmst paste an End instruction at the

end of each If-Then group and each If-Then-Else group.

Pause suspends execution of the program so that you can

see answers or graphs, During the pause, the pause

indicator is on in the top-right corner. Press _ to

resume execution.

Pause without a value temporarily pauses the pr()gram.

If the DispGraph or Disp instruction has been executed,

the appropriate screen is displayed.

Pause with value displays value on the current home

screen, value can be scrolled.

Pause [value]

Program

PROGRRM: PRUSE

: 10+X

:"XZ+2"÷y1

:DisP "X=", X

:Pause

:DisPGraF-h

I: Pause

l:OisP

output

PPgF_PRUSE

X= 10

16-12 Programming

Lbl, Goto

IS>(

Lbl (label) and Goto (go to) are used together for

branching.

Lbl specifies the label for a conlnland, label can be one or

two characters (A through Z, 0 through 99, or 0).

Lbl label

Goto causes the program to branch to label when Goto is

encountered.

Goto label

Pro_lram

PROGRRM: CUBE

:Lbl 99

: Input R

: If' R._100

:Stop

:Dise R-_

I:Pause

I:Goto 99

output

IPegmCUBE?31105 Done278

IS>( (inc_ment and skip) adds 1 to variable. If the answer

]s > value (which can be an expression), the next

command is skipped; if the answer is _<value, the next

command is executed, variable cannot be a system

variable,

:lS>(variable,value)

:command (if answer _<value)

:command (if answer > value)

Program Output

IPROGRRM:::::DispDi-_pT÷RIs>(R;'6)NOT>ISKIP6> 6 " I_r_mISKIP Done

Note: IS>( is not a looping instruction.

Programming 16-13

DS<(

Menu(

DS<( (decrement and skip) subtracts 1 fronl variable. If the

answer is < value (which can be an expression), the next

command is skipped; if the answer is _>value, the next

command is executed, variable cannot be a system

variable,

:DS<(variable,wdue)

:command (if answer _>value)

:command (if answer < value)

Pro_lram

PROGRRM::I+R DSKIP I

:DS\ (A, 6>

:DisP "> 6"

:DisP 'NOT > 6

Note: DS<( is not a looping instruction.

Menu( sets up branching within a program. If Menu( is

encountered during prograln execution, the menu screen is

displayed with the specified menu items, the pause

indicator is on, and execution pauses until you select a

menu item.

The lnenu title is enclosed in quotation lnarks ( " ). Up to

seven pairs of menu items follow. Each pair conlprises a

text item (also enclosed in quotation marks) to be

displayed as a menu selection, and a label item to which to

branch if you select the corresponding menu selection.

Menu("title","te:ct l",label l ,"te:ct2",label2 .... )

Program

PROGRR_,!: TOSSDICE i

:Menu( TOSS DICE

","FRIR OICE",R, DICE

;WEIGHTED DICE ,

The progranl above pauses until you select 1or 2. If you

select 2, for example, the menu disappears and the

program continues execution at Lbl B.

16-14 Programming

prgm [ _se prgm to execute other programs as subroutines (page

16-22). When you select prgm, it is pasted to the cut, or

location. Enter characters to spell a program name. Using

prgm is equivalent to selecting existing programs fronl the

PRGM EXEC menu; however, it allows you to enter the

name of a program that you have not yet created.

prgmname

Note: You cannot directly enter the subroutine name when using RCL.

You must paste the name from the PRGM EXEC menu (page I6-7).

Return Return quits the subroutine and returns execution to the

calling program (page 16-22), even if encountered within

nested loops. Any loops are ended. An implied Return

exists at the end of any- program that is called as a

subroutine. Within the main program, Return stops

execution and retut_ls to the honle screen.

Stop Stop stops execution of a program and returns to the home

screen. Stop is optional at the end of a program.

DelVar

GraphStyle(

DelVar deletes fronl nlenlory the contents of variable.

DelVar variable

PROGRRH: DELMRTR I

: DelUar. [R]I

GraphStyle( designates the style of the graph to be drawn.

fanction# is the number of the Y= function name in the

current graphing mode. graphstyle is a number from 1to 7

that corresponds to the graph style, as shown below.

1 = ". (line) 5 = '_.)(path)

2 = "i (thick) 6 = .'.'.'(animate)

3=![ (shade above) 7 = ". (dot)

4=[k (shade below)

GraphStyle{fanction#,graphstyle)

For example, GraphStyle(1,5) in Func mode sets the graph

style for Y1 to '_.)(path; 5).

Not all graph styles are available in all graphing modes. For

a detailed description of each graph style, see the Graph

Styles table in Chapter 3,

Programming 16-15

PRGM I/0 (Input/Output) Instructions

PRGM I/0 Menu

Displaying a

Graph with Input

To display the PRGM I/0 (progranl input/output) menu,

press _ [] fronl within tile prograln editor only.

CTL I10 EXEC

i: Input

2: Prompt

3: Disp

4: DispGraph

5: DispTable

6:Output(

7: getKey

8:C1 rHome

9: ClrTable

O: GetCalc(

A: Get(

B: Send(

Enters a value or uses the cursor.

Prompts for enhT of variable values.

Displays text, value, or the home screen.

Displays the current graph.

Displays the current table.

Displays text at a specified position.

Cheeks the keyboard for a keystroke.

Clears the display.

Clears the current table.

Gets a wtriable froln another TI-83.

Gets a varialfle from CBL 2/CBL or CBR.

Sends a variable to CBL 2JCBL or CBR.

These instructions control input to and output fronl a

program during execution. They allow you to enter values

and display- answers during program execution.

To return to the program editor without selecting an item,

press @.

Input without a variable displays the current graph. You

can move the free-moving cursor, which updates X and Y

(and R and 0 for PolarGC format). The pause indicator is

on. Press [gNYgmto resulne prograln execution.

Input

Program

PROGRRM: GIHPUT

:FnOff

:ZOeoimal

I:Input

: Dise X, V

Output

Pr, gmG IHPUTI

I1=_:,6 ?=:!..5

PrgmG IHPUT 2.6

1.5

Done

16-16 Programming

Storing a

Variable Value

with Input

Input with variable displays a ? (question nlark) prompt

dm'ing execution, variable may be a real number, complex

number, list, matrix, string, or Y= function. Dm'ing program

execution, enter a wdue, which can be an expression, and

then press [_T_]. The value is evaluated and stored to

variable, and the program resumes execution.

Input [variable]

You can display- text or the contents of Strn (a string

variable) of up to 16 ehm'acters as a prompt. During

program execution, enter a value after the prompt and then

press [_T_]. The value is stored to variable, and the

progranl resunlos execution.

Input ["text",variable]

Input [Strn,variable]

Program

PROGRRM: HINPUT

-'InPut "YI=",YI

-'InPut "DRTR=",

DRTR

:OisP VI(R)

:OisP YI(LI)

-"Oi_P '_t (LORTR)

output

Pr.gFiH INPUT

?{1,2,3}

Vt ="2X+2"

DRTR={4, 5, 6} 6

{4 6 8}

{10 12 14}

Oone

Note: When a program prompts for input of lists and Yn functions

during execution, you must include the braces ( { } ) around the list

elements and quotation marks ( ") around the expressions.

Programming 16-17

Prompt

Displaying the

Home Screen

During program execution, Prompt displays each variable,

one at a time, followed by =?. At each prompt, enter a

value or expression for each variable, and then pl_ss

[ggT_. The values are stored, and the prograln resulnes

execution.

Prompt variableA [,variableB,...,variable n]

Program

PROGRAM:WINDOW

:PronPt XMin

:Pror_Pt XMax

:ProMPt Ymin

:PromPt YMax

output

PrgMWINOOW Done

XMin=?-le

X_ax=?lO

_Min=?-3

V_ax=?3

Note: Y= functions are not valid with Prompt.

Disp (display) without a value displays the home screen.

To _ew the home screen during program execution, follow

the Disp instruction with a Pause instruction.

Disp

Displaying

Values and

Messages

Disp with one or more values displays the value of each.

Disp [valueA,valueB,valueC,...,value n]

• If value is a variable, the current value is displayed.

• If value is an expression, it is evaluated and the result is

displayed on tile right side of the next line.

• If value is text within quotation marks, it is displayed on

the left side of the current display- line. -) is not valid as

text.

Program

PROGRRM:R RNSWE

:OisP "THE

R IS ,x/2

Output

PPgNA

THE ANSWER IS

1.578796327

Done

If Pause is encountered after Disp, the program halts

temporarily so you can examine the screen, To resume

execution, press [_T_].

Note: If a matrix or list is too large to display in its entirety, ellipses (...)

are displayed in the last column, but the matrix or list cannot be

scrolled. To scroll, use Pause w/ue (page I6-I2).

16-18 Programming

DispGraph

DispTable

Output(

DispGraph (display- graph) displays the current graph. If

Pause is encountered after DispGraph, the program halts

temporarily so you can examine the screen. Press _ to

resume execution,

DispTable (display table) displays tile current table, The

program halts temporarily so you can examine the screen.

Press _ to resume execution,

Output( displays text or value on the current home screen

beginning at row (1 through 8) and column (1 through 16),

ove_vriting any existing characters.

Tip: You maywantto precede Output( with ClrHome (page 16-20).

Expressions are evaluated and values are displayed

according to the current mode settings. Matrices are

displayed in entw format and wrap to the next line. ->is

not valid as text.

Output(fvw,column,"text")

Output(row,column,v_ue)

Program • I

PROGRRM.OJTPUT

:3+5+B

:CIrHoMe

:OutPut(5,4,"RHS

WER:"

:Out.eut.(5,12,B)

For Output( on a Horiz split screen, the nlaxinlunl value for

row is 4.

Programming 16-19

getKey getKey returns a number corresponding to the last key

pressed, according to the key code diagraln below. If no

key- has been pressed, getKey t_turns O. Use getKey inside

loops to transfer control, for example, when creating video

gaines.

Program

PROGRRM:GETKEV

:While 1

:getKeu+K

:While K=O

:getKe_eK

:End

:OisP K

:I¢ K=105

:Stop

:End

Output

PPg_GETKEV 1

Done

Note: _, [_, [_, and

were pressed during

program execution.

Note: You can press [_ at any time during execution to break the

program (page 16-5).

TI-83 Key Code

Diagram C15D12_22!IZD C_ Ei_

IZ] --E521-

ClrHome,

CIrTable ClrHome (clear home screen) clears the home screen

during program execution.

ClrTable (clear table) clears the values in the table during

program execution.

16-20 Programming

GetCalc(

Get(, Send(

GetCalc( gets the contents of variable on another TI-83 and

stores it to variable on the receiving TI-83. variable can be

a real or complex number, list element, list name, matrix

element, matrix name, string, Y= variable, graph database,

or picture.

GetCalc(variable)

Note: GetCalc( does not work between TI-82s and TF83s.

Get( gets data fronl the Calculator-Based Laboratory TM

(CBL 2 TM, CBL TM) System or Calculator-Based Ranger TM

(CBR TM) and stores it to variable on the receiving TI-83.

variable can be a real number, list element, list name,

nmtrix element, nmtrix name, string, Y= variable, graph

database, or picture.

Get(variable)

Note: If you transfer a program that references the Get( command to

the TF83 from a TI-82, the TF83 will interpret it as the Get( described

above. Use GetCalc( to get data from another TI-83.

Send( sends the contents of variable to the CBL 2/CBL or

CBR. You cannot use it to send to another TI-83. variable

can be a real nmnber, list element, list name, matrix

element, matrix name, string, Y= variable, graph database,

or picture, variable can be a list of elements.

Send(variable)

PROGRRM:GETSOUND

:Send({3,.000_5,

99,1,0,0,0,0,1})

:Get(L1)

:Get(Lz)

Note: This program gets sound data

and time in seconds from

CBL 2/CBL.

Note: You can access Get(, Send(, and GetCalc( from the

CATALOG to execute them from the home screen (Chapter 15).

Programming 16-21

Calling Other Programs as Subroutines

Calling a

Program from

Another Program

Notes about

Calling Programs

On the TI-83, any stored program can be called fronl

another program as a subroutine, Enter the name of the

program to use as a subroutine on a line by itself,

You can enter a program name on a conunand line in either

of two ways,

• Press NggM][] to display the PRGM EXEC menu and

select the name of the program (page 16-7). prgmname is

pasted to the cm_'ent cm_sor location on a conullalld line.

• Select prgm from the PRGM CTL menu, and then enter

the program name (page 16-15),

prgmnome

When prgmname is encountered during execution, the next

command that the program executes is the first command

in the second program. It returns to the subsequent

conunand in the first program when it encounters either

Return or the implied Return at the end of the second

program.

Pro_lram

PROGRAM: VOLCYL

:Input "D=",D

:InPut. "H=",H

:PPgrIRRERCIR

:RmH÷V

:DisP V

Output

H=5 62. 83185307

Done

Subroutine I t

PROGRRM:RRERCIR:Return:n.RZ÷A:D/2÷RI

Variables are global.

label used with Goto and kbl is local to the program where

it is located, label in one program is not recognized by

another program. You cannot use 6oto to branch to a label

in another program.

Return exits a subroutine and returns to the calling

program, even if it is encountered within nested loops.

16-22 Programming

7Applications

Contents Comparing Test Results Using Box Plots ................ 17-2

Graphing Pieeewise Functions ........................... 17-4

Graphing Inequalities .................................... 17-5

Sohdng a System of Nonlinear Equations ................ 17-6

Using a Program to Create the Sierpinski Triangle ....... 17-7

Graphing Cobweb Attractors ............................ 17-8

Using a Program to Guess the Coefficients ............... 17-9

Graphing the Unit Circle and Trigonometric (;ma_es ...... 17-10

Finding the Area between Curves ........................ 17-11

Using Parametric Equations: Ferris Wheel Problem ...... 17-12

Demonstrating the Fundamental Theorem of ('aleulus... 17-14

('omputing Areas of Regular N-Sided Polygons .......... 17-16

Computing and Graphing Mortgage Payments ........... 17-18

TEXAS INSTRUMENTS TI-83

STATPLOT TBLSET FORMAT CALC TABLE

Applications 17-1

Comparing Test Results Using Box Plots

Problem

Procedure

An experiment found a significant difference between boys

and gifts pertaining to their ability to identify objects held

in their left hands, which are controlled by the right side of

their brains, versus their right hands, which are controlled

by the left side of their brains, The TI Graphics team

conducted a similm" test for adult men and women.

The test involved 30 slnall objects, which pm'ticipants were

not allowed to see. First, they held 15 of the objects one by

one in their left hands and guessed what they were. Then

they held the other 15 objects one by one in their right hands

and guessed what they were. Use box plots to compare

_isually the eotTect-guess data from this table.

Correct Guesses

Women

Le_

Women

Right

Men

Left

Men

Right

1, Press _ 5to select 5:SetUpEditor, Enter list names

WLEFT, WRGHT, MLEFT, and MRGHT, separated by

conlnlas, Press [_. The stat list editor now contains

only these four lists.

2. Press [_Y] 1 to select 1:Edit.

3. ]_nter into WLEFT the number of correct guesses each

woman made using her left hand (Women Left). Press []

to move to WRGHT and enter the number of correct

guesses each woman made using her right hand (Women

Right).

4. Likewise, enter each lnan's correct guesses in MLEFT

(Men Left) and MRGHT (Men Right).

5. Press [_ [STAT PLOT], Select 1:Plot1. Turn on plot 1;

define it as a modified box plot 4>- that uses WLEFT.

Move the eta'sot to the top line and select Plot2. Turn on

plot 2; define it as a modified box plot that uses WRGHT,

17-2 Applications

6.Press@.Turnoffallfunctions,

7.Press_. SetXscl=landYscl=0.Press_ 9to

select9:ZoomStat.Thisadjuststheviewingwindowand

displaystheboxplotsforthewomen'sresults.

8. Press_.

kd=9.5

Use [] and [] to exalnine minX, Ol, Med, O3, and maxX

for each plot. Notice the outlier to the women's right-

hand data. What is the median ff)r the left hand? For the

right hand? With which hand were the women more

accurate guessers, according to the box plots?

9. Examine the men's results. Redefine plot 1 to use

MLEFT, redefine plot 2 to use MRGHT. Press _.

_" Men's right-hand data

d=7.5 ""

Press [] and [] to examine minX, Q1, Med, Q3, and maxX

for each plot. What difference do you see between the

plots?

10.Compare the left-hand results. Redefine plot 1 to use

WLEFT, redefine plot 2 to use MLEFT, and then press

to examine minX, Q1, Med, Q3, and maxX for each

plot. Who were the better left-hand guesse_\% men or

women?

11. Company the right-hand results. Define plot 1 t_) use

WRGHT, define plot 2 to use MRGHT, zu_d then press

to examine minX, OI, Med, O3, and maxX for each

plot. Who were the better right-herod guesse_?

In the original experiment boys did not guess as well

with right hands, while girls guessed equally well with

either hand. This is not what our box plots show for

adults. Do you think that this is because adults have

learned to adapt or because our sample was not large

enough?

Applications 17-3

Graphing Piecewise Functions

Problem

Procedure

The fine for speeding on a road with a speed limit of 45

kilometers per hour (kph) is 50; plus 5 for each kph from

46 to 55 kph; plus 10 for each kph froln 56 to 65 kph; plus

20 for each kph from 66 kph and above. Graph the

piecewise function that describes the cost of the ticket.

The fine (Y) as a function of kilometers per horn" (X) is:

Y=0 0<X_<45

Y= 50 + 5 (X- 45) 45 < X_< 55

Y= 50 + 5 *10 +10 (X - 55) 55<X_<65

Y= 50 + 5. 10 + 10. 10 + 20 (X- 65) 65 < X

Press Noel. Select Func and the default settings.

Press @. Tm'n off all functions and stat plots. Enter the

Y= function to describe the fine. Use the TEST menu

operations to define the pieeewise function. Set the

graph style for Y1 to ". (dot).

PloLt F'lol:2 PI<,I:_:

'..Y1 B(50+5(X-45) )

(45<X) (X_<55)+(10

0+10(X-55) ) (5.J< X

)(X_<65)+(200+20(

X-65) ) (65< X)I

,,yz=

,,V_=

Press _ and set Xmin=-2, Xscl=10, Ymin=-5, and

Yscl=10. Ignore Xmax and Ymax; they are set by AX and

AY in step 4.

Press [_ [QUIT] to return to the holne screen. Store 1to

AX, and then store 5to AY, AX and AY m'e on the

VARS Window X/Y secondary menu. AX and AY specify

the horizontal and vertical distance between the centers

of adjacent pixels, Integer values for AX and AY produce

nice values for tracing,

Press _ to plot the function. At what speed does

the ticket exceed 250?

17-4 Applications

Graphing Inequalities

Problem

Procedure

Graph the inequality 0.4X;_ - 3X + 5 < 0.2X + 4. Use the

TEST menu operations to explore the values of X where the

inequMity is true and where it is false,

Press [M0_]. Select Dot, Simul, and the default settings.

Setting Dot mode changes 'all graph style icons to

'. (dot) in the Y= editor.

Press @. Turn off all functions and stat plots. Enter the

left side of the inequality as Y4and the right side as Y5.

'..9 _B. 4X^3-3X+5

I"-Y _B. 2X+411

...Yti=

[..Y?=

Enter the statement of the inequality as Y6. This

function evaluates to 1if true or 0 if false.

'..Y_B. 4X"3-3X+5

'..Y_B; 2X+4

'-.Y_B_<Y_II

.5??=

Press _ 6 to graph the inequality in the standard

window.

Press _ [] [] to move to Y6, Then press [] and []

to trace the inequality, observing the value of Y,

--' ;' = [

11=.ti_8;;9;_87 I?=i.

Press @. Turn off Y4,Y5,and Y6.Enter equations to

graph only the inequality.

'..'.?_=, 4X"3-3X+5

".Y_=. _.X+4

'..9_=_,_<9_

..YnBYt*9_

Press _. Notice that the values of Y7 and Y8 are

zero where the inequality- is false.

ll:':t._Bg._6;_ !Y:0

?ll=¥fi_?_;

:I=':L4Bg._fi,_ t=0

Applications 17-5

Solving a System of Nonlinear Equations

Problem

Procedure

Using a graph, solve the equation X :_- 2X = 2cos(X). Stated

another way-, solve the system of two equations and two

unknowns: Y = X:_-2X and Y = 2cos(X), Use ZOOM factors

to control the decimal places displayed on the graph.

Press [_, Select the default lnode settings. Press @.

Turn off 'all functions and stat plots. Enter the functions.

\V_BX_-2X

",'toB2cos (X) I

Press _ 4 to select 4:ZDecimal, The display shows

that two solutions may exist (points where the two

functions appear to intersect).

Press _ [] 4 to select 4:SetFactors fi'om the ZOOM

MEMORY menu. Set XFact=lO and YFact=lO.

Press _ 2 to select 2:Zoom In. Use [_, [], [], and []

to move the free-moving cm_or onto the apparent

intersection of the functions on the right side of the

display. As you move the cursor, notice that the X and Y

values have one decimal place.

5, Press [_ to ZOOln in. Move the cursor over the

intersection, As you move the cursor, notice that now

the X and Y values have two decimal places.

6, Press [_ to zoom in again. Move the free-lnoving

cursor onto a point exactly- on the intersection, Notice

the number of decimal places.

7. Press K_ [CALC] 6 to select 6:intersect. Press _ to

select the first cmwe and [_ to select the second

cm_'e. To guess, move the trace cursor near the

intersection, Press [_. What are the coordinates of

the intersection point?

8, Press _ 4 to select 4:ZDecimal to redisplay the

original graph,

9. Press _. Select 2:Zoom In and repeat steps 4

through 8 to explore the apparent function intersection

on the left side of the display.

17-6 Applications

Using a Program to Create the Sierpinski Triangle

Setting up the

Program

This program creates a drawing of a falnous ffactal, the

Sietpinski Triangle, and stores the drawing to a picture. To

begin, press #ggM] [] [] 1. Name the prograln SlERPINS,

and then press [gg7_l. The program editor is displayed.

Program PROGRAM:SIERPI NS

:FnOff :ClrDraw

:Pl otsOff

:AxesOff

::0->Ymi0->Xminn::l->Ymaxl->Xmax } Set _qewing window.

:rand->X: rand->Y

: Fo r ( K, 1,3 00 0 ) -1-- Beginning of Fo rgroup.

:rand->N

:If N<1/3 }

:Then

:. 5X->X If/Then group

:.SY->Y

:End

:If I/3<N and N<2/3 7

:Then

:. 5(, 5+X)->X If/Then group.

:. 5( I+Y)->Y

:End

:If 2/3<N }

:Then

:. 5 ( l+X )->X If/Then group,

:.5Y->Y

:End

: Pt On( X, Y ) Draw point.

: End End of For group.

:StorePi c 6 Store picture.

After you execute the prograln above, you can recall and

display the picture with the instruction RecallPic 6.

Applications 17-7

Graphing Cobweb Attractors

Problem

Procedure

Using Web format, you can identify points with attracting

and repelling behavior in sequence graphing,

Press [MO0_. Select Seq and the default nlode settings.

Press _ [FORMAT]. Select Web format and tile default

fonnat settings,

Press @, Clear all functions and tul_ off all stat plots.

Enter the sequence that corresponds to the expression

Y = K X(1-X),

u(n)=Ku(n- 1)(1 - u(n- 1))

u(nMin)=.01

Press [g_ [QUIT] to return to tim holne screen, and then

store 2.9 to K.

Press _, Set the window variables,

nMin=0 Xmin=0 Ymin=-.26

nMax=lO Xmax=l Ymax=l.1

PlotStart=l Xscl=l Yscl=l

PlotStep=l

Press _ to display- the graph, and then press [] to

trace the cobweb. This is a cobweb with one attractor,

lu=Hu,:_-:i.XI-u(_-I)) ..- I

Change K to 3.44 and trace the graph to show a cobweb

with two attractors.

Change Kto 3.54 and trace the graph to show a cobweb

with four attractors,

U=I_u{_-lXl-uCo-1))

17-8 Applications

Using a Program to Guess the Coefficients

Setting Up the

Program

This program graphs the function A sin(BX) with random

integer coefficients between 1 and 10. Try to guess the

coefficients and graph your guess at C sin(DX). The

program continues until your guess is correct.

Program PROGRAM:GUESS

:PlotsOff :Func

:FnOff :Radian

:ClrHome

:"Asin(BX)"_Yl

:"Csin(DX)"_Y2

:GraphStyle(l,l)

:GraphStyle(2,5)

:FnOff 2

:randlnt(l,lO)_A

:randlnt(l,lO)_B

:O_C:O_D

:-2_Xmin

:2_Xmax

:_/2_Xscl

:-lO_Ymin

:lO_Ymax

:l_Yscl

:DispGraph

:Pause

:FnOn 2

:Lbl Z

:Prompt C,D

:DispGraph

:Pause

:If C=A

:Text(l,l,"C IS OK")

:If C_A

:Text(l,l,"C IS WRONG")

:If D=B

:Text(l,50,"D IS OK")

:If D_B

:Text(l,50,"D IS WRONG")

:DispGraph

:Pause

:If C=A and D=B

:Stop

:Goto Z

Define equations,

Set line and path graph

styles.

- Initialize coefficients.

Set viewing window.

=Display graph,

Prompt for guess,

- Display graph,

Display results,

- Display graph.

Quit if guesses are

-- correct,

Applications 17-9

Graphing the Unit Circle and Trigonometric Curves

Problem

Procedure

[ _sing parametric graphing mode, graph the unit circle and

tile sine curve to show the relationship between them.

Any function that can be plotted in Func mode can be

plotted in Par mode by defining the X component as T and

the Y component as F(T).

1. Press [MffffE].Select Par, Simul, and the default settings.

2. Press _. Set the viewing window.

Tmin=0 Xmin=-2 Ymin=-3

Tmax=2_ Xmax=7.4 Ymax=3

Tstep=.1 Xscl=_/2 Yscl=l

3, Press @, Turn off all functions and stat plots. Enter the

expressions to define the unit circle centered on (0,0).

Not:J, PI0L2 P10t)

",XIT_cos (T)

Y1T lisin(T)

\XzT fiT

YzT lisin(T)

4. Enter the expressions to define the sine curve.

PlotJ. Plot_ PloI:3

",X1T lic.os(T)

YIT lisin(T)

"..XzTliT

Y.-Tlisin(T)

5. Press _. As the graph is plotting, you may press

[ggT_ to pause and [ggT_ again to resulne graphing as

you watch the sine function "unwrap" from the unit

circle.

:{IT=C.,:,;(T) Y1T=_irff.T)

== =

Note: You can generalize the unwrapping. Replace sin(T) in Y2Twith

anyother trigfunction to unwrapthatfunction.

17-10 Applications

Finding the Area between Curves

Problem

Procedure

Find the area of the region bounded by

fix) = 300x/(x 2 + 625)

g(x) = 3cos(. ix)

x = 75

Press [MffffE].Select the default lnode settings.

Press _. Set the viewing window.

Xmin=0 Ymin=-5

Xmax=100 Ymax=10

Xscl=10 Yscl=l

Xres=l

3. Press @. Turn off all functions and stat plots. Enter the

upper and lower functions.

Y1=a00x/(x2+625)

Y2=3COS(.1X)

4. Press [g_] [CALC]5to select 5:Intersect. The graph is

displayed. Select a first cutwe, second cut,'e, and guess

for the intersection toward the left side of the display.

The solution is displayed, and the value of X at the

intersection, which is the lower limit of the integral, is

stored in Ans and X.

Press _ [QUIT] to go to the home screen. Press

[_ [DRAW]7and use Shade( to see the area graphically.

Shade(Y2,Y1,Ans,75)

6, Press [2_] [QUIT] to return to tile honle screen. Enter tile

expression to evaluate the integral for the shaded

region,

fnlnt(Y1-Y2,X,Ans,75)

The area is 325.839962.

Applications 17-11

Using Parametric Equations: Ferris Wheel Problem

Problem

Procedure

[ _sing two pai_\q of parametric equations, determine when

two objects in motion are closest to each other in the Salne

plane.

A ferris wheel has a diameter (d) of 20 meters and is

rotating counterclockwise at a rate (s) of one revolution

ever T 12 seconds. The paralnetric equations below

describe the location of a fen'is wheel passenger at time T,

where (x is the angle of rotation, (0,0) is the bottom center

of the fen'is wheel, and (10,10) is the passenger's location

at the rightmost point, when T=0.

X(T) = r cos (x where (x = 2xTs and r = d/2

Y(T) = r + r sin (x

A person standing on the ground throws a ball to the ferds

wheel passenger. The thrower's ann is at the sanle height as

the bottoln of the ferds wheel, but 25 meters (b) to the right

of the fen'is wheel's lowest point (25,0). The person throws

the ball with velocity (v0) of 22 meters pet" second at an

angle (0) of 66 ° froln the horizontal. The parametric

equations below describe the location of the ball at tinle T.

X(T) = b - Tv0 cos0

Y(T) = Tv0 sin0 - (g/2) T _ where g =

9,_ nl/see 2

1, Press [MO0_. Select Par, Simul, and the default settings.

Simul (sinmltaneous) mode sinmlates the two objects in

nlotion over tinle.

Press _. Set the viewing window.

Tmin=0 Xmin=-13 Ymin=0

Tmax=12 Xmax=34 Ymax=31

Tstep=.l Xscl=lO Yscl=lO

Press @. Turn off all functions and stat plots. Enter tile

expressions to define tile path of the ferris wheel and tile

)ath of the ball. Set tile graph style for X2T to 4j (path).

i PloL:L Plot_: Plot_:

",X1T B1Ocos(xT/6)

YITBlO+lOsin(_T

t6)

*)XzT B25-22Toos(6

5 ° )

ViT B22Tsin(66 ° )

-(9.8/2)TZ

Tip: Try setting the graph styles to ",.'_XlT and 0X2T, which simulates a

chair on the ferris wheel and the bal! flying through the air when you

press _.

17-12 Applications

4. Press [_ to graph the equations. Watch closely as

they are plotted. Notice that the ball and the ferris

wheel passenger appear to be closest where the paths

cross in the top-right quadrant of the ferris wheel,

5, Press [_. Change the _iewing window to

concentrate on this portion of the graph.

Tmin=l Xmin=0 Ymin=10

Tmax=3 Xmax=23.5 Ymax=25.5

Tstep=.03 Xscl=10 Yscl=10

6. Press _. After the graph is plotted, press [] to

nlove neat" tile point on the ferris wheel where the paths

cross, Notice the values of X, Y, and T,

IIT=t0_.O_;(1T_ YtT=IO÷10;;_

7, Press [] to nlove to the path of the ball. Notice the

values of X and Y (T is unchanged). Notice where the

cursor is located. This is the position of the ball when

the fetTis wheel passenger passes the inter\section. Did

the ball or the passenger reach the intersection first?

You can use _ to, in effect, take snapshots in tilne

and explore the relative behavior of two objects in

motion,

Applications 17-13

Demonstrating the Fundamental Theorem of Calculus

Problem 1

Procedure 1

Using the functions fnlnt( and nDeriv( fronl the MATH menu

to graph functions defined by integrals and derivatives

demonstrates graphically that:

F(x)= 1 1/tdt=ln(x),x>0 and that

Ifx 1

Dx 1 1/t dt = 1/x

Press 1_. Select tile default settings.

Press _. Set the viewing window.

Xmin=.01 Ymin=-l.5

Xmax=10 Ymax=2.5

Xscl=l Yscl=l

Xres=3

Press @, Turn off 'allfunctions and stat plots. Enter tile

numerical integral of 1/T from 1 to X and the function

ln(X). Set the graph style for Y1 to "..(line) and Y2 to

.4:,(path).

Plot:l. Pl¢,t2 P1ot_

",Yt Bi'n InL( l/T, T,

1,X)

_¢2Bln(g)

Press _. Press [], [], [], and [] to eolnpare the

values of Y1 and Y2,

Press @. Turn off Y1 and Y2, and then enter the

numerical derivative of the integral of 1/X and the

function 1/X. Set the graph style for Y3 to ', (line) and Y4

to _. (thick),

Ploti p1,,:,l:2 Plot_:

:,Y:,_oior_1_T,T,

_Y2'=In(g)

_BnOeri_,(Y1 ,X,

_,YuBI/X

Press _. Again, use the cursor keys to compare the

values of the two graphed functions, Y3 and Y4.

17-14 Applications

Problem 2

Procedure 2

Explore the functions defined by

X X X

Y:f-2 t2dt' f0 t2dt' and f2 t2dt

Press @, Turn off all functions and stat plots. Use a list

to define these three functions sinmltaneously. Store

the function in Ys.

_'_=nDerib=(Yt"°Yz=lr_(x)l'x)Pl°t:LPlol:Z F'loL_. _ _

'_Y_=I/X T, (

,,Y_B?nlnL(T z ,

i-::,o,2>,x)

Press _ $ to select $:ZStandard.

Press _. Notice that the functions appear identical,

only shifted vertically by a constant.

Press @, Enter the numerical derivative of Y5 in Y6,

\Y_=nDeriv(Y1, X,

"*Y_=I/X

"..Y_B_nIn÷.(TZ, T, (

-2,0,2>,X)

\YeBnOer iv(Y_, X,

Press _. Notice that although the three graphs

defined by Y5 are different, they share tile same

derivative,

N="t.9£_Bi!_?i¢).6_,fiBt?9

Applications 17-15

Computing Areas of Regular N-Sided Polygons

Problem Use the equation solver to store a fornmla ff)r the m'ea of a

regulm" N-sided polygon, and then solve for each vm'iable,

given the other variables. Explore the fact that the limiting

case is the area of a circle, _r 2.

Consider the fonnula A = NB 2 sin(_/N) cos(_/N) for the

m'ea of a regulm' polygon with N sides of equal length and

B distance from the center to a vertex.

N = 4 sides N = 8 sides N = 12 sides

Procedure 1, Press [_ 0to select 0:Solver froln the MATH menu,

Either the equation editor or the interactive solver

editor is displayed. If the interactive solver editor is

displayed, press [] to display the equation editor,

2, Enter the fonnula as 0=A-NB2sin(_ /N)cos(_ /N), and

then press [_. The interactive solver editor is

displayed.

R_NBZsin(_/N).,,=O

bound={ -1 E99, 1...

3, Enter N=4 and B=6 to find the area (A) of a square with

a distance (B) from center to vertex of 6 centimeters,

4, Press [] [] to nlove the cursor onto A, and then press

@ [SOLVE], The solution for Ais displayed on the

interactive solver editor.

:l-NBZsin(_/N)...=el

: 2.00o000000I

B=6

bound={ -1 E99, 1...

le_t-rt=e

5. Now solve for Bfor a given area with vm'ious number of

sides. Enter A=200 and N=6. To find the distance B,

lnove the cursor onto B, and then press @ [SOLVE].

6, Enter N=8, To find the distance B, nlove the cursor onto

B, and then press @ [SOLVE]. Find Bfor N=9, and

then for N=10.

17-16 Applications

FindtheareagivenB=6, and N=10, 100, 150, 1000, and

10000. Compare your results with =62 (the area of a circle

with radius 6), which is approximately 113.097.

7. Enter B=6. To find the area A, move the cursor onto A,

and then press @ [SOLVE]. Find Afor N=10, then

N=100, then N=160, then N=1000, and finally N=10000.

Notice that as N gets large, the area A approaches _B 2.

Now graph the equation to see visually how the area

changes as the number of sides gets lm'ge.

8, Press NgffE].Select the default lnode settings,

9. Press _. Set the viewing window.

Xmin=O Ymin=O

Xmax=200 Ymax=150

Xscl=lO YscI=IO

Xres=l

10.Press @. Turn off all functions and stat plots. Enter the

equation for the m'ea. I Jse X in place of NSet the graph

styles as shown.

Plot]. F'10t2 F'10t._

xViBXBZsin<_/X)c

os(_/X)

-W._BnB z

,.'-,as=

xY.1=

,,V_:=

,&'6=

11.Press _. After the graph is plotted, press I O0[gNgggl

to trace to X=100. Press 150 [ggTgm.Press 188 [ggTg_.

Notice that _LsX increases, the value of Yconverges to

=62, which is approximately 113.097. Y2=_B2 (the area of

the circle) is a horizontal asymptote to Y1. The area of

an N-sided regular polygon, with r as the distance fl'om

the center to a vertex, approaches the area of a circle

with radius r (_r 2) as N gets large.

;' 1:1-,'B;a_;ir=r..'n"r'N),2.o_;( Tr_'g:E '¢_::Tr£:::

8:tBB _Y=lt3.0762B, 8:tEE _Y:ti3.0973_ •

Applications 17-17

Computing and Graphing Mortgage Payments

Problem

Procedure

You at_ a loan officer at a mortgage conlpany, and you

recently closed on a 30-yem' holne lnortgage at 8 percent

interest with monthly payments of 800, The new home

owners want to know how nmch will be applied to the

interest and how nmch will be applied to the principal

when they make the 240th payment 20 years from now.

1, Press [_ and set the fixed-decimal lnode to 2decimal

places. Set the other mode settings to the defaults.

2. Press [_ [FINANCE] 1to display" the TVM Solver. Enter

these values.

N=360.00

I_=8.00

PV=0.00

PMT=800.00

FV=0.00

P/V=I2.00

C/V=12,00

PMT:[_=[II_BEGIN

Note: Enter a positive number (800) to show PMT as a cash

inflow. Payment values will be displayed as positive numbers on

the graph. Enter 0 for FV, since the future value of a loan is 0 once

it is paid in ful!. Enter PMT: END, since payment is due at the end

of a period.

3, Move the cursor onto the PV= prompt, and then press

@ [80LYE], The present value, or lnortgage amount,

of the house is displayed at the PV= prompt,

N=360.00

I%=8.00

PV=-IO9026,B0

PMT=B00.00

FV=0.00

P/V=12.00

C/Y=12.00

PMT:LqIL_ BEGIN

17-18 Applications

Nowcomparethegraphoftheamountofinterestwiththe

graphoftheamountofprincipalforeachpayment.

4, Press[NffffE].Set Par and Simul.

5, Press @, Turn off all functions and stat plots. Enter

these equations and set the graph styles as shown.

Plot1 Plol:_ Plot_:

",XIT BT

Vi TBFPr'n(T, T)

_XzT BT

'Y'zT B_- Int.< T, T)

".X_T BT

V:_T BVIT +VZT

Note: ZPrn( and ZInt( are located on the FINANCE CALC menu,

6, Press _. Set these window variables.

Tmin=l Xmin:0 Ymin=0

Tmax=360 Xmax=360 Ymax=1000

Tstep=12 Xscl=10 Yscl=100

Tip: To increase the graph speed, change Tstep to 24.

7. Press _. After the graph is drawn, press 240

to move the trace cursor to T=240, which is equivalent

to 20 years of payments.

IIT=T ?tT='_F'r_rKT__

The graph shows that ff)r the 240th payment (X=240),

358.03 of the 800 pay3nent is applied to principal

(Y:368.03).

Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.

Applications 17-19

8. Press[] tomovethecursorontothefunctionfor

interestdefinedbyX2TandY2T.Enter240.

The graph shows that for the 240th payment (X=240),

441.97 of the 800 payment is interest (Y=441 .gT).

9. Press _ [QUIT] [_ [FINANCE] 9to paste 9:bal( to the

home screen. Check the figures from the graph.

_ai(239) -66295.33

_nsm(.08/12)

-441,97

At which monthly payment will the principal allocation

surp_kss the interest allocation?

17-20 Applications

18Menrn2gq/ement

Contents Checking A_ailable MemolTy ............................. I8-2

Deleting Items from MemmTy ............................ I8-3

Clearing Entries and List Elements ...................... 18-4

Resetting the TI-83 ...................................... 18-5

TEXAS INSTRUMENTS TF83

RRM_

Delete...

3:Clear Entries

4: CIRRI ILists

5: Reset...

STAT PLOT TBLSET FORMAT CALC TABLE

Memory Management 18-1

Checking Available Memory

MEMORY Menu To display the MEMORY menu, press [_ [MEM].

MEMORY

i: Check RAM...

2: Delete...

3: Clear Entries

4: ClrAllLists

5: Reset..,

Reports memory availability/usage,

Displays DELETE FROM menu,

Clem's ENTRY (l_kst-entry storage).

Clears all lists in memo_T.

Displays RESET menu (all/defaults).

Displaying the

Check RAM

Screen

Check RAM displays the Check RAM screen. The top line

t_ports the total amount of available nlenlol_y-. The

remaining lines report the amount of lnelnot7 each

variable type is using. You can check this screen to see

whether you need to delete variables from memo_T to

nmke room for new data, such as programs.

To check RAM usage, follow these steps.

1. Press [2_] [MEM] to display the MEMORY menu.

RRM...

_:Clear Entries

_:ClrRllLists

5:Reset...

2. Select I :Check RAM to display the Check RAM screen.

The TI-S3 expresses memory quantities in bytes.

MEM FREE 27285

Real 15

ComPlex 8

List 8

Matrix 8

Y-Vats 248

Prgm 14

4Pio 8

GOB 0

String 0

Note: The J_in the left column of

the bottom row indicates that you

can scroll or page down to view

more variable types.

Note: Real, List, Y-Vars, and Prgm variable types never reset to

zero, even after memory is cleared.

To leave the Check RAM screen, press either [_ [QUIT] or

@. Both options display- the home screen.

18-2 Memmw Management

Deleting Items from Memory

Deleting an Item To increase available nlenlol_ by deleting the contents of

any- variable (real or colnplex nulnber, list, matrix,

Y= variable, prograln, picture, graph database, or string),

follow these steps.

1. Press [2_] [MEN]to display the MEMORY lnenu.

2. Select 2:Delete to display- the DELETE FROM secondalTy-

nleno.

3. Select the type of data you want to delete, or select 1:All

for a list of all variables of 'all types. A screen is

displayed listing each variable of the type you selected

and the number of bytes each variable is using.

For exalnple, if you select 4:List, the DELETE:List screen

is displayed.

DELETE: Li_t

_LI 63

DATA 39

4. Press [] and [] to nlove tile selection cursor (_) next to

the item you want to delete, and then press _. The

variable is deleted fronl nlenlot_y-. You Call delete

individual vm'iables one by one froln this screen.

To leave ally DELETE: screen without deleting anything,

press [_ [QUIT],which displays the home screen.

Note: You cannot delete some system variables, such as the last-

answer variable Ans and the statistical variable RegEQ

Memory Management 18-3

Clearing Entries and List Elements

Clear Entries

CIrAIILists

Clear Entries clears the contents of the ENTRY (last entry)

storage area (Chapter 1). To cleat" the ENTRY storage area,

follow these steps.

1, Press [_ [MEM] to display the MEMORY menu.

2, Select 3:Clear Entries to paste the instruction to the

home screen.

3. Press [_ to clear the ENTRY storage area.

IcleaP Entt'ie_one I

To cancel Clear Entries, press @,

Note: If you select 3:Clear Entries from within a program, the Clear

Entries instruction is pasted to the program editor, and the Entry

(last entry) is cteared when the program is executed.

CIrAIILists sets to 0tile dimension of each list in lllelllOl_yL

To clear all elements from all lists, follow these steps,

1, Press [_ [MEM] to display the MEMORY menu,

2, Select 4:ClrAIIkists to paste the instruction to the home

screen.

3. Press _ to set to 0the dimension of each list in

nlenlory.

IC1rA11Lists lionel

To cancel CIrAIILists, press @.

CIrAIILists does not delete list nanles fronl nlenlol_y-, fronl

the LiST NAMES menu, or froln the stat list editor.

Note: If you select 4:CIrAIIkists from within a program, the

CIrAIILists instruction is pasted to the program editor. The lists are

cleared when the program is executed.

18-4 MemolT Management

Resetting the TI-83

RESET

Secondary Menu

Resetting All

Memory

The RESET seconda[7 lnenu gives you the option of

resetting all memory (including default settings) or

_setting the default settings while prese_Mng other data

stored in lnelno_T, such as programs and Y= functions.

Resetting all nlenloFy Oil the TI-83 restores nlenlory to the

factor7 settings, It deletes all nonsystem variables and all

programs. It resets all system variables to the default

settings.

Tip: Before you reset all memory, consider restoring sufficient

available memory by deleting only selected data (page I8-3).

To reset all nlenlory on the TI-83, follow these steps.

1. Press [2_] [MEM] to display the MEMORY menu.

2. Select 5:Reset to display the RESET secondary menu.

.._. Mer_or-u...

2:: Defau lts...

3, Select 1:All Memory to display the RESET MEMORY

tertimT nlenu.

Resetting memoru

erases all data

and Programs,

4. Read the message below tile RESET MEMORY menu.

• To cancel memoL_- reset and retm'n to tile home

screen, select 1:No.

• To erase fronl lnelnol T all data and progralns, select

2:Reset. All factory defaults are restored.

Mere cleared is displayed on the home screen.

IMem cleared

Note:When you clearmemory, thecontrastsometimeschanges.If

thescreenisfadedorblank,adjustthecontrast(ChapterI).

Memory Management 18-5

Resetting

Defaults When you reset defaults on the TI-83, all defaults are

restored to the factory settings. Stored data and programs

are not changed.

These are some examples of TI-83 defaults that are

restored by resetting the defaults.

• Mode settings such as Normal (notation); Func

(graphing); Real (numbers); and Full (screen)

• Y= functions off

• Window variable values such as Xmin=-lO; Xmax=lO;

Xscl=l; YscI=I; and Xres=l

• Stat plots off

• Format settings such as eoordOn (graphing coordinates

on); AxesOn; and ExprOn (expression on)

• rand seed value to 0

To reset all TI-83 factory defaults, follow these steps.

1. Press [g_] [MEM] to display the MEMORY menu.

2. Select 5:Reset to display the RESET secondary menu.

3. Select 2:Defaults to display the RESET DEFAULTS

tertimT menu.

4. Consider the consequences of resetting defaults.

• To cancel reset and return to the home screen, select

1:No.

• To restore factory default settings, select 2:Reset.

Default settings are restored. Defaults set is

displayed on the home screen.

Defaults set

18-6 Memmw Management

19 ci° municati°n

Contents Getting Started: Sending Variables ....................... 19-2

TI-83 kINK ............................................... 19-3

Selecting Items to Send .................................. 19-4

Receiving Items .......................................... 19-5

Transmitting Items ....................................... 19-6

Transmitting Lists to a TI-82 ............................. 19-8

Transmitting from a TI-82 to a TI-8:I ..................... 19-9

Backing Up MemmTy"..................................... 19-10

TEXAS INSTRUMENTS 1"1=83

RECEIVE

to TI82...

STAT PLOT TBLSET FORMAT CALC T._,B LE

Communication Link 19-1

Getting Started: Sending Variables

Getting Started is a fast-paced introduction. Read the chapter for details.

Create and store a wu'iable and a matrix, and then transfer then] to another

TI-83.

On the home screen of the sending unit,

press 5[] 5Fgg6gl@ O. Press [gfff_ to

store 5.5 to Q.

Press[_[[][_[[l 1[]2[_[11[_[[

] 3 _ 412_ [1 ] [2_ [1 ] _ [NN_ 1.

Press [_ to store the lnatrix to [A].

3. Connect the calculators with the link

cable. Push both ends in firmly.

4. On the receiving unit, press [_ [LINK] [] tO

display tile RECEIVE menu. Press 1to

select 1:Receive. The message Waiting... is

displayed and the busy indicator is on.

SEHD [_

IERec.e ive

5, On the sending unit, press [2_] [LINK] to

display the SENDmenu.

6, Press 2to select 2:All-. The All- SELECT

screen is displayed.

Z,_AI RECEIVE

3:Prgm...

4:List...

5:List.s to TI82...

6:GOB...

7gPic...

TRRNSMIT

k_ LIST

.L_ LIST

[R] MRTRX

Window WINOW

RclWindouZSTO

TblSet TABLE

_Q RERL

Press [] until the selection cursor ( _) is

next to [A] MATRX.Press [ggTEg].

Press [] until the selection cursor is next

to QREAL. Press [_. A square dot next

to [A] and Oindicates that each is selected

to send.

9. On the sending unit, press [] to display the

TRANSMIT menu.

10. On the sending unit, press 1to select

1:Transmit and begin transmission. The

receiving unit displays the message

Receiving....When the items are

transmitted, both units display the name

and type of each transmitted variable.

SELECT IdII._IIIiIIi

[llTransr_it

Receiving,..

[ R]MRTRX

'Q REDRLne

19-2 Conununication Link

TI-83 LINK

TI-83 Link

Capabilities

Linking Two

TI-83s

Linking a TI-82

and a TI-83

Connecting Two

Calculators with

the Cable

Linking to a CBR

or the CBL 2/CBL

System

Linking to a PC

or Macintosh

The TI-83 has a port to connect and conlnlunicate with

another TI-83, a TI-82, the Calculator-Based Lal)oratory TM

(CBL 2 TM, CBL TM) System, the Calculator-Ba_ed Ranger TM

(CBWM), or a personal conlputer. The unit4o-unit link

cable is included with the TI-83. This chapter describes

how to comnmnicate with another calculator.

You can transfer all variables and programs to another

TI-83 or backup the entire nlenlol'y of a TI-83. The

softwm'e that enables this communication is built into the

TI-83. To transmit from one TI-83 to another, follow the

steps on pages 19-6 and 19-7.

You can transfer fronl a TI-82 to a TI-83 all variables and

programs. Also, you cal_ tral_sfer from a TI-83 to a TI-82 lisL_

L1 through L6.

The softwaxe that enables this conunm_ication is built int_) the

TI-83. To tral_nlit data from a TI-82 t_) a TI-83, follow the

steps on pages 19-6 at_d 19-7.

• You cannot perform a memory backup from a TI-82 to a

TI-83,

• The only data type you can transmit from a TI-83 to a

TI-82 is list data stored in L1 through L6, Use the kINK

SEND menu item 5:Lists to TI82 (page 19-8).

1. Insert either end of the cable into the port very firmly.

2. Insert the other end of the cal>le into the other

calculator's port.

CBR and the CBL 2/CBL System are optional accessories

that connect to a TI-83 with the unit-to-unit link cal fie,

With a CBR or a CBL 2/CBL and a TI-83, you can collect

and analyze real-world data.

TI-GRAPH LINK TM is an optional accessory- that links a TI-S3

to enable conmmnication with a personal conlputer.

Communication Link 19-3

Selecting Items to Send

LINK SEND Menu

Selecting Items

to Send

To display the LINK SEND menu, press [_ [LINK].

SEND RECEIVE

i:A11 +.., Displays

2:A11 -.., Displays

3 : P rgm... Displays

4: Li st... Displays

5: Lists to T182... Displays

6 : GDB... Displays

7 : Pi c... Displays

8 : Matrix... Displays

9 : Real ... Displays

0 : Compl ex.., Displays

A: Y Vars... Displays

B: String.,.

C: Back Up.,,

M1 items selected.

'all items deseleeted.

all progranls names.

'all list names,

list names L1 through Ls.

'all graph databases.

M1 picture data types,

'all matrix data types.

M1 real vmiables,

'all complex variables.

M1 Y= variables.

Displays all string variables.

Selects all for backup to TI-83.

When you select an item on the LINKSEND menu, the

corresponding SELECT screen is displayed.

Note: Each SELECT screen, except All+ SELECT, is displayed

initially with no data selected.

To select items to send on the sending unit, follow these

steps.

1. Press [2_] [LINK]to display" the LINKSEND menu.

2. Select the menu item that describes the data type to

send. The corresponding SELECT screen is displayed.

3. Press [] and [] to nlove the selection cursor (_) to an

item you want to select or deselect.

4. Press _ to select or deselect the iteln. Selected

nalnes are nlarked with a ..

_ TRRNSMIT

EQU

• Y_ EQU

Xl T EQU

Vi T EQU

u EQU

FWindow WINDW

RclWindowZSTO

5, Repeat steps 3 and 4 to select or deselect additional items.

19-4 Conununication Link

Receiving Items

LINK RECEIVE

Receiving Unit

DuplicateName

Insufficient

Memory in

Receiving Unit

To display the LINK RECEIVE menu, press _ [LINK] C_.

SEND RECEIVE

1 : Re ee i v e Sets unit to receive data transmission.

VClmnyou select 1:Receivefrom the LINK RECEIVE menu on

the receiving unit, the message Waiting... and the busy

indicator are displayed. The receiving unit is ready to

t_eeive transmitted items. To exit the receive mode

without receiving items, press [0N],and then select 1:Quit

from the Error in Xmit menu.

To transmit, follow the steps on page 19-6.

When transmission is complete, the unit exits the receive

mode. You can select 1:Receive again to receive mot_

items. The receiving unit then displays a list of items

received. Press [_ [QUIT] to exit the receive mode.

During transmission, if a variable name is duplicated, the

Dup[icateName menu is displayed on the receixqng unit.

Dupl i cateName

i : Rename

2: Overwrite

3: Omit

4: Quit

Prompts to rename receiving variable.

Ove_wvrites data in receiving variable.

Skips transmission of sending variable.

Stops transmission at duplicate variable.

When you select 1:Rename,the Name=prompt is displayed,

and alpha-lock is on. Enter a new variable name, and then

press [_. Transinission resuines.

When you select 2:Overwrite, the sending unit's data

ovet_vrites the existing data stored on the receiving unit.

Transmission resumes.

When you select 3:Omit, the sending unit does not send the

data in the duplicated variable name. Transmission

resumes with the next item.

When you select 4:Quit, transmission stops, and the

receiving unit exits receive mode.

During transmission, if the receiving unit does not have

sufficient lnelnol T to receive an item, the Memory Full lnenu

is displayed on the receiving unit.

• To skip this item for the current transmission, select

1:Omit. Transmission resumes with the next item.

• To cancel the transmission and exit receive mode,

select 2:Quit.

Communication Link 19-5

Transmitting Items

Transmitting

Items

Stopping a

Transmission

Error Conditions

To transmit selected items after you have selected items to

send on the sending unit (page 19-4) and set the receiving

unit to receive (page 19-5), follow these steps.

1. Press [] on tile sending unit to display- the TRANSMIT

nlenu,

I T%Ts I

2. Confirm that Waiting,.. is displayed on the receiving

unit, which indicates it is set to receive (page 19-5).

3. Press [g_-gm to select 1:Transmit. The name and type of

each item are displayed line by line on the sending unit

as the item is queued for transmission, and then on tile

receiving unit as each item is accepted.

*'799t EQoUoneEQUI*V_VIRotei_,,ing...EQ_oneEQUI

After all selected items have been transmitted, the lnessage

Done is displayed on both calculators. Press [] and [] to

scroll through the names.

To stop a link transmission, press []_]. The Error in Xmit

menu is displayed on both units. To leave the error menu,

select 1:Quit.

A transnlission error occurs after one or two seconds if:

• A cable is not attached to the sending unit.

• A cable is not attached to the receiving unit.

Note: If the cane is attached, push it in firmly and try again.

• The receiving unit is not set to receive transmission.

•You attempt a backup between a TI-82 and a TI-Sa.

•You attempt a data transfer from a TI-83 to a TI-82 with

data other than lists L1 through L6 or without using

menu item 5:Lists to TI82.

Although a transmission error does not occur, these two

conditions nlay prevent successful transmission.

• You ttT to use Get( with a calculator instead of a

CBL 2/CBL or CBR.

• You tit to use GetCalc( with a TI-82 instead of a TI-83,

19-6 Conununication Link

Transmitting

Items to an

Additional TI-83

After sending or receiving data, you can repeat the same

transmission to additional TI-83 units--from either the

sending unit or the receiving unit--without having to

reselect data to send. The current items remain selected.

Note: You cannot repeat transmission if you selected All+ or All-.

To transmit to an additional TI-83, follow these steps.

1, Set the TI-83 to receive (page 19-5),

2, Do not select or deselect any new items to send. If you

select or deselect an item, all selections or deselections

from the previous transmission are cleared.

3, Disconnect the link cable from one TI-S3 and connect it

to the additional TI-83,

4. Set the additional TI-83 to receive (page 19-5),

5, Press [7_ [LINK] on the sending TI-83 to display the

LINK SEND menu.

6, Select the menu item that you used for the l_kst

transmission. The data from your last transmission is

still selected.

7, Press [] to display the LINK TRANSMIT menu,

8, Confirm that the receiving unit is set to receive

(page 19-5).

9, Press [EfiY_ to select 1:Transmit and begin translnitting.

Communication Link 19-7

Transmitting Lists to a TI-82

Transmitting

Lists to a TI-82 The only data type you can transmit fronl a TI-83 to a TI-82

is list data stored in L1 through L6.

To transmit to a TI-82 the list data that is stored to TI-83

lists L1, L2, L3, L4, LS, or L6, follow these steps.

1, Set the TI-82 to receive (page 19-5).

2, Press [_ [LINK] 5on the sending TI-83 to select

5:Lists to TI82. The SELECT screen is displayed.

3, Select each list to transmit.

4. Press [] to display the LINK TRANSMIT menu,

5, Confirm that the receiving unit is set to receive

(page 19-5).

6, Press [_ to select 1:Transmit and begin transmitting.

Note: If dimension > 99 for a T1-83 list that is selected to send, the

receiving TI-82 will truncate the list at the ninety-ninth element during

transmission.

19-8 Coinnmnication Link

Transmitting from a TI-82 to a TI-83

Resolved

Differences

between the TI-82

and TI-83

Unresolved

Differences

between the TI-82

and TI-83

GenerMly, you can transmit items to a TI-83 fronl a TI-82,

but differences between tile two products may affect some

transmitted data, This table shows differences for which

the software built into the TI-83 automatically adjusts

when a TI-83 receives TI-82 data,

TI-82 TI-83

nMin PlotStart

nStart nMin

Un u

Vn v

UnStart u(nMin)

VnStart v(nMin)

TblMin TblStart

For example, if you transmit from a TI-82 to a TI-83 a

program that contains nStart on a command line and then

display" the p_ogram on the receiving TI-83, you will see

that nMin has automatically replaced nStart on the

conlnland line,

The s(dtware built into the TI-S3 cannot resolve some

differences between the TI-82 and TI-83, which are

described below. You nmst edit the data on the TI-83 after

you transmit to account for these differences, or the TI-83

will misinterpret the data.

The TI-83 reinterprets TI-82 prefix functions to include

()pen parentheses, which may add extraneous parentheses

to transmitted expressions.

For example, if you transmit sin X+5 from a TI-82 to a

TI-83, the TI-83 reinteq_rets it as sin(×÷5. Without a closing

parenthesis after ×, the TI-83 interprets this as sin(×÷5), not

the stun of 5and sin(X).

If a TI-82 instruction that the TI-83 cannot translate is

transmitted, the ERR:INVALID menu is displayed when the

TI-83 attempts to execute the instruction. For example, on

the TI-82, the chm'acter group Un-1 is pasted to the cursor

location when you press _ [un- 1]. The TI-83 cannot

directly translate Un-1 to the TI-83 syntax u(n-1), so the

ERR:INVALID menu is displayed.

Note: T1-83 implied multiplication rules differ from those of the T1-82.

For example, the TI-83 evaluates 1/2X as (1/2)*X, while the TI-82

evaluates 1/2X as 1/(2"X) (Chapter 2).

Communication Link 19-9

Backing Up Memory

Memory Backup

Receiving Unit

To copy the exact contents of lnelnol_y- in the sending TI-83

to the lnelnory of the receiving TI-83, put the other unit in

t_ceive mode. Then, on the receiving unit, select C:Back Up

fronl the LINK SEND menu.

Warning: C:Back Up ove_wvrites the lnelnol_y- in the

receiving unit; all information in the lnelnory of the

receiving unit is lost.

Note: If you do not want to do a backup, select 2:Quit to return to

the LINK SEND menu.

•Select 1:Transmit to begin transmission.

BItTt-ansr_ i t

2: Quit

As a safety check to prevent accidental loss of nlenlory,

the message WARNING - Backup is displayed when the

t_cei_lng unit receives notice of a backup.

• To continue with the backup process, select 1:Continue.

The backup transmission begins.

• To prevent the backup, select 2:Quit.

Note:If a transmissionerroris returnedduring a backup, the receiving

unitisreset.

Memory Backup When the backup is complete, both the sending calculator

Complete and receiving calculator display a confirlnation screen.

IMEMOR'? BACKUDPonel

19-10 (domnmnication Link

ATablesand Reference

Information

Contents Table of Functions and Instructions ..................... A-2

TI-83 Menu Map ......................................... A-39

Variables ................................................ A-49

Statistics Formulas ...................................... A-50

Financial Formulas ...................................... A-54

Tables and Reference Information A-1

Table of Functions and Instructions

Functions return a value, list, or matrix. You can use functions in an expression.

Instructions initiate an action. Some functions and instructions have arguments.

Optional arguments and accompanying conunas are enclosed in brackets ( [ ] ).

For details about an item, including argument descriptions and restrictions, turn

to the page listed on the right side of the table.

From the CATALOG, you can paste any function or instruction to the home

screen or to a conunand line in the program editor. However, some functions

and instructions are not wflid on the home screen. The items in this table

appear in the same order as they- appear in the CATALOG.

f indicates keystrokes that are valid in the program editor only. Some keystrokes

display menus that are available only in the program editor. Others paste mode,

fommt, or table-set instructions only- when you are in the program editor.

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

abs(value) Returns the absolute value of a [_

real number, expression, list, NUM

or matrix. 1:abs( 2-13

10-10

abs(complex 'value) Returns the nmgnitude of a

complex nmnber or list. CPX

5:abs( 2-19

valueA and valueB Returns 1 if both valueA and [_ [TEST]

valueB are € 0. valueA and LOGIC

valueB ean be real numbers, 1:and

expressions, or lists. 2-26

angle{value) Returns the polar angle of a [_

complex number or list of CPX

complex numbers. 4:angle( 2-19

ANOVA(listl,list2 Performs a one-way analysis of [gg_]

[,list3,...,list20]) variance for comparing the TESTS

means of two to 20 F:ANOVA(

populations. 13-25

Ans Returns the last answer. [_ [ANS] 1-18

A-2 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

augment(matrixA,matrixB) Retm'ns a mahlx, width is

matrixB appended to matrixA MATH

as new colunms. 7:augment( 10-14

augment(listA,listB) Returns a list, which is listB _ [LIST]

concatenated to tile end of OPS

listA. 9:augment( 11-15

AxesOff Turns off the graph axes. ; [2_ [FORMAT]

AxesOff 3-14

AxesOn Turns on tile graph axes. ; [2_ [FORMAT]

AxesOn 3-14

a+bl Sets tile mode to reetangular i I_

complex number mode (a+bi). a+bi 1-12

bal(npmt[,roundvalue]) Computes the balance at npmt [_ [FINANCE]

for an amortization schedule CALC

using stored values for PV, I%, 9:bal(

and PMT and rounds the

computation to roundvalue. 14-9

binomcdf(numtrials,p[,x]) Computes a cumulative [_ [D}STR]

probability at xfor the discrete DISTR

binomial distribution ,slth tile A:binomcdf(

specified numtrials and

probabilityp of success on

each trial. 13-33

binompdf(numtriols,p[,x]) Computes a probability at xfor [_ [DtSTR]

tile discrete binomial DISTR

distribution _ith tile specified 0:binompdf(

nuratrials and probabilityp of

success on each trial. 13-33

x2cdf(low6_pbound, Computes tile g2distribution _ [DISTR]

upperbound,dy') probability between DISTR

lower'bound and upped)ound 7:x2cdf(

for the specified degrees of

freedom dJ2 13-31

Tables and Reference Information A-3

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

z2pdf(x,dj ") Computes the probabi]ity [_ [DISTR]

density function (pdf) for tile DISTR

X2 distribution at a specified x6:z2pdf(

value for the specified degrees

of freedom df 13-31

z2-Test(observedmatrix, Performs a ehi-square test. i [_

expeetedmatrix drmqflag=l draws results; TESTS

[,drawflag]) drmqflag=O calculates results. C:x2-Test( 13-22

Circle(X,Y, radius) Draws a circle with center [_ [DRAW]

(X,Y) and radius. DRAW

9:Circle( 8-11

Clear Entries Clears the contents of the Last [_dl [MEM]

EntKy storage area. MEMORY

3:Clear Entries 18-4

ClrAIILists Sets to 0the dimension of all [_ [MEM]

lists in memoKy'. MEMORY

4:ClrAIIkists 18-4

ClrDraw Clears all drawn elements from [_ [DRAW]

a graph or dra_lng. DRAW

1:ClrDraw 8-4

ClrHome Clears the home screen, i [0ggM]

IIO

8:Clrl-tome 16-20

Clrkist listnamel Sets to 0the dimension of one [gg_]

[,listuame2, ..., or more listnames. EDIT

listname n] 4:ClrList 12-20

ClrTable Clears all values from the i [gggM]

table. I/O

9:ClrTable 16-20

conj(value) Returns tile complex conjugate [_TH]

of a complex number or list of CPX

complex numbers. 1:conj( 2-18

Connected Sets connected plotting mode; i

resets all Y= editor graph-style Connected

settings to "... 1-11

A-4 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

CoordOff TLims oft" cursor coordinate i- _ [FORMAT]

value display. CoordOff 3-14

CoordOn Turns on cursor coordinate 1 [2_ [FORMAT]

value display. CoordOn 3-14

cos(value) Returns cosine of a [g6N]

real nunlber, expression, or

list. 2-3

cos-l(volue) Returns arccosine of areal Kffd] [cos -1]

number, expression, or list. 2-3

cosh(value) Returns hyperbolic cosine of a Kffd] [CATALOG]

real number, expression, or cosh(

list. 15-10

cosh-l(value) Returns hyperbolic arccosine Kffd] [CATALOG]

of a real number, expression, cosh-l(

or list. 15-10

CubicReg [Xlistname, Fits a cubic regression model NTAf]

Ylistname_fr_qlist, to Xlistname and Ylistname CALC

regequ] with frequencyfrvqlist, and 6:CubicReg

stores tile regression equation

to vegequ. 12-26

cumSum(list) Returns a list of the cumulative [_ [LIST]

stuns of tile elements in list, OPS

starting _lth the first element. 6:cumSum( 11-12

cumSum(matrix) Returns a matrix of tile

cunmlative sums of matrix MATH

elements. Each element inthe 0:cumSum(

returned nmtrlx is a cunmlative

SUnl of a matrix cohlnln fi'om

to[) to bottom. 10-15

dbd(datel,date2) Calculates the number of days Kffa] [F,NANCE]

between date1 ram date2 using CALC

the actual-day-count method. D:dbd( 14-13

value_Dec Displays a real or complex

number, expression, list, or MATH

matrix in decimal format. 2:_Dec 2-5

Tables and Reference Information A-5

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Degree Sets degree angle mode. i

Degree 1-11

DelVar variable Deletes from nlemolTy" the i

contents of .variable. CTL

G:DelVar 16-15

DependAsk Sets table to ask for -1-[_ [TBLSET]

dependent-variable values. Depend: Ask 7-3

DependAuto Sets table to generate -;- [_ [TBLSET]

dependentwariable values Depend: Auto

automatically. 7-3

det(matrix) Returns determinant of

matrix. MATH

l:det( 10-12

DiagnosticOff Sets dia_lostlcs-offmode; r, r2, _ [CATALOG]

and R2 are not displayed as DiagnosticOff

regression model results. 12-23

DiagnosticOn Sets diagnostics-on mode; r, r2, [_ [CATALOG]

and R2 m'e displayed as DiagnosticOn

regression model results. 12-23

dim(listname) Returns tile dilnenslon of [_ [LIST]

listname. OPS

3:dim( 11-11

dim(matri:vname) Returns tile dimension of

matri:_'name as a list. MATH

3:dim( 10-12

length->dim(listname) Assigns anew dimension _[LIST]

(length) to a new or existing OPS

listname. 3:dim( 11-11

{rows,columns}-> Assigns new dimensions to a

dim(matri:vname) new or existing matri:vname. MATH

3:dim( 10-13

Disp Displays the home screen. i IIO

3:Disp 16-18

Disp [valueA,valueB, Displays each value, i

valueC,...,value n] I/O

3:Disp 16-18

A-6 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

DispGraph Displays tile graph. ; I_

I/O

4:DispGraph 16-19

DispTable Displays tile table. -;-IIO

5:DispTable 16-19

value_DMS Displays value il1 [)MS fornlat. [_ [ANGLE]

ANGLE

4:_DMS 2-24

Dot Sets (lot plotting mode; resets i [_

all.Y= editor graph-style settings Dot

to ... 1-11

DrawF expression Draws expression (in terms of [_ [DRAW]

X) on the graph. DRAW

6:OrawF 8-9

Drawlnv expression Draws the immerse of [_ [DRAW]

expression by plotting X values DRAW

on the y-axis and Y values on 8:Drawlnv

the x-axis. 8-9

:DS<(variable,value) Decrements variable by 1; i

:commandA skips cornmandA if variable < CTL

:commands value. B:DS<( 16-14

e^(power) Returns e raised to power. _ [ex] 2-4

e^(list) Returns a list of e raised to a _ [ex]

list of powers. 2-4

Exponent: Returns value times 10 to the [_ [EE]

valueEexponez_t exponez_t. 1-7

Exponent: Retm'ns list elements times 10 [_ tEE]

listEe_onent to the exponent. 1-7

Exponent: Returns matrix elements times [_ tEE]

rnatrixEexponecnt 10 to the exponea_t. 1-7

_Eff(nominal rate, Computes the effective interest [_ [FINANCE]

compounding periods) rate. CALC

C:_Eff( 14-12

Else

See If:Then:Else

Tables and Reference Information A-7

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

End Identifies end of For(, -;-

If-Then-Else, Repeat, or While CTL

loop. 7:End 16-12

Eng Sets engineering display mode. i

Eng 1-10

Equ)String(Y= va_;Stru) Converts tile contents of a Y= [_ [CATALOG]

vat to a string and stores it in Equ)String(

Stru. 15-7

expr(string) Com_erts SD'_ng to all [_ [CATALOG]

expression and executes it. expr( 15-7

ExpReg [Xlistname, Fits an exponential regression

}qistuame,flreqlist,regequ] model to Xlistuame and CALC

lqistuame with frequency 0:ExpReg

freqlist, and stores the

regression equation to regequ. 12-26

ExprOff Turns off the expression -;- [_ [FORMAT]

display during TRACE. ExprOff 3-14

ExprOn Turns on the expression -;- [_ [FORMAT]

display during TRACE. ExprOn 3-14

Fcdf(lowerbound, Computes the F distribution _M] [DISTR]

upperbound, probability between DISTR

numerator df, lowerbound and upperbound 9:Fcdf(

denominator dr) for the specified numerator df

(degrees of freedom) and

denominator djr 13-32

Fill(value,raatri:_name) Stores value to each element in

mat.ri:vname. MATH

4:Fill( 10-13

Fill(volue,listuame) Stores value to each element in _ [LIST]

listuame. OPS

4:Fill( 11-11

Fix # Sets fixed-decimal mode for # i

of decimal places. 0123456789

(select one) 1-10

Float Sets floating decimal mode. i Float 1-10

A-8 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

fMax(expression,variable, Retm'ns the value of variable

lower',upper'[,tolerance]) where the local maximum of MATH

expression occm's, between 7:fMax(

lower" and upper', with

specified toleronee. 2-6

fMin(expression,variable, Returns tile value of variable

lower',upper'[,toleranee]) where the local mininmn] of MATH

expression occm's, between 6:fMin(

lower" trod upper', with

specified toleronee. 2-6

fnlnt(expression,variable, Returns the function integral of [_

lower',upper'[,tolerance Dexpression with respect to MATH

variable, between/ower, and 9:fntnt(

upper', with specified

toleronce. 2-7

FnOff [function#, Deselects all Y= functions or

function#,...,function n] specified Y= functions. Y-VANS On/Off

2:FnOff 3-8

FnOn [function#, Selects all Y= fimctions or

.function#,..._function n] specified Y= functions. Y-VANS On/Off

1:FnOn 3-8

:For(variable,begin,er_d Executes commands through i [gggM]

[,incremer_t]) End, incrementing variable CTL

:commands fi'om begin by increment until 4:For(

:End variable>end.

:commands 16-10

fPart(value) Returns the fractional part or [_

pm'ts of a real or complex NUM

number, expression, list, or 4:fPart( 2-14

matrix. 10-11

Fpdf(x,numerotardf, Computes tile g distribution [_ [DtSTR]

denominator dy) probability between DISTR

lower'bound and upperbound 8:Fpdf(

for tile specified numerator df

(degrees of freedom) and

dermminator df 13-32

Tables and Reference Information A-9

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

value_Frac Displays a real o1"eon]plex [_

nmnber, expression, list, or MATH

matrix as a fraction simplified 1 :_Frac

to its simplest terms. 2-5

Full Sets full screen mode. i [_

Full 1-12

Func Sets function graphing mode. i Func 1-11

gcd(valueA, valueB) Returns the greatest common [_

divisor of volueA and valueB, NUM

which can be realnmnbers or 9:gcd(

lists. 2-15

geometcdf_,x) (;omputes a emnulative [_ [DISTR]

probability at x, the number of DISTR

the trial on which the first E:geometcdf(

suceess oeeurs, for tile diserete

geometric distribution with tile

specified probability of success

p. 13-34

geometpdf(p,x) Computes a probability at x, the [_ [DISTR]

number of the trial on which the DISTR

first success occurs, for the D:geometpdf(

discrete geometric distribution

wlth the specified probability of

success p. 13-34

Get(variable) Gets data from the CBL 2/CBL -;-

System or CBR and stores it in I/O

variable. A:Get( 16-21

GetCalc(variable) Gets contents of variable on i

another TI-83 and stores it to I/O

variable on the receix_ N TI-83. 0:GetCalc( 16-21

getKey Returns tile key code for the i [0_

current keystroke, or 0, if no IIO

key is pressed. 7:getKey 16-20

Goto label Transfers control to label. iCTL

O:Goto 16-13

A-IO Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

GraphStyle(function#, Sets a grophstyle for -;-

grophstyle#) function#. CTL

H:GraphStyle( 16-15

GridOff Turns off grid format, i- _ [FORMAT]

6ridOff 3-14

GridOn Turns on grid format. -;- _ [FORMAT]

GridOn 3-14

G-T Sets graph-table vertical i

split-screen mode. G-T 1-12

Horiz Sets horizontal i I_bg]

split-sereen mode. Horiz 1-12

Horizontal yDraws a horizontal line at y. [_ [DRAW]

DRAW

3:Horizontal 8-6

identity(dimension) Returns the identity matrix of

dimension rows x dimension MATH

eolumns. S:identity( 10-13

:If condition If condition = O (false), skips i [g_

:commandA commandA. CTL

:commands 1:If 16-9

:If condition Executes commands from i [0ggM]

:Then Then to End if condition = 1 CTL

:commands (true). 2:Then

:End

:commands 16-9

:If condition Executes commands from i [0ggM]

:Then Then to Else if condition = 1 CTL

:commands (true); from Else to End if 3:Else

:Else condition =O(false).

:commands

:End

:commands 16-10

imag(value) Returns the imaginmTy

(nonreal) part of a complex CPX

number or list of complex 3:imag(

numbers. 2-18

Tables and Reference hfformation A-11

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

IndpntAsk Sets table to ask for -;-[_ [TBLSET]

independent-variable values. Indpnt: Ask 7-3

IndpntAuto Sets table to generate -1-[2_ [TBLSET]

independent-variable values Indpnt: Auto

automatically. 7-3

Input Displays graph. -1-

IIO

1:Input 16-16

Input [.variable] Prompts for value to store to i

Input ["text",variable] variable. I/0

1:Input 16-17

Input [Strn,variable] Displays Strn and stores -;-

entered value to variable. I/O

1:Input 16-17

inString(s#qng,subs#qng Returns tile (-haraeter position [_ [CATALOG]

[,start]) in string of tile first eharaeter inString(

of substring beginning at start. 15-7

int(value) Returns the lm'gest integer _<a [_TH]

real or complex ntmlber, NUM

expression, list, or matrkx. 5:int( 2-14

10-11

Elnt(pmtl,pmt2 Conlputes tile sum, rounded to [_ [FINANCE]

[,roundvalue]) roundvalue, of the interest CALC

amount between pmtl and A:Zlnt(

pint2 for an amortization

schedule. 14-9

invNorm(area[,p,_;]) Computes tile inverse _ [DtSTR]

emnulative normal distribution DISTR

funetion for a given area under 3:invNorm(

the normal distribution curve

specified by/_ and a. 13-30

iPart(value) Returns tile integer part of a

real or eomplex number, NUM

expression, list, or matrix. 3:iPart( 2-14

10-11

A-12 Tables and Reference Inforination

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

irr(OFO,OFList[,OFF_q]) Returns the interest rate at [_ [FINANCE]

which the net present vahle of CALC

file cash flows is equal to zero. 8:irr( 14-8

:lS>(variable,value) Increments variable i

:commandA by 1; skips commandA if CTL

:commands variable>volue. A:IS>( 16-13

Llistname Identifies the next one to five [_ [UST]

characters as a user-created OPS

list name. B:L 11-16

LabelOff Turns off axes labels. -1-[_ [FORMAT]

LabelOff 3-14

LabelOn Turns ol1 axes labels, i- [_ [FORMAT]

LabelOn 3-14

Lbl label Creates a label of one or two i

characters. CTL

9:Lbl 16-13

Icm(valueA,valueB) Returns the least conunon [_

inultiple of volueA and valueB, NUM

which can be real nulnbers or 8:lcm(

lists. 2-15

length(string) Returns the number of [_ [CATALOG]

chm'aeters in st_ng, length( 15-8

Line(X1,Y1Jd2,Y2) [)raws a line from (X1,Y1) to [_ [DRAW]

(X2,Y2). DRAW

2:Line( S-5

Line(X1,Y1,X2,Y2,0) Erases a line from (X1,Y1) to [_ [DRAW]

(X2,Y2). DRAW

2:Line( 8-5

Tables and Reference Information A-13

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

LinReg(a+bx) [Xlistname, Fits a linear regression inodel

Iqistname,freqlist, to Xlistname and Iqistname CALC

regequ] with frequencyfrvqlist, and 8:LinReg(a+bx)

stores the regression equation

to regequ. 12-26

kinReg(ax+b) [Xlistname, Fits a linear regression model [g_g]

Iqistname_freqlist, to Xlistname and Iqistname CALC

regequ] with frequency.fr_qlist, and 4:kinReg(ax+b)

stores the regression equation

to regequ. 12-25

LinRegTTest [Xlistname, Performs a linear regression i [g_g]

Iqistname,freqlist, and a t-test, alternative=-1 is TESTS

olternative,regequ] <; alternative=O is €; E:LinRegTTest

alternative=l is >. 13-24

AList(list) Returns a list containing the _[LIST]

differences between OPS

consecutive elements in list. 7:AList( 11-12

List_ matr(listnamel,..., Fills matrixname colunm by [_ [LIST]

listname n,matri:_'name) cohmm with the elements from OPS

each specified listuame. 0:List _matr( 10-14

11-15

In(value) Returns the natural logarithm @

of a real or complex number,

expression, or list. 2-4

knReg [Xlistname, Fits a logarithmic regression [g_T]

Ylistname,fr_qlist, model to Xlistuame and CALC

regequ] }qistuame with frequency 9:LnReg

freqlist, and stores the

regression equation to regequ. 12-26

log(value) Returns logarithm of a real or [[OG]

complex nilnlber, expression,

or list. 2-4

A-14 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Logistic [Xlistname, Fits a logistie regression mode] [gTAT]

YTist.name,fr_ql.ist, to Xlistname and YTistname CALC

regequ] with frequeneyfr_qlist, and B:kogistic

stores the regression equation

to regequ. 12-27

Matr_ list(matrix, Fills each listname with [_ [LIST]

listnameA,...,listname n) elements from eaeh column in OPS 10-14

matrix. A:MatO list( 11-16

MatrMist(mat.rix, Fills a listuame _lth elements [_ [LIST]

column#,listname) from a specified eoluran# in OPS 10-14

matrix. A:MatO list( 11-16

rnax(valueA,valueB) Returns the larger of valueA

and valueB. NUM

7:rnax( 2-15

max(list) Returns largest real or [2_] [LIST]

complex element in list. MATH

2:max( 11-16

rnax(listA,listB) Retm'ns a real or eomplex list of [2_] [LIST]

the larger of each pair of MATH

elements in listA and listB. 2:max( 11-16

max(value, list) Retm'ns a real or complex list of [_ [LIST]

the larger of value or each list MATH

element. 2:max( 11-16

rnean(list[,frvqlist]) Returns the mean of list with [_ [LIST]

frequeney frvqlist. MATH

3:mean( 11-16

median(list[,fr_qlist]) Returns the median of list with [_ [LIST]

frequeney frvqlist. MATH

4:median( 11-16

Med-Med [Xlistname, Fits a median-median model to

Ylistname_fr_qlist, Xlistname and Ia'ist'name _lth CALC

regequ] frequeneyfrvqlist, and stores 3:Ned-Ned

the regression equation to

regequ. 12-25

Menu("title","textl"',labell Generates a menu of up to i [_

[,...,"textT',labelT]) seven items during program CTL

exeeution. C:Menu( 16-14

Tables and Reference hfformation A-15

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

min(valueA,valueB) Returns smaller of valueA and

valueB. NUM

6:min( 2-15

min(list) Returns smallest real or _ [LIST]

complex element in list. MATH

l:min( 11-16

min(listA,listB) Returns real or complex list of [_ [LIST]

tile smaller of each pair of MATH

elements in listA and listB. 1:min( 11-16

min(value,list) Returns a real or complex list _ [LIST]

of the smaller of value or each MATH

list element. 1 :min( 11-16

valueA nCr valueB Returns the number of [_

combinations of valueA taken PRB

valueB at a time. 3:nOr 2-21

value nCr list Returns a list of the

combinations of value taken PRB

each element in list at a time. 3:nCr 2-21

list nCr value Returns a list of the

combinations of each element PRB

in list taken value at a time. 3:nCr 2-21

listA nCr listB Returns a list of the [_TH]

combinations of each element PRB

in listA taken each element in 3:nOr

listB at a time. 2-21

nDeriv(expression,variable, Returns approximate [_

value[,e]) numerical derivative of MATH

expression with respect to 8:nDeriv(

variable at value, with

specified e. 2-7

*Nom(ef_t_ct'ive rate, Computes the nominal interest [2_] [FINANCE]

compounding pe/riods) rate. CALC

B:*Nom( 14-12

Normal Sets normal display mode. i Normal 1-1O

A-16 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

normalcdf(low_rbound, (;omputes tile normal [_ [DISTR]

upperbound [,_,(_])distribution probability D IST R

between low_rbound and 2:normalcdf(

upperbound for the specified p

and _. 13-27

normalpdf(x[,p,(_]) (;omputes tile probability [_ [DtSTR]

density function for the nornlal DISTR

distribution at a specified x1 :normalpdf(

value for tile specified/_ and c_. 13-29

not(value) Returns 0if value is :/: 0. value [_ [TEST]

can be a real number, LOG IC

expression, or list. 4:not( 2-26

valueA nPr valueB Returns tile number of [_TH]

permutations of volueA taken PRB

valueB at a time. 2:nPr 2-21

value nPr list Returns a list of tile [_TH]

permutations of value taken PRB

each element in list at a time. 2:nPr 2-21

list nPr value Returns a list of tile [_TH]

permutations of each element PRB

in list taken value at a time. 2:nPr 2-21

listA nPr listB Returns a list of tile [_TH]

permutations of each element PRB

in listA taken each element in 2:nPr

listB at a time. 2-21

npv(interest rate,CFO, Computes the sum of the [2_] [FINANCE]

CFList[,CFFreq]) present values for cash inflows CALC

and outflows. 7:npv( 14-8

valueA or volueB Returns 1 if valueA or volueB [2_] [TEST]

is € 0. volueA and valueB can LOGIC

be realnumbers, expressions, 2:or

or lists. 2-26

Tables and Reference hfformation A-17

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Output(vow,coluran,"text") Displays text beginning at i [P_M]

specified row and column. I/O

6:Output( 16-19

Output(row,column,value) Displays value begiJming at i [gggN]

specified row and column. I/O

6:Output( 16-19

Param Sets parametric graphing i

mode. Par 1-11

Pause Suspends program execution i [gggN]

until you press _. CTL

8:Pause 16-12

Pause ['value] Displays value; suspends i

program execution until you CTL

press [_. 8:Pause 16-12

Plot#(type,Xlistuame, Defines Plot# (1, 2, or 3) of 1 [2_] [STAT PLOT]

YTistname,mark} type Scatter 05"xyLine for PLOTS

Xlistuame and Iqistuame 1:Plot1(

using mark. 2:Plot2(

3:Plot3( 12-37

Plot#(type,Xlistuame, Defines Plot# (1, 2, 05"3) of ; [2_] [STAT PLOT]

,frvqlist) type Histogram 05"Boxplot for PLOTS

Xlistuame _lth frequency 1:Plot1(

fr_qlist. 2:Plot2(

3:Plot3( 12-37

Plot#(type,_istuame, Defines Plot# (1, 2, or 3) of -;-[_ [STAT PLOT]

.fr_qlist,mark) type ModBoxplot for PLOTS

Xlistname _lth frequency 1:Plot1(

frvqlist using mark. 2:Plot2(

3:Plot3( 12-37

Plot#(type,datalistname, Defines Plot# (1, 2, 05"3) of -;-[_ [STAT PLOT]

data axis,mark) type NormProbPIot for PLOTS

datalistuame on data axis 1:Plot1(

using mark. data axis can be X 2:Plot2(

or Y. 3:Plot3( 12-37

PlotsOff [1,2,3] Deseleets all star plots or one _ [STAT PLOT]

or more specified stat [)lots (1, STAT PLOTS

2, 05"3). 4:PlotsOff 12-35

PlotsOn [1,2,3] Selects all stat plots o1" one or [_ [STAT PLOT]

more specified stat plots (1, 2, STAT PLOTS

or 3). 5:PlotsOn 12-35

A-18 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Pmt_Bgn Specifies an mmuity due, F2Ta] [FINANCE]

where payments occur at the CALC

beginning of each payment F:Pmt_Bgn

period. 14-13

Pmt_End Specifies an ordinary annuity, F2na][FINANCE]

where payments occur at the CALC

end of each payment period. E:Pmt_End 14-13

poissoncdf(,u,x) (;omputes a cumulative [_ [DtSTR]

probability at xfor the discrete DISTR

Poisson distribution with C:poissoncdf(

specified mean ,u. 13-34

poissonpdf(_,x) Computes a probabilii7 at xfor F2na][DtSTR]

the discrete Poisson distribution DISTR

with the specified nlean _. B:poissonpdf( 13-33

Polar Sets polar graphing mode. iPol 1-11

eomplex 'value i.Polar Displays eomplex 'value in

polar format. CPX

7:_Polar 2-19

PolarGC Sets polar graphing ; r2_ [FORMAT]

coordinates fornmt. PolarGC 3-13

prgmname Executes the program name. iCTRL

D:prgm 16-15

EPrn(pmtl,pmt2 Computes the sum, rounded to [_ [FINANCE]

[,roundvolue]) roundvalue, of the prineipal CALC

amount between pmtl and 0:EPrn(

pint2 for an amortization

schedule. 14-9

prod(list[,sta,r¢,e/nd]) Returns product of list [_ [LIST]

elements between start and MATH

end. 6:prod( 11-18

Prompt variableA Prompts for value for i [0ggM]

[,variableB,...,vaviable n] variableA, then variableB, and I/O

so on. 2:Prompt 16-18

Tables and Reference hfformation A-19

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

1-PropZlnt(x,n Computes a one-proportion i

[,confidence level]) z eonfidence interval. TESTS

A:l-PropZlnt( 13-20

2-PropZlnt(xl,nl ,x2,n2 Computes a two-proportion i

[,confidence level]) z eonfidence interval. TESTS

B:2-PropZlnt( 13-21

1-PropZTest(pO,x,n Computes a one-proportion i

[,alternative,drawflag]) ztest. olternative=-I is <; TESTS

alternative=O is _; 5:1-PropZTest(

alternative=l is >. d'rmqflog=l

draws results; drawflog=O

calculates results. 13-14

2-PropZTest(xl ,nl ,x2,n2 Computes a two-proportion i [g_g]

[,alternative,drawflog]) ztest. olternative=-I is <; TESTS

alternative=O is €; 6:2-PropZTest(

alternative=l is >. drmqflog=l

draws results; drawflog=O

calculates results. 13-15

Pt-Change(x,y) Reverses a point at (x,y). [_ [DRAW]

POINTS

3:Pt-Change( 8-15

Pt-Off(x,y[,mark]) Erases a point at (x,y) using [_ [DRAW]

mark. POINTS

2:Pt-Off( 8-15

Pt-On(x,y[,mark]) Draws a point at (x,y) using [_ [DRAW]

mark. POINTS

l:Pt-On( 8-14

PwrReg [Xlistname, Fits a power regression model [g_

Ylistname,freqlist, to Xlistname and Ylistname CALC

regequ] with frequencyfr_qlist, and A:PwrReg

stores the regression equation

to regequ. 12-27

A-20 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Pxl-Change(row,column) Reverses pixel at [_ [DRAW]

(_w,column); 0 <_row <_62 POINTS

and 0 _<column <_94. 6:Pxl-Change( S-16

Pxl-Off(row,column) Erases pixel at (_vw,eolumn); [_ [DRAW]

0 <-row <_62 and POINTS

0 <_column <_94. 5:PxI-Off( 8-16

Pxl-On(row,column) Draws pixel at (row,column); [_ [DRAW]

0 <-row <-62 and POINTS

0 <_column <_94. 4:PxI-On( 8-16

pxI-Test(row,column) Returns 1 if pixel (row, [_ [DRAW]

column) is on, 0 if it is oft'; POINTS

0 <_row <_62 and 7:pxI-Test(

0 <_column <_94. 8-16

P)Rx(r,0) Returns X, given polar [_ [ANGLE]

coordinates rand O or a list of ANGLE

polar coordinates. 7:P_.Rx( 2-24

P)Ry(r,O) Returns Y, given polar [_ [ANGLE]

eoordflmtes rand O or a list of ANGLE

polar coordinates. 8:P_.Ry( 2-24

QuadReg [Xlistname, Fits a quadratic regression [g_

Ylistname,fr_qlist, model to Xlistname and CALC

regequ] Iqist,name with frequency 5:OuadReg

frvqlist, and stores the

regression equation to regequ. 12-25

OuartReg [Xlistname, Fits a quartie regression model [gTfT]

Iqistname,frvqlist, to Xlistname and Iqistname CALC

regequ] with frequeneyfrvqlist, and 7:QuartReg

stores the regression equation

to regequ. 12-26

Radian Sets radian angle mode. i 1_

Radian 1-11

rand [(numtrials)] Returns a ral]dom nt:[mber [_

between 0 and 1 for a PRB

speeified number of trials 1 :rand

numtrials. 2-20

randBin(numtrials,prob Generates and displays a

[,numsimulations]) random real number from a PRB

specified Binonfial distribution. 7:randBin( 2-22

Tables and Reference hfformation A-21

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

randlnt( lower, upper Generates all(] displays a [_tH]

[,numtrials]) randoln integer withil] a range PRB

specified by lower and upper S:randlnt(

integer bounds for a specified

number of trials numtrials. 2-22

randM(rows,columns) Returns a random matrix of [_

rows (1-99) x columns (1-99). MATH

6:randM( 10-13

randNorm(p,c_[,numtrials]) Generates and displays a

random real number from a PRB

specified Normal distribution 6:randNorm(

specified by p and _ for a

specified number of trials

numtriols. 2-22

re^Oi Sets tile mode to polar i

complex number mode (re^Oi). re^Oi 1-12

Real Sets inode to display complex i [M0_]

results only when you enter Real

complex numbers. 1-12

real(value) Returns the real part of a [_

complex number or list of CPX

complex numbers. 2:real( 2-18

RecaIIGDB nRestores all settings stored in [_ [DRAW]

tile graph database variable STO

GDBn. 4:RecallGDB 8-20

RecallPic nDisplays tile graph 31l(1 adds [_ [DRAW]

tile picture stored in Picn. STO

2:RecallPic S-1S

complex 'value _Rect Displays complex 'value or list

in rectangular format. CPX

6:_Rect 2-19

RectGC Sets rectangular graphing 1 _ [FORMAT]

coordinates format. RectGC 3-13

ref(matrix) Returns tile row-echelon forln

of a matrix. MATH

A:ref( 10-15

A-22 Tables and Reference Inforination

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

:Repeat condition Executes eommands until i [_

:commands condition is true. CTL

:End 6:Repeat 16-11

:commands

Return Returns to tile calling program. i [0ggM]

CTL

E:Return 16-15

round(value[,#deeimals]) Returns a number, expression, [_

list, or matrix rounded to NUM

#decimols (<_9). 2:round( 2-13

*row(value,matrix,row) Returns a matrix _lth row of

matrix nmltiplied by volue and MATH

stored in row. E:*row{ 10-16

row+(matrix,rowA,rowB) Returns a matrix _lth rowA of

matrix added to rowB and MATH

stored in rowB. D: row+( 10-16

*row+(value,matrix, Returns a matrix _lth rowA of

rowA,rowB) matrix nmltiplied by volue, MATH

added to rowB, and stored in F:*row+(

rowB. 1O- 16

rowSwap(matrix,rowA, Returns a matrix _lth rowA of

rowB) matrix swapped _lth rowB. MATH

C:rowSwap( 10-16

rref(matrix) Returns the reduced row-

echelon form of a matrix. MATH

B:rref( 10-15

R_Pr(x,y) Returns R, given reetanguhu" [2_ [ANGLE]

coordinates xand yor a list of ANGLE

rectangular coordinates. 5:R_Pr( 2-24

R_PO(x,y) Returns 0, given rectangular [_ [ANGLE]

coordinates xand yor a list of ANGLE

rectangular coordinates. 6:R_PO( 2-24

Tables and Reference hfformation A-23

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

2-SampFTest [listnameZ, Performs a two-san]pie Ftest. i

listname2_fr_qlistl, alternative=-1 is <; TESTS

fr_qlist2,alternative, alternative=O is _; D:2-SampFTest

drowflag] alternative= l is >. drawflag= l

(Data list input) draws results; drawflag=O

calculates results. 13-23

2-8ampFTest Sxl,nl, Performs a two-sample F test. i

Sx2,n2[,alternative, alternative=-1 is <; TESTS

drowflag] alternative=O is _; D:2-SampFTest

(Summary stats input) alternative=l is >. drawflag=l

draws results; drawflog=O

calculates results. 13-23

2-SampTInt [listnamel, Computes a two-sample ti

listname2, confidence intm_'al, pooled=l TESTS

frvqlistl _frvqlist2, pools variances; pooled=O does 0:2-SampTInt

canfidezwe level,pooled] not pool variances.

(Data list input) 13-19

2-SampTInt 21,Sx1,n1, Computes a two-sample ti

22,Sx2,n2 confidence intm_,al, pooled=l TESTS

[,confidence level,pooled] pools variances; pooled=O does 0:2-SampTInt

(Sununary stats input) not pool variances. 13-19

2-SampTTest [listnamel,

listname2_frvqlistl ,

frvqlist2,alternative,

pooled,draw flag]

(Data list input)

Computes a two-sample ttest. i

alternative=-1 is <; TESTS

alternative=O is _; 4:2-SampTTest

alternative= l is >. pooled= l

pools variances; pooled=O does

not pool vm'iances, drawflog=l

draws results; drawflog=O

calculates results. 13-13

A-24 Tables and Reference Information

Function or Instruction/

Arguments

2-Sam pTTest 5l,Sxl,nl,

22 ,Sx2 ,n2[ ,olternative

pooled,draw.flag]

(Smmnary stats input)

2-SampZInt(_l,a,

[,listnamel ,listname2

frvqlistl _frvqlist2,

canfidence level])

(Data list input)

2-SampZlnt(_l,_,

_1,nl ,_2,n2

[,confidence level])

(Smmnary stats input)

2-SampZTest(_l,_

[,listnamel ,listname2

.frvqlistl ,frvqlist2,

alternative,drowflag])

(Data list input)

2-SampZTest(61 ,_,

_1 ,nl ,_2,n2

[,alternative,drawflog])

(Summary stats input)

Key or Keys/

Result Menu or Screen/Item

_r_tq

TESTS

4:2-SampTTest

TESTS

9:2-SampZlnt(

Computes a two-sample ttest.

alternative=-1 is <;

alternative=O is _;

alternative= l is >. pooled= l

pools variances; pooled=O does

not pool variances, drawflog=l

draws results; drawflog=O

calculates results.

Computes a two-sample z

confidence intm_al.

Computes a two-sample z

confidence intm_al.

13-13

13-18

TESTS

9:2-SampZlnt( 13-18

TESTS

3:2-SampZTest(

Computes a two-sample ztest.

alternative=-1 is <;

alternative=O is _ ;

alternative=l is >. drawflag=l

draws results; drawflag=O

calculates results. 13-12

Computes a two-sample ztest. i [gt_]

alternative=-1 is <; TESTS

alternative=O is ;_; 3:2-SampZTest(

alternative= l is >. draw.flag= l

draws results; drawflog=O

calculates results. 13-12

Sci Sets scientific notation display i [MODEl

mode. Sci 1-10

Select(Xlistname, Seleets one o1" more speeific _ [LIST]

Iqistname) data points from a scatter plot OPS

or xyLine plot (only), and then 8:Select(

stores the selected data points

to two new lists, Xlistname

and Ylistname. 11-12

Tables and Reference hfformation A-25

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Send(variable} Sends contents of variable to -;-

the CBL 2/CBL System or CBR. I/O

B:Send( 16-21

seq(expression,variable, Returns list ereated by _ [LIST]

begin,end[,increment]) evaluating expression _lth OPS

regard to 'variable, from begin 5:seq(

to end by incremez_t. 11-11

Seq Sets sequence graphing mode. i

Seq 1-11

Sequential Sets mode to graph ftmetions i

sequentially. Sequential 1-12

SetUpEditor Removes all list names from

the stat list editor, all(] then EDIT

restores list names L1 through 5:SetUpEditor

L6 to eolumns 1 through 6. 12-21

SetUpEditor listnamel Removes all list names from

[,listname2,..., the stat list editor, then sets it EDIT

listname20] up to display one or more 5:SetUpEditor

listnames in the specified

order, starting _lth eohmm 1. 12-21

Shade(lowe:rfune, Draws lowerfune and [_ [DRAW]

upperfunc[,Xleft_rqght, upperfune in terms of Xon the DRAW

pattern,patres]) current graph and uses 7:Shade(

pattern and pat'r_s to shade the

area bounded by lowerfunc,

upperfunc, Xleft, and X'rqght. 8-10

Shadez2(lowerbound, Draws the density function for [_ [DISTR]

upperbound,dy') the Z2 distribution specified by DRAW

degrees of freedom dfand 3:Shade)_2(

shades tile area between

lowerbound and upper_ound. 13-36

A-26 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

ShadeF(lowerbound, Draws the density function for _ [DISTR]

upperbound, the F distribution specified by DRAW

numerator df, numerator (lf and 4:ShadeF(

denominator d,f) denorainator df and shades the

area between lower'bound and

upperSound. 13-36

$hadeNorm(lower'bound, Draws the normal density _ [DISTR]

upper'bound[,p,G]) function specified by p and (_ DRAW

and shades the area between 1:ShadeNorm(

lower'bound and upper'bound. 13-35

Shade_t(lower'bound, Draws the density function for [_ [DISTR]

upperbound,dJ') the Student-t distribution DRAW

specified by degrees of 2:Shade_t(

freedom df, and shades the

area between lower'bound and

upperSound. 13-36

Simul Sets mode to graph functions i [_Dg]

simultaneously. Simul 1-12

sin(volue) Returns tile sine of a real Ig]N]

number, expression, or list. 2-3

sin-l(volue) Returns tile m-csine of a real [_ [SIN-1]

number, expression, or list. 2-3

sinh(volue) Returns tile hypet%olic sine of _ [CATALOG]

areal number, expression, or sinh(

list. 15-10

sinh-l(value) Returns the hyperbolic arcsine _ [CATALOG]

of a real number, expression, sinh -1(

or list. 15-10

Tables and Reference hfformation A-27

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

SinReg [iterations, Attempts iterations times to fit

Xlistname,I_istname, a sJnusoJdal regression model to CALC

period,regequ] Xlistname and Iqistname using C:SinReg

aperiod guess, and stores the

regression equation to regequ. 12-27

solve(expression,variable, Solves expression for variable, i

guess,{lower',upper_) given an initial guess and lower" MATH

and upper" bounds within 0:solve(

which the solution is sought. 2-12

SortA(listuame) Sorts elements of listname in _ [LIST]

ascending order. OPS 11-10

1:SortA( 12-20

SortA(keylistuame, Sorts elements of keylistuame [2_] [LIST]

dependlistl [,dependlist2, in ascending order, then sorts OPS

...,dependlist n]) each dependlist as a dependent l:Sorth( 11-10

list. 12-20

SortD(listuame) Sorts elements of listname in [_ [LIST]

descending order. OPS 11-10

2:SortD( 12-20

SortD(keylistuarae, Sorts elements of keylistuarae [_ [LIST]

in descending order, then sorts OPS

de_er_dlistl [,deper_dlist2,..., each dependlist as a dependent 2:SortD( 11-10

dependlist n]) list. 12-20

stdDev(list[,frvqlist]) Returns the standard deviation [_ [LIST]

of the elements in list with MATH

frequencyfrvqlist. 7:stdDev( ll-lS

Stop Ends program execution; i [gggM]

returns to home screen. CTL

F:Stop 16-15

Store: value_variable Stores value in variable. _ 1-14

StoreGDB nStores current graph in [_ [DRAW]

datahase GDBn. STO

3:StoreGDB 8-19

A-28 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

StorePic nStores eun'ent pleture in [_ [DRAW]

picture Picn. STO

l:StorePic 8-17

String_*Equ(string,Y= vat') Converts stt'ing iJlto an _ [CATALOG[

equation and stores it in Y: String_Equ(

vat_ 15-8

sub(string,begin,h_.ngth) Returns a string that is a subset [gffd][CATALOG]

of another string, from begin sub(

to length. 15-9

sum(list[,stat't,end]) Returns the sum of elements of [gffd][LIST]

list from start to end. MATH

5:sum( 11-18

tan(value) Returns the ttmgent of a real

nunlber, expression,

or list. 2-3

tan-l(value) Returns the aretangent of a [gffd][TAN-1]

real nunlber, expression, or

list. 2-3

Tangent(ea_ression,value) Draws a line tangent to [gffd][DRAW]

expression at X=value. D RAW

5:Tangent( 8-8

tanh(value) Returns hyperbolic tangent of a [_ [CATALOG]

real number, expression, or list. tanh( 15-10

tanh-l(value) Returns the hyperbolic _ [CATALOG]

aretangent of a real number, tanh-l(

expression,

or list. 15-10

tcdf(lowerbound, Computes the Student-t [2_ [DISTR]

upp_rbound,dJ_ distribution probability DISTR

between lower_ound and 5:tcdf(

upperSound for the specified

degrees of freedom 4/: 13-31

Text(row,column,textl, Writes text on graph beginning [_ [DRAW]

text2,...,text n) at pixel (row,column), where DRAW

0 <_row <_57 and 0:Text(

0 <_column <_94. 8-12

Then

See If:Then

Tables and Reference hfformation A-29

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Time Sets sequenee graphs to plot -;-[_ [FORMAT]

with respect to time. Time 6-8

Tlnterval [listname, Computes a tconfidence i

.fr_qlist,eonfidence level] inte_ral. TESTS

(Data list input) 8:Tlnterval 13-17

Tlnterval ;7,Sx,n Computes a tconfidence i

[,confidence level] inte_ral. TESTS

(Summary stats input) 8:Tlnterval 13-17

tpdf(x,df) Computes the probability" [_ [DISTR]

density" function (pdf) for the DISTR

Student-t distribution at a 4:tpdf(

specified xvalue _ith specified

degrees of freedom ddq 13-30

Trace Displays the graph and enters

TRACE mode. 3-18

Performs a ttest with i

frequeneyfrvqlist. TESTS

alternative=-1 is <; 2:T-Test

alternative=O is €;

alternative= lis >. drawflag= l

draws results; drawfiag=O

calculates results. 13-11

Performs a ttest with i

frequeneyfrvqlist. TESTS

alternative=-1 is < ; 2:T-Test

alternative=O is €: ;

alternative=l is >. drawflag=l

draws results; drawf!og=O

ealeulates results. 13-11

T-Test pO[,listname,

frvqlist,alternative,

d'r'o_ag]

(Data list input)

T-Test pO, _,Sx,n

[,olternative,drawflag]

(Summary stats input)

A-30 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

tvm_FV[(N,I%,PV,PMT, Conlptltes tile ftlture va]ue. [_ [FINANCE]

P/Y,C/Y) ] CALC

6:tvm_FV 14-7

tvm_I%[(N, PV,PMT,FV, (;omputes tile annual interest [_ [FINANCE]

PlY, C/Y)] rate. CALC

3:tvm_I% 14-7

tvm_N[(I%,PV, PMT,FV, (;omputes tile number of _ [FINANCE]

P/Y,C/Y)] payment periods. CALC

5:tvm_N 14-7

tvm_Pmt[(N,I%,PV,FV, (;omputes the amount of eaeh [_ [FINANCE]

P/If, C/Y)] payment. CALC

2:tvm_Pmt 14-6

tvm_PV[(N,I%,PMT,FV, (;omputes tile present value. [_ [FINANCE]

P/Y,C/Y) ] CALC

4:tvm_PV 14-7

uvAxes Sets sequence graphs to [)lot ; [2_] [FORMAT]

u(n)on the x-axis and v(n)on uv

the y-axis. 6-8

uwAxes Sets sequence graphs to [)lot ; [2_] [FORMAT]

u(n) on the x-axis and w(n) on uw

the y-axis. 6-8

1-Mar Stats [Xlistname, Performs one-variable analysis [gT_]

.frwqlist] on tile data in XTistname _ith CALC

frequeneyfrvqlist, l:l-Var Stats 12-25

2-Mar Stats [Xlistname, Performs two-variable analysis [gT_]

Ylistnarae,fr_qlist] on the data in Xlistnarae and CALC

Iaistname with frequeney 2:2-Mar Stats

fr_qlist. 12-25

variance(list[,fr_qlist]) Returns the variance of the [g_] [LIST]

elements in list wlth frequeney MATH

frvqlist. 8:variance( 11-18

Vertical xDraws a vertical line [_ [DRAW]

at x. DRAW

4:Vertical S-6

vwAxes Sets sequenee graphs to [)lot i- [2_] [FORMAT]

v(n) on the x-axis and w(n) on vw

the y-axis. 6-8

Web Sets sequence graphs to trace ; [2_] [FORMAT]

as webs. Web 6-8

Tables and Reference hfformation A-31

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

:While condition Executes commands while i

:commands condition is true. CTL

:End 5:While 16-11

:command

valueA xor valueB Returns 1 if only valueA or _ [TEST]

valueB = O. valueA and valueB LOGIC

can be real numbers, 3:xor

expressions, or lists. 2-26

ZBox Displays a graph, lets you draw -;-

a box that defines a new- ZOOM

_ewing window, and updates 1:ZBox

the window. 3-20

ZDecimal Adjusts tile _dewing window so i

that aX=0.1 and AY=0.1, and ZOOM

displays tile graph screen with 4:ZDecimal

tile origin centered on the

screen. 3-21

Zlnteger Redefines tile viewing window i

using these dimensions: ZOOM

AX=I XscI=10 8:Zlnteger

AY=I YscI=I 03-22

Zlnterval c_[,listname, Computes a zconfidenee i

.fr_qlist,confidence level] intel_al. TESTS

(Data list input) 7:Zlnterval 13-16

Zlnterval c_,;7,n Computes a zconfidenee i [_

[,confidence level] intel_al. TESTS

(Summary stats input) 7:Zlnterval 13-16

Zoom In Magnifies tile part of the graph i

that surrounds the eursor ZOOM

location. 2:Zoom In 3-21

Zoom Out Displays a greater portion of i

the graph, centered on the ZOOM

cursor location. 3:Zoom Out 3-21

A-32 Tables and Reference Inforination

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

ZoomFit Recalculates Ymin and Ymax i

to hmlude tile nlininluni and ZOOM

nlaxinmm Yvalues, between O:ZoomFit

Xmin and Xmax, of the

selected functions and replots

tile functions. 3-22

ZoomRcl Graphs tile selected functions i

in a user-defined _dewing MEMORY

window. 3:ZoomRcl 3-23

ZoomStat Redefines tile viewing window i

so that all statistical data ZOOM

points are displayed. 9:ZoomStat 3-22

ZoomSto Immediately stores tile current i

viewing window. MEMORY

2:ZoomSto 3-23

ZPrevious Replots tile graph using the i

window variables of the graph MEMORY

that was displayed before you 1:ZPrevious

executed the last ZOOM

instruction. 3-23

ZSquare Adjusts tile X or Ywindow i

settings so that each pixel ZOOM

represents m] equal width and 5:ZSquare

height in the coordinate

system, and updates the

viewing window. 3-21

ZStandard Replots the functions i

immediately, updating the ZOOM

window variables to the 6:ZStandard

default values. 3-22

Tables and Reference Information A-33

Functionor Instruction/

Arguments

Z-Test(pO,_[,listname, Performs a ztest with i [_

f_qlist,elternative, frequencyfreqlist. TESTS

drawflag]) alterr_ative=-I is <; 1:Z-Test(

(Data list input) alterr_ative=O is €;

alterr_ative= l is >. drawflag= l

draws results; drawflag=O

calculates results. 13-10

Z-Test(pO,_,_,n Performs a ztest. i

[,olterr_ative,drawflag]) alterr_ative=-I is <; TESTS

(Smmnary stats input) alterr_ative=O is €; 1:Z-Test(

alterr_ative=l is >. draw.flag=l

draws results; drawflog=O

calculates results. 13-10

ZTrig Replots the functions i

immediately, updating the ZOOM

window variables to preset 7:ZTrig

values for plotting trig

functions. 3-22

Factorial: value! Returns faetodal of value. PRB

4:! 2-21

Factorial: list! Returns factorial of list

elements. PRB

4:! 2-21

Degrees notation: value ° Interprets value as degrees; [_ [ANGLE]

designates degrees in [)MS ANGLE

fornlat. 1:° g-23

Radian: angle r Interprets angle as radim]s. [_ [ANGLE]

ANGLE

3: r g-24

Transpose: matrix T Retrains a matrix in wltich each

element (row, column) is MATH

swapped with tile 2: T

corresponding element

(cohmm, row) of matrix. 10-12

Key or Keys/

Result Menu or Screen/Item

A-34 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

xt_ZrootX_value Retm'ns x_root of value. MATH

5:x_ 2-6

xtlZrootX_list Returns xthroot of list

elements. MATH

5:x-_ 2-6

listX_value Returns list roots of value. MATH

5:x-_ 2-6

listAX_listB Returns listA roots of listB. MATH

5:x-_ 2-6

Cube: value 3 Returns the cube of a real or [_TH]

complex nmnber, expression, MATH

list, or square matrix. 3:3 2-6

10-10

Cube root: 3_(value) Remms tile cube root of a real or

complex nmnber, expression, or MATH

list. 4:3_( 2-6

Equal: valueA=valueB Returns l lfvalueA = valueB. [_ [TEST]

Returns 0 if valueA _valueB. TEST

valueA and valueB can be real 1 :=

or complex numbers, 2-25

expressions, lists, or matriees. 1O- 11

Not equal: valueAcvalueB Returns 1 if valueA _valueB. [_ [TEST]

Returns 0 if valueA =volueB. TEST

valueA and volueB can be real 2:€

or complex nmnbers, 2-25

expressions, lists, or matrices. 10-11

Less than: valueA<valueB Returns 1 if volueA <volueB. [2T3] [TEST]

Returns 0 if volueA >_valueB. TEST

valueA and volueB can be real S:<

o1"eomplex nunlbers,

expressions, or lists. 2-25

Tables and Reference hfformation A-35

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Greater than: Returns 1 if valueA > valueB. [_ [TEST]

valueA>valueB Returns 0 if valueA <_valueB. TEST

valueA and valueB can be real 3:>

O1" eonlplex llUIslbers_

expressions, or lists. 2-25

Less than or equal: Returns 1 if valueA <_valueB. _ [TEST]

volueA<_volueB Returns 0 if valueA >volueB. TEST

valueA and volueB can be real 6:_<

O1"eoIslplex nunlbers,

expressions, or lists. 2-25

Greater than or equal: Returns 1 if volueA 2 valueB. _ [TEST]

valueA>valueB Retunls 0 if volueA <valueB. TEST

valueA and volueB can be real 4:>

O1"eonlplex nunlbers,

expressions, or lists. 2-25

Inverse: value -1 Returns 1 dix_ded by a real or []

eonsplex nunsber or

expression. 2-3

Inverse: list -1 Returns 1 divided by list []

elements. 2-3

Inverse: matrix -1 Returns matrix inverted. [] 10-10

Squm'e: value 2 Returns value multiplied by []

itsel£ value can be a real or

eonlplex nunlber or

expression. 2-3

Square: list 2 Returns list elements squared. [] 2-3

Square: mat'ri:_ _ Returns matrix multiplied by []

itsel£ 10-10

Powers: value^power Returns value raised to power. []

value can be a real 05"eoinplex

number or expression. 2-3

Powers: list^power Returns list elements raised to []

power'. 2-3

Powers: value^list Returns value raised to list []

elements. 2-3

A-36 Tables and Reference Information

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Powers: mat'rix^pow_" Returns matrix elements []

raised to power. 1O- 10

Negation: -volue Returns the negative of a real []

o1"complex number, 2-4

expression, list, o1"matrix. 10-9

Power of ten: lo^(volue) Returns 10 raised to tile value _ [10x]

power, volue can be a real or

conlplex ntlnlber or

expression. 2-4

Power of ten: lo^(list) Returns a list of 10 raised to _ [10x]

the list power. 2-4

Square root: ,[(value) Returns square root of a real or _ [_]

complex number, expression,

or list. 2-3

Multiplication: Returns volueA times volueB. []

volueA*valueB 2-3

Multiplication: Returns volue times each list []

volue*list element. 2-3

Multiplication: Returns each list element []

list*value times volue. 2-3

Multiplication: Returns listA elements times []

listA*listB listB elements. 2-3

Multiplieation: Returns value times matrix []

value*matrix elements. 10-9

Multiplication: Returns matrixA times []

matrixA*matrixB matrixB. 10-9

Division: valueA/valueB Returns valueA dMded by []

valueB. 2-3

Division: list/value Returns list elements dMded []

by value. 2-3

Division: value/list Returns value dMded by list []

elements. 2-3

Division: listA/listB Returns listA elements dMded []

by listB elements. 2-3

Tables and Reference hfformation A-37

Function or Instruction/ Key or Keys/

Arguments Result Menu or Screen/Item

Addition: valueA+valueB Returns valueA plus valueB. [] 2-3

Addition: list+value Returns list in which value is []

added to each list element. 2-3

Addition: listA+listB Returns listA elements plus []

listB elements. 2-3

Addition: Returns matrixA elements []

matrixA+matrixB plus matrixB elements. 10-9

Concatenation: Concatenates two or more []

string l +string2 strings. 15-6

Subtraction: Subtracts valueB from val'ueA. []

valueA -valueB 2-3

Subtraction: Subtracts list elements from []

value-list value. 2-3

Subtraction: Subtracts value from list []

list- value elements. 2-3

Subtraction: Subtracts listB elements from []

listA-listB listA elements. 2-3

Subtraction: Subtracts matrixB elements []

matrixA-matrixB from matrixA elements. 10-9

Minutes notation: Interprets minutes angle [_ [ANGLE]

degrees°minutes ' nleasurement as minutes. ANGLE

seeonds" 2:' 2-23

Seconds notation: Interprets seconds angle @ [.]

degrees°minutes ' nleasurenlent as seconds.

seeonds" 2-23

A-38 Tables and Reference Information

TI-83 Menu Map

The TI-83 Menu Map begins at the top-left corner of the keyboard and follows

tile keyboard layout from left to right. Default values and settings are shown,

IIII

(Func mode) (Par mode) (Pol mode) (Seq mode)

Plotl Plot2 Plotl Plot2 Plotl Plot2 Plotl Plot2

Plot3 Plot3 Plot3 Plot3

",,YI= ",XIT= ",rl= nMin=l

",,Y2= YIT= ",r2= ",u(n)=

",Y3= ",X2T= ",r3= u(nMin)=

",,Y4= Y2T= ",r4= ",v(n)=

...... ",rS= v(nMin)=

",,Y9= ",X6T= ",r6= ",w(n)=

",,YO= Y6T= w(nMin)=

[STATPLOT] [_][STATPLOT]

__1 I

I I I

STAT PLOTS (PRGM editor) (PRGM editor)

l:Plotl...Off PLOTS TYPE

_:L LI L2 m l:Plotl( l:Scatter

2:Plot2...Off 2:Plot2( 2:xyLine

_:L LI L2 _ 3:Plot3( 3:Histogram

3:Plot3...Off 4:PlotsOff 4:ModBoxplot

_:L LI L2 m 5:PlotsOn 5:Boxplot

4:PlotsOff 6:NormProbPlot

5:PlotsOn

(PRGM editor)

MARK

Z:D

2:+

3:,

III

(Func mode) (Par mode) (Pol mode)

WINDOW WINDOW WINDOW

Xmin= i0 Tmin=O Omin=O

Xmax=lO Tmax=_2 Omax=_2

Xscl=1 Tstep=_/24 Ostep=_/24

Ymin= 10 Xmin= 10 Xmin= 10

Ymax=10 Xmax=iO Xmax=iO

Yscl=1 Xscl=1 Xscl=1

Xres=1 Ymin= 10 Ymin= 10

Ymax=iO Ymax=iO

Yscl=1 Yscl=1

(Seq mode)

WINDOW

nMin=1

nMax=10

PlotStart=1

PlotStep=1

Xmin= i0

Xmax=lO

Xscl=l

Ymin= i0

Ymax=lO

Yscl=l

[TBLSET] _ [TBLSET]

iI FI

TABLE SETUP (PRGM editor)

TblStart=O TABLE SETUP

ATbI=I Indpnt:Auto Ask

Indpnt:Auto Ask Depend:Auto Ask

Depend:Auto Ask

Tables and Reference Information A-39

i I

ZOOM

1:ZBox

2:Zoom In

3:Zoom Out

4:ZDecimal

5:ZSquare

6:ZStandard

7:ZTrig

8:Zlnteger

9:ZoomStat

O:ZoomFit

I I

MEMORY MEMORY

1:ZPrevious (Set Factors,.,)

2:ZoomSto ZOOM FACTORS

3:ZoomRcl XFact=4

4:SetFactors_ YFact=4

[FORMAT]

(Func/Par/Po] modes)

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

(Seq mode)

Time Web uv vw uw

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

[CALC]

(Func mode)

CALCULATE

1:value

2:zero

3:minimum

4:maximum

5:intersect

6:dy/dx

7:if(x)dx

(Par mode)

CALCULATE

1:value

2:dy/dx

3:dy/dt

4:dx/dt

(Pol mode)

CALCULATE

1:value

2:dy/dx

3:dr/dO

Normal Sci Eng

Float 0123456789

Radian Degree

Func Par Pol Seq

Connected Dot

Sequential Simul

Real a+bt re^Bt

Full Horiz G T

(Seq mode)

CALCULATE

1:value

A-40 Tables and Reference Information

SEND

1:A11+...

2:All-...

3:Prgm...

4:List._

5:Lists to T182...

6:GDL

7:Pic._

8:Matrix...

9:Real._

O:Complex._

A:Y Vars...

B:String._

C:Back Up...

RECEIVE

1:Receive

i I

EDIT

1:Edit._

2:SortA(

3:SortD(

4:ClrList

5:SetUpEditor

CALC

1:1Var Stats

2:2 Var Stats

3:Med Med

4:LinReg(ax+b)

5:QuadReg

6:CubicReg

7:QuartReg

8:LinReg(a+bx)

9:LnReg

O:ExpReg

A:PwrReg

B:Logistic

C:SinReg

TESTS

I:Z Test...

2:T Test...

3:2 SampZTest...

4:2 SampTTest...

5:1 PropZTest...

6:2 PropZTest...

7:Zlnterval...

8:Tlnterval...

9:2 SampZlnt._

0:2 SampTlnt._

A:I PropZlnt._

B:2 PropZlnt._

C:Z 2 Test...

D:2 SampFTest._

E:LinRegTTest...

F:ANOVA(

Tables and Reference Information A-41

[LIST]

NAMES

l:listname

2:listname

3:listname

1 1

OPS MATH

l:SortA( 1:min(

2:SortD( 2:max(

3:dim( 3:mean(

4:Fill( 4:median(

5:seq( 5:sum(

6:cumSum( 6:prod(

7:AList( 7:stdDev(

8:Select( 8:variance(

9:augment(

O:List_matr(

A:Matr_list(

B:L

I I 1 1

MATH NUM CPX

l:_Frac l:abs( 1:conj(

2:_Dec 2:round( 2:real(

3:3 3:iPart( 3:imag(

4:3_r( 4:fPart( 4:angle(

5: x_ 5:int( 5:abs(

6:fMin( 6:min( 6:_Rect

7:fMax( 7:max( 7:_Polar

8:nDeriv( 8:Icm(

9:fnlnt( 9:gcd(

O:Solver._

[2nd][TEST]

I I

TEST LOGIC

i:= l:and

2:_ 2:or

3:> 3:xor

4:> 4:not(

5:<

6:<

PRB

1:rand

2:nPr

3:nCr

4:!

5:randlnt(

6:randNorm(

7:randBin(

A-42 Tables and Reference Information

I I I

NAMES MATH

I:[A] 1:det(

2:[B] 2: I

3:[C] 3:dim(

4:[D] 4:Fill(

5:[E] 5:identity(

6:[F] 6:randM(

7:[G] 7:augment(

8:[H] 8:Matr_list(

9:[I] 9:List_matr(

O:[J] O:cumSum(

A:ref(

B:rref(

C:rewSwap(

D:row+(

E:*row(

F:*row+(

I I

EXEC EDIT

l:nan_ l:name

2:na_ 2:na_e

(PRGM editor)

CTL

1:If

2:Then

3:Else

4:For(

5:While

6:Repeat

7:End

8:Pause

9:Lbl

O:Goto

A:IS>(

B:DS<(

C:Menu(

D:prgm

(PRGM editor)

I/0

1:Input

2:Prompt

3:Disp

4:DispGraph

5:DispTable

6:Output(

7:getKey

8:ClrHeme

9:ClrTable

O:GetCalc(

A:Get(

B:Send(

E:Return

F:Stop

G:DelVar

H:GraphStyle(

EDIT

I:[A]

2:[B]

3:[C]

4:[D]

5:[E]

6:[F]

7:[G]

8:[H]

9:[I]

O:[J]

NEW

1:Create New

(PRGM editor)

EXEC

m:name

2:name

r_q [AN_LE]

F--

ANGLE

1: °

2:'

3: r

4:_DMS

5:R_Pr(

6:R_PO(

7:P_Rx(

8:P_Ry(

Tables and Reference Information A-43

DRAW

l:C]rDraw

2:Line(

3:Horizontal

4:Vertical

5:Tangent(

6:DrawF

7:Shade(

8:Drawlnv

9:Circle(

O:Text(

A:Pen

POINTS

1:Pt On(

2:Pt Off(

3:Pt Change(

4:Pxl On(

5:Pxl Off(

6:Pxl Change(

7:pxl Test(

STO

1:StorePic

2:RecallPic

3:StoreGDB

4:RecalIGDB

VARS

1:Window._

2:Zoom._

3:GDB...

4:Picture._

5:Statistics...

6:Table...

7:String._

Y VARS

1:Function._

2:Parametric...

3:Polar._

4:On/Off...

VARS

i I

(Window...)

X/Y

l:Xmin

2:Xmax

3:Xscl

4:Ymin

5:Ymax

6:Yscl

7:Xres

8:AX

9:AY

0:XFact

A:YFact

I I

(Window...) (Window...)

T/e U/V/W

1:Tmin 1:u(nMin)

2:Tmax 2:v(nMin)

3:Tstep 3:w(nMin)

4:emin 4:nMin

5:6max 5:nMax

6:6step 6:PlotStart

7:PlotStep

A-44 Tables and Reference Information

VARS

I I I

(Zoom...) (Zoom...) (Zoom...)

ZX/ZY ZT/Ze ZU

l:ZXmin l:ZTmin l:Zu(nMin)

2:ZXmax 2:ZTmax 2:Zv(nMin)

3:ZXscl 3:ZTstep 3:Zw(nMin)

4:ZYmin 4:ZOmin 4:ZnMin

5:ZYmax 5:Z@max 5:ZnMax

6:ZYscl 6:Z@step 6:ZPlotStart

7:ZXres 7:ZPlotStep

VARS

(GDB...)

GRAPH DATABASE

I:GDB1

2:GDB2

9:GDB9

O:GDBO

VARS

(Statistics...)

l:n

2:_

3:Sx

4:_x

6:Sy

7:_y

8:minX

9:maxX

O:minY

A:maxY

(Picture...)

PICTURE

1:Picl

2:Pic2

9:Pic9

O:PicO

(Statistics...)

I:Zx

2:Zx 2

3:Zy

4:Zy 2

5:Zxy

I I I

(Statistics...) (Statistics...) (Statistics...)

EQ TEST PTS

I:RegEQ 1:p i:xl

2:a 2:z 2:yi

3:b 3:t 3:x2

4:c 4:Z 2 4:y2

5:d 5:F 5:x3

6:e 6:df 6:y3

7:r 7:# 7:Q1

8:r 2 8:#1 8:Med

9:R 2 9:#2 9:Q3

O:s

A:_I

B:_2

C:Sxl

D:Sx2

E:Sxp

F:nl

G:n2

H:lower

I:upper

Tables and Reference Information A-45

VARS

I I

(Table...) (String...)

TABLE STRING

1:TblStart 1:Strl

2:ATbl 2:Str2

3:TbIInput 3:Str3

4:Str4

9:Str9

O:StrO

Y VARS

III

(Function...) (Parametric...) (Polar...)

FUNCTION PARAMETRIC POLAR

I:YI I:XIT i:ri

2:Y2 2:YIT 2:r2

3:Y3 3:X2T 3:r3

4:Y4 4:Y2T 4:r4

5:r5

O:Yo B:Y6T

(On/Off._)

ON/OFF

1:FnOn

2:FnOff

A-46 Tables and Reference Information

[_ [DISTR]

DISTR

1:normalpdf(

2:normalcdf(

3:invNorm(

4:tpdf(

5:tcdf(

6:z2pdf(

7:z2cdf(

8:Fpdf(

9:Fcdf(

O:binompdf(

A:binomcdf(

B:poissonpdf(

C:poissoncdf(

D:geometpdf(

E:geometcdf(

I_ [FINANCE]

CALC

I:TVM Solver...

2:tvm Pmt

3:tvm I%

4:tvm PV

5:tvm N

6:tvm FV

7:npv(

8:irr(

9:hal(

O:XPrn(

A:glnt(

B:_Nom(

C:_Eff(

D:dbd(

E:Pmt End

F:Pmt Bgn

DRAW

1:ShadeNorm(

2:Shade t(

3:Shadez2(

4:ShadeF(

VARS

I:N

2:1%

3:PV

4:PMT

5:FV

6:P/Y

7:C/Y

Tables and Reference Information A-47

[MEM]

i--J

MEMORY

l:Check RAM_

2:Delete._

3:Clear Entries

4:ClrAllLists

5:Reset...

MEMORY

I I

(Check RAM...) (Delete...)

MEM FREE 27225 DELETE FROM...

Real 15 1:All...

Complex 0 2:Real._

List 0 3:Complex._

Matrix 0 4:List...

Y Vars 240 5:Matrix...

Prgm 14 6:Y Vars...

Pic 0 7:Prgm...

GDB 0 8:Pic...

String 0 9:GDB...

O:String...

MEMORY (Reset...)

I I

(All Memory...) (Defaults...)

RESET MEMORY RESET DEFAULTS

1:No 1:No

2:Reset 2:Reset

Resetting memory

erases all data and

programs•

12_]_ALOG]

CATALOG

cosh(

cosh-l(

Equ_String(

expr(

inString(

length(

sinh(

sinh-1(

String_Equ(

sub(

tanh(

tanh-1(

(Reset...)

RESET

1:All Memory...

2:Defaults._

A-48 Tables and Reference Information

Variables

User Variables

System Variables

The TI-83 uses the variables listed below in various ways,

Some variables are restricted to specific data types.

The variables A through Z and 0 are defined as real or

complex numbers. You may store to them. The TI-83 can

update X, Y, R, 0, and T dm'ing graphing, so you may want

to avoid using these varial)les to store nongraphing data.

The variables (list nalnes) L1 through LS are restricted to

lists; you cannot store another type of data to them.

The wu'iables (matrix names) [A] through [J] are restricted

to matrices; you cannot store another type of data to them,

The vm'iables Pie1 through Pie9 and Pic0 are restricted to

pictures; you cannot store another type of data to them.

The variables GDB1 through GDB9 and GDB0 are restricted

to graph databases; you cannot store another type of data

to them,

The variables Strl through Str9 and StrO m'e restricted to

strings; you cannot store another type of data to them.

You can store any string of characters, functions,

instructions, or vm'iables to the functions Yn, (1 through 9,

and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n),

and w(n) directly or through the Y= editor. The validity of the

string is determined when the function is evaluated.

The variables below nmst be real numbers. You may store

to them. Since the TI-83 can update some of them, as the

result of a ZOOM, for example, you nlay want to avoid

using these variables to store nongraphing data.

• Xmin, Xmax, Xsel, AX, XFact, Tstep, PlotStart, nMin, and

()tiler window variables,

•ZXmin, ZXmax, ZXscl, ZTstep, ZPIotStart, Zu(nMin), and

other ZOOM variables.

The variables below are resetwed for use by the TI-83. You

cannot store to them.

n, _, Sx, _x, minX, maxX, Ey, Ey2, Exy, a, b, e, RegEQ, xl, x2,

yl, z, t, F, Z2, p, xl, Sxl, nl, lower, upper, r2, R2 aft(] other

statistical variables,

Tables and Reference hfformation A-49

Statistics Formulas

This section contains statistics fornmlas for the Logistic and SinReg

regressions, ANOVA, 2-SampFTest, and 2-SampTTest.

Logistic The logistic regression algorithm applies nonlinear

t_cursive least-squares techniques to optimize the

following cost function:

j c

:z(-i÷o>,4

which is the sunl of the squares of the residual errors,

where: x= the independent variable list

y= the dependent variable list

N= the dimension of the lists

This technique attempts to estimate the constants a, b, and

et_cursively to make Jas small as possible.

SinReg The sine regression algorithm applies nonlinear recut_ive

least-squares techniques to optimize the following cost

function:

J= E[a siyt(bxi + e)+ d- yi]2

i=1

which is the sunl of the squares of the residual errors,

where: x= the independent variable list

y= the dependent variable list

N= the dimension of the lists

This technique attempts to recursively estimate the

c()nstants a, b, c, and dto make Jas small as possible.

A-50 Tables and Reference Inforination

ANOVA( The ANOVA Fstatisticis:

Factor MS'

FError MS

The mean squares (MS) that make up F are:

Factor SS

Factor MS' Factor df

Error SS

Error MS' =Error df

The sum of squares (SS) that make up the mean squares

are:

Factor SS = E ni(xi -2) 2

i=1

Error SS = E (ni - 1)Sxi 2

i=l

The degrees of freedoln dfthat make up the mean squares

are:

Factor df =I- 1 = numerator df for V

Ermrdf = E (hi - 1) = denolninator df if)r F

i=l

where: I= number of populations

_:i = the mean of each list

Sxi = the standard deviation of each list

ni = the length of each list

_: = the mean of all lists

Tables and Reference Information A-51

2-SampFTest Below is the definition for the 2-SampFTest.

Sxl, Sx2 = Sample standard deviations having

nl-1 and n2-1 degrees of freedom df,

respectively.

F = F-statistic [ Sx2 )

dr(x, nl-1 ,n2-1 ) = Fpdf( ) with degrees of

fl'eedom df, hi-1 , and n2-1

p= reportedp wdue

2-SampFTest for the alternative hypothesis (s 1 > (s2.

p= i f(x, nl - 1,n 2 - 1)dx

2-SampFTest for the alternative hypothesis (_1< (_2-

p= ff(x,n 1-1,n 2-1)dx

2-SampFTest for the alternative hypothesis (_1 :_ (_2.Limits

nmst satisfy the following:

Lb nd

/92=f f(x'nl- l'n2-1)dx= ff(x,n 1-1,n 2-1)dx

0U_,_

where: [Lbnd, Ubnd] = lower and upper limits

The F-statistic is used as the bound producing the smallest

integral. The reinaining bound is selected to achieve the

preceding integral's equality relationship.

A-52 Tables and Reference Information

2-SampTTest The following is the definition for the 2-SampTTest, The

two-sample tstatistic with degrees of freedom dfis:

t= Xl--X2

where tile computation of Sand df are dependent on

whether the variances are pooled. If the variances are not

pooled:

S = ]_/$2b'12qSX22

Vnl n2

d f-

S:t;12 + ,gXd2 )2

l l (s.s/,,

nl-lk nl } nz-lk nz )

otherwise:

(n I -1)SXl 2 +(n 2 -1)SX2 2

_:t;p = df

S= J1 +1Sxp

V)'_I n2

df =nl+n2-2

and Sxp is the pooled variance.

Tables and Reference Information A-53

Financial Formulas

This section contains financial fommlan for computing time value of money,

amortization, cash flow, interest-rate conve_\sions, and days between dates.

Time Value of i=[e(y×ln(x+l))]_l

Money

where: PMT € 0

y=C/Y +P/Y

x= (.01 ×1%) + C/Y

C/Y = compounding periods per year

P/Y = payment periods per year

I% = interest rate per yem"

i= (-FV + PV)( 1+ N) _1

where: PMT = 0

The iteration used to compute i:

[1-(1+i) NI+FV×(I+i) N

0 = PV +PMT xG i

1% = 100 × C/Y × [e(Y × ln(x + 1)) _ 1]

where: x=i

y=P/Y+C/Y

G i = l+i×k

where: k= 0 for end-of-period payments

k= 1 for beginning-of-period payments

N- [PMTxGi+PVxi)

ln(1 +i)

where: i€ 0

N= -(PV + FV) +PMT

where: i = 0

A-54 Tables and Reference Information

PMT=-ix[PV_ PV+FV ]

Gi [ (I+i)N- lJ

where: i€ 0

PMT = -(PV + FV) +N

where: i= 0

J(l+i)

where: i€ 0

PV = -(FV + PMT ×N)

where: i= 0

PMT xGi

FV PMT xGi (

i (l+i)N× PV-_

where: i€ 0

FV = -(PV + PMT xN)

where: i= 0

PMT×Gi.)

Tables and Reference Information A-55

Amortization If computing bal(), pint2 =npmt

Let hal(O) =RND(PV)

Iterate fronl m= 1 to pint2

Lm =RND[RND12(-i xbal(m - 1))]

hal(m) =bal(m - 1) -[m+ RND(PMT)

then:

hal() =hal(pint2)

EPrn( ) = bal(pmt2) -bal(pmtl)

ZInt( ) = (pint2 - pmtl + 1) x RND(PMT) - Z Prn( )

where: RND = round the display- to the number of

decimal places selected

RND12 = round to 12 decimal places

Balance, principal, and interest are dependent on the

values of PMT, PV, I°/o,and pmtl and pint2.

A-56 Tables and Reference Information

Cash Flow N

npv() = CF0 + _CFj(1 +/) & _(1 - (1 _/) rq)

j=l

where:Sj= ni J >-1

j= 0

Net present value is dependent on the values of the initial

cash flow (CFII), subsequent cash flows (CFj), frequency of

each cash flow (nj), and the specified interest rate (i),

irr() = 100 × i, where isatisfies npv() = 0

Internal rate of return is dependent on the values of the

initial c_h flow (CFo) and subsequent cash flow. (CFj),

i=I% + 100

Interest Rate

Conversions VEff( ) = 100 × (e cT × Zn(x+ 1)_1)

where: x= ,01 x NOM+ CP

_Nom( ) = 100 × CP × [ei + cP × z,.(x+ 1)_ 1]

where: x=,01 ×EFT"

EFF =effective rate

CP =compounding periods

NOM =nominal rote

Tables and Reference Information A-57

Daysbetween Withthedbd(function,youcanenterorcomputeadate

Dates within the range Jan. 1, 1950, through Dec. 31, 2049.

Actual/actual day-count method (assunles actual

number of days per month and actual number of day-s per

year):

dbd( (days between dates) =

Number of Days II - Number of Days I

Number of Days I = (Y1-YB) × 365

+ (number of days MB to M1)

+DT1

(Y1 - YB)

Number of Day-s II = (Y2-YB) x 365

+ (number of days MB to 11//2)

+DT2

(Y2 - YB)

where: M1 = month of first date

DT1 = day of first date

Y1 = year of first date

M2 = month of second date

DT2 = day of second date

Y2 = year of second date

MB = base month (January)

DB = base day (1)

YB = base year (first year _ter leap year)

A-58 Tables and Reference Information

BGeneralInformation

Contents Batte_" Infommtion ...................................... B-2

In Case of Difficulty ..................................... B-4

Error Conditions ......................................... B-5

Accuracy Infomlation .................................... B-10

Support and Sep_iee Information ......................... B-12

Warranty Infornlation .................................... B-13

General Information B-1

Battery Information

When to Replace

the Batteries

Effects of

Replacing the

Batteries

Battery

Precautions

The TI-83 uses five batteries: four AAA alkaline batteries

and one lithium battery-. The lithium battery pro_qdes

auxilimTF power to retain menlot T while you replace the

AAA batteries.

When the battery voltage level drops below a usable level,

the TI-83 displays this message when you turn on the unit.

_Jour batteries

are low.

Reco_r_end

change o?

batteries.

Alter this message is first displayed, you can expect the

batteries to function for about one or two weeks,

depending on usage. (This one-week to two-week period is

based on tests with alkaline batteries; the performance of

other kinds of batteries may vm3z.)

The low-battery message continues to be displayed each

time you turn on the unit until you replace the batteries. If

you do not replace the batteries within about two weeks,

the calculator may turn off by itself or fail to turn on until

you install new batteries.

Replace the lithimn batte_y- eve_3z three or four years.

Do not remove both types of batteries (AAA and lithium

auxiliat_F) at the same time. Do not allow the batteries to

lose power completely. If you follow these guidelines and

the steps for replacing batteries on page B-3, you can

replace either type of batter T without losing any

information in memo_7.

Take these precautions when replacing batteries.

• Do not mix new and used batteries. Do not mix brands

(or types within brands) of batteries.

• Do not mix rechm'geable and nonrechargeable

batteries.

• Install batteries according to polarity (+ and -)

diagrams.

• Do not place nonreehargeable batteries in a battery

recharger.

• Properly dispose of used batteries immediately. Do not

leave them within the reach of children.

• Do not incinerate batteries.

B-2 General hfformation

Replacing the

Batteries

To replace the batteries, follow these steps.

1. Turn offthe calculator. Replacethe slide cover over the

keybom'd to avoid inadvertently turning on the

calculator. Turn the back of the calculator toward you.

Hold the cMeulator upright. Place your thumb on the

oval indentation on the battetsz cover. Push down and

toward you to slide the cover al_out IAinch (6 nlnl). Lift

off the cover to expose the batte_3z eolnpartment.

Note: To avoid loss of infornmtion stored in

memory, you nmst turn off the calculator. Do not

remove the AAA batteries and the lithium battery

simultaneously.

3. Replace all four AAA alkaline batteries at the same

time. Or, replace the lithium batte_Ty-.

• To replace the AAA alkaline batteries, remove all

four discharged AAA batteries and install new ones

according to the polm'ity (+ and -) diagrams in the

batte_3z compartment.

• To remove the lithimn batte_Ty-,place your index

finger on the battet3z. Insert the tip of a ball-point pen

(or similar instrument) under the battery at the small

opening provided in the batte_sz compartment.

Carefully P_TY"the battetsz upward, holding it with

your thumb and finger. (There is a spring that pushes

against the underside of the battet3z.)

• Install the new batte_sz, + side up, by inserting the

batte_3z and gently- snapping it in with your finger.

Use a CR1616 or CR1620 (or equivalent) lithium

batte_y-.

4. Replace the batte_y- compartment cover. Turn the

calculator on and adjust the display contrast, if

necessmTy- (step 1; page B-4).

General Information B-3

In Case of Difficulty

Handling a

Difficulty

To handle a difficulty, follow these steps.

1. If you cannot see anything on the screen, the contrast

nlay need to be adjusted.

To darken the screen, press and release [2_, and then

press and hold [] until the display- is sufficiently dark.

To lighten the screen, press and release [_], and then

press and hold [] until the display is sufficiently light.

2. If an error menu is displayed, follow the steps in

Chapter 1. Refer to pages B-5 through B-9 for details

about specific errors, if necessatT.

3. If a checkerboard cursor ( N ) is displayed, then either

you have entered the nlaxinlunl number of characters in

a prompt, or nlenlory is full. If nlenlory is full, press [_

[MEM]2 to select 2:Delete, and then delete some items

fronl nlenlory (Chapter 18).

4, If the busy indicator (dotted line) is displayed, a graph

or program has been paused; the TI-83 is waiting for

input, Press [gNT_ to continue or press [_] to break,

5, If the calculator does not seem to work at all, be sure

the batteries are flesh and that they are installed

properly. Refer to battew information on pages B-2 and

B-3.

B-4 General Information

Error Conditions

When the TI-83 detects an error, it displays ERR:message and an error menu.

Chapter 1 describes the general steps for eotTeeting errors, This table contains

each etTor type, possible causes, and suggestions for correction,

Error Type Possible Causes and Suggested Remedies

ARCHIVED VAR A function or instruction is archived and therefore cannot

be executed or edited. [_se the unto'chive command to

mmrehive the variable before using it.

ARGUMENT A function or instruction does not have the co_Tect number

of arguments. See Appendix A and the appropriate chapter.

BADGUESS • In a CALC operation, you specified a Guess that is not

between Left Bound and Right Bound.

• For the solve( function or the equation solver, you

specified a guess that is not between lower and upper.

• Your guess and severM points around it are undefined.

Exa]nine a graph of the function. If the equation has a

solution, change the bounds and/or the initial guess.

BOUND • In a CALC operation or with Select(, you defined

Left Bound >Right Bound,

• In fMin(, fMax(, solve(, or the equation solver, you

entered lower >_upper.

BREAK You pressed the [ON]key to break execution of a prograln,

to halt a DRAW instruction, or to stop evaluation of an

expression.

DATATYPE You entered a value or variable that is the wrong data type.

• For a function (including implied lnultiplication) or an

instruction, you entered an argument that is an invalid

data type, such _ts a complex number where a real

number is required. See Appendix A and the appropriate

chapter.

• In an editor, you entered a type that is not allowed, such

as a matrix entered as an element in the stat list editor.

See the appropriate chapter.

•You attelnpted to store to an incorrect data type, such as

a nmtrix, to a list.

DIMMISMATCH You attempted to perform an operation that references

more than one list or lnatrix, but the dimensions do not

lnateh.

DIVIDE BY0 • You attempted to dixqde by zero. This error is not

returned during graphing. The TI-83 allows for

undefined values on a graph.

•You attelnpted a linear regression with a vertical line.

General Infornmtion B-5

Error Type Possible Causes and Suggested Remedies

DOMAIN • You specified an argument to a function or instruction

outside the wdid range, This elTor is not returned during

graphing. The TI-83 allows for undefined values on a

graph, See Appendix A and tile appropriate chapter.

• You attempted a logarithmic or power regression with a

-X or an exponential or power regression with a -Y.

• You attempted to compute XPrn( or Xlnt( with

pint2 <pint1.

Duplicate Name A variable you attempted to transmit cannot be translnitted

because a variable with that name already exists in the

receiving unit.

Error in Xmit • The TI-83 was unable to transmit an item. Check to see

that the cable is firnfly connected to both units and that

the receiving unit is in receive mode.

• You pressed [_ to break during transmission.

• You attempted to perform a backup from a TI-82 to a

TI-83.

• You attempted to transfer data (()tiler than kl through

1.6) from a TI-83 to a TI-82.

• You attempted to transfer kl through L6 from a TI-83 to

a TI-82 without using 5:Lists to TI82 on the LINK SEND

nlenu,

ILLEGAL NEST You attempted to use an invalid function in an argument to

a function, such as seq( within e_ression for seq(.

INCREMENT • The increment in seq( is 0 or has the wrong sign. This

error is not returned during graphing. The TI-83 allows

for undefined values on a graph,

• The increment in a For( loop is 0,

INVALID • You attempted to refel_nce a variable or use a function

where it is not valid. For example, Yn cannot reference

Y, Xmin, AX, or TblStart,

• You attempted to reference a variable or function that

was transferred from the TI-82 and is not valid for the

TI-S3. For example, you may have transfen'ed Un-1 to

the TI-83 from the TI-82 and then tried to reference it.

•In Seq mode, you attempted to graph a phase plot

without defining both equations of the phase plot.

B-6 General hfformation

Error Type

INVALID (cont.)

Possible Causes and Suggested Remedies

• In Seq nlode, you attempted to graph a recursive

sequence without having input the correct number of

initial conditions.

• In Seq mode, you attempted to reference terms other

than (n-l) or (n-2).

You attelnpted to designate a graph style that is invalid

within the eutTent graph mode.

You attempted to use Select{ without having selected

(turned on) at least one xyLine or scatter plot.

INVALIDDIM You specified dimensions for an argument that are not

appropriate for the operation.

You specified a list dimension as something other than

an integer between 1 and 999.

You specified a matrix dimension as something other

than an integer between 1 and 99.

You attempted to invert a matrix that is not square.

ITERATIONS • The solve( function or the equation solver has exceeded

the nmximum number of permitted iterations. Examine

a graph of the function. If the equation has a solution,

change the bounds, or the initial guess, or both.

•irr( has exceeded the nmxinmm number of permitted

iterations.

• When computing 1%,the nl_Lxinlunl number of iterations

was exceeded.

LABEL The label in the Goto instruction is not defined with a Lbl

instruction in the program.

MEMORY Memory is insufficient to perform the instruction or

function. You nmst delete items from memory (Chapter 18)

before executing the instruction or function.

Reeursive problems return this error; for example,

graphing the equation YI=Y1.

Branching out of an If/Then, For(, While, or Repeat loop with

aGoto also can return this error because the End statelnent

that terminates the loop is never reached.

General Information B-7

Error Type

MemoryFull

Possible Causes and Suggested Remedies

• You are unable to transmit an item because tile receiving

unit's available lnelnol_y- is insufficient. You lnay skip the

iteln or exit receive triode,

• During a lnelnol_y- backup, the receiving unit's available

nlenlory is insufficient to receive all itelns in the sending

unit's lnelnot_yL A lnessage indicates the number of bytes

the sending unit nmst delete to do the lnetnol_- backup.

Delete items and try again.

MODE You attempted to store to a window variable in another

graphing mode or to perform an instruction while in the

wrong nlode; for exaInple, Drawlnv in a graphing nlode

other than Func.

..............................The saiv;{ function _;i the equation ......

a sign change.

• You atteinpted to compute I%when FV, (N*PMT), and PV

are all _>O, or when FV, (N*PMT), and PV are all _<O.

• You attempted to eonlpute irr( when neither CFList nor

CFO is > O, or when neither CFList nor CFO is < O.

NONREAL ANS In Real mode, the result of a calculation yielded a complex

result. This error is not returned during graphing. The TI-83

allows fox"undefined values oil a graph.

OVERFLOW You attempted to enter, or you have calculated, a number

that is beyond the range of the calculator. This error is not

returned during graphing. Tile TI-83 allows for undefined

wdues on a graph.

RESERVED You attempted to use a wsteln variable inappropriately.

See Appendix A.

SINGULAR MAT • A singular matrix (determinant = 0) is not valid as the

argument for %

• The 8inReg instruction or a polynomial regression

generated a singular matrix (determinant = 0) because it

could not find a solution, or a solution does not exist.

This error is not returned during graphing. Tile TI-83

allows for undefined values on a graph.

B-8 General hfformation

Error Type Possible Causes and Suggested Remedies

SINGULARITY expression ill the solve( function or the equation solver

contains a singularity (a point at which the function is not

defined). Examine a graph of the function. If the equation

h_s a solution, change the bounds or the initial guess or

both.

STAT You attempted a stat calculation with lists that are not

appropriate.

• Statistical analyses must have at least two data points.

• Ned-Ned must have at least three points in each

partition.

• When you use a frequency list, its elements must be _>0.

•(Xmax - Xmin) /Xscl nmst be <_47 for a histogram.

STAT Pt_OT Y0u atte;_pted to display a graph when a stat plot that uses

an undefined list is turned on.

SYNTAX The connnand contains a syntax error. Look for lnisplaced

functions, arguments, parentheses, or colnnlas. See

Appendix A and the appropriate chapter,

TOL NOT MET You requested a tolerance to which the algorithln cannot

retum an accurate result.

UNDEFINED You referenced a variable that is not currently defined. For

example, you referenced a stat variable when there is no

current calculation because a list has been edited, or you

referenced a variable when the variable is not valid for the

current calculation, such as a 'after Med-Med.

WINDOW RANGE A probleln exists with the window variables.

•You defined Xmax _<Xmin or Ymax _<Ymin.

•You defined 0max _<0min and 0step > 0(or xqce versa).

• You attempted to define Tstep=0.

• You defined Tmax _<Train and Tstep > 0 (or vice versa).

• Window variables are too SLUM1or too large to graph

correctly. You may have attempted to zoom in or zoom

out to a point that exceeds tile TI-83's nulnerical range.

ZOOM • A point or a line, instead of a box, is defined in ZBox.

• A ZOOM operation returned a math error.

General Information B-9

Accuracy Information

Computational

Accuracy

Graphing

Accuracy

To maximize accuracy-, the TI-83 carries more digits

internally than it displays. Values m_ stored in nlemo_-

using up to 14 digits with a two-digit exponent.

• You can store a value in the window vm'iables using up

to 10 digits (12 for Xscl, Yscl, Tstep, and 0step).

• Displayed values are rounded as specified by the mode

setting with a nlaxinmln of 10 digits and a two-digit

exponent.

• ReflEO displays up to 14 digits in Float mode. [ Mng a

fixed-decilnal setting other than Float causes ReflEO

results to be rounded and stored with the specified

number of decimal places.

Xmin is the center of the leffmost pixel, Xmax is the center

of the next-to-the-rightmost pixel. (The rightmost pixel is

reserved for the busy indicator,) AX is the distance

between the centers of two adjacent pixels.

• In Full screen mode, AX is calculated zks

(Xmax - Xmin) /94. In G-T split-screen mode, AX is

calculated as (Xmax - Xmin) /46.

• If you enter a value ff)r AX from the home screen or a

program in Full screen mode, Xmax is calculated as

Xmin + AX * 94. In G-T split-screen mode, Xmax is

calculated as Xmin + AX * 46,

Ymin is the center of the next-to-the-bottom pixel; Ymax is

the center of the top pixel. AY is the distance between the

centers of two adjacent pixels.

• In Full screen mode, AY is calculated as

(Ymax -Ymin) /62. In Horiz split-screen nlode, AYis

cMculated as (Ymax - Ymin) /30. In G-T split-screen

mode, AY is c'Mculated as (Ymax - Ymin) /50.

• If you enter a vMue for AYfronl the home screen or a

program in Full screen mode, Ymax is calculated as

Ymin + AY * 62. In Horiz split-screen nlode, Ymax is

eMculated as Ymin + AY * 30. In G-T split-screen nlode,

Ymax is calculated _ksYmin + AY* 50,

B-IO General Information

Cursorcoordinatesaredisplayedaseight-character

numbers(whichmayincludeanegativesign,decimal

point,andexponent)whenFloatmodeisselected.XandY

areupdatedwithanlaxinmlnaccuracyofeightdigits.

minimum and maximum on the CALCULATE menu are

calculated with a tolerance of 1E-5; _f(x)dx is calculated at

1E-3. Therefore, the result displayed nlay not be accurate to

'all eight displayed digits. For most functions, at least five

accurate digits exist. For fMin(, fMax(, and fntnt( on the

MATH menu and solve( in the CATALOG, the tolerance can

be specified.

Function Limits

Function Results

Function Range of Input Values

sn cos. " ....................0 .......

sin-12a',COS-1 X...........-1 < x<_1 ...............................

ex-10100< x-<230.25850929940

1_ -10 i00 < x< 100

sinh x, cosh wIxl _<230.25850929940

tanh xIxl < 10 i°°

sinh :_ xIxl < 5 x 109!_..............................

cosh-1 .%, <l_<x 5x 1()9!_

tanh :_ x...........................................................-1 <x< .........................1

_x (real lnode) 0 < x < 10100

_X (complex mode) Ixl < 10 t°°

x! -.5 -<x-< 69, where xis a multiple of .5

Function Range of Result

1 1 o o )

tan- x-90 to 90 or-_/2 t0_/2 (radians)

cos-1x0° to 180° or 0 to x (radians)

General Information B-11

Support and Service Information

Product Support

Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands

For general questions, contact Texas Instrunmnts Customer Support:

phone: 1-800-TI-CARES (1-800-842-2737)

e-mail: ti-cares@ti.com

For technical questions, call the Progrannning Assistance Group of Custonler

Support:

phone: 1-972-917-8324

Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands

Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.

e-mail: ti-cares@ti.com

Internet: education.ti.com

Product Service

Customers in the U.S. and Canada Only

Always contact Texas Instrmnents Customer Support before returning a product

for service.

Customers outside the U.S. and Canada

Refer to the leaflet enclosed with this product or contact your local Texas

Instruments retaileddistributor.

Other TI Products and Services

Visit the TI calculator honle page on the World Wide Web.

education.ti.com

Refer to the leaflet enclosed with this product or contact your local Texas

Instruments retailer/distributor.

B-12 General Information

Warranty Information

Customersinthe U,S.andCanadaOnly

One-Year Limited Warranty for Electronic Product

This Texas Instruments ("TI") electronic product warranty extends only to the original

purchaser and user of the product.

Warranty Duration. This TI electronic product is warranted to the original purchaser

for a period of one (1) year fl'om the original purchase date.

Warranty (;overage. This TI electronic product is warranted against defective

rnaterials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN

DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER

SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS

OR CONSTRUCTION.

Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,

INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF

MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED

IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL

NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL

OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE

CONSUMER OR ANY OTHER USER.

Sortie states/provinces do not allow the exclusion or limitation of implied warranties or

consequential damages, so the above limitations or exclusions may not apply to you.

Legal Remedies. This warranty gives you specific legal rights, mid you may also have

other rights that vat_ fl'om state to state or province to province.

Warranty Performance. [)tiring the above one (1) year warranty period, your defective

product will be either repaired or replaced with a reconditioned model of an equivalent

quality (at TI's option) when the product is returned, postage prepaid, to Texas

Instruments Service Facility. The warranty of the repaired or replacement unit will

continue for the warranty of the original unit or six (6) months, whichever is longer.

Other than the postage requirement, no charge will be made for such repair and/or

replacernent. TI strongly recommends that you insure the product for value prior to

rnailing.

Software. Software is licensed, not sold. TI and its licensom do not warrant that the

software will be free fl_m errom or rneet your specific requirements. All software is

provided "AS IS."

protected by copyright.

General Information B-13

Australia &New Zealand Customers only

One-Year Limited Warranty for Commercial Electronic Product

This Texas Instruments electronic product wmTanty extends only to the

original purchaser and user of the product.

Warranty Duration. This Tex_Ls Instruments electronic product is warranted

to the original purchaser for a period of one (1) year from the original

purchase date.

Warranty Coverage. This Texas Instruments electronic product is warranted

against defective materials and construction. This warranty is void if the

product luks been damaged by accident or unreasonable use, neglect, improper

set_ice, or other causes not arising out of defects in materials or construction.

Warranty Disclaimers. Any implied warranties arising out of this sale,

including but not limited to tile implied warranties of merchantability

and fitness for a particular purpose, are limited in duration to tile

above one-year period. Texas Instruments shall not be liable for loss

of use of the product or other incidental or consequential costs,

expenses, or danlages incm'red by the consuiner or any other user.

Sonic jurisdictions do not allow the exclusion or limitation of implied

warranties or consequential damages, so the al)ove limitations or exclusions

nlay not apply to you.

Legal Remedies. This warranty gives you specific legal rights, and you nlay

also have other rights that vm_- from jurisdiction to jm'isdiction.

Warranty Performance. Dm'ing the above one (1) year warranty period,

your defective product will be either repaired or replaced with a new or

reconditioned model of an equivalent quality (at TI's option) when the product

is returned to the original point of purchase. The repaired or replacement unit

will continue for the warranty of the original unit or six (6) months, whichever

is longer. Other than your cost to return the product, no charge will be made

for such repair and/or replacement. TI strongly recommends that you insm'e

the product for value if you mail it.

Software. Software is licensed, not sold. TI and its licensors do not warrant

that the software will be free from errors or meet your specific requirements.

All software is provided "AS IS."

are protected by copyright.

All CustomersOutsidethe U.8. andCanada

For information about the length and terms of the warranty, refer to your package

and/or to the warranty statement enclosed with this product, or contact your local Texas

Instruments retailer/distributor.

B-14 General Information

Index

+(addition), 2-3, A-38

z2cdf( (chi-square cdf), 13-31, A-3

x2pdf( @hi-square pdf), 13-31, A-4

x2-Test (ehi-square test), 13-22, A-4

: (colon), 6, 16-5

+ (concatenation), 15-6, A-38

3 (cube), 2-6, A-35

3_( (cube root), 2-6, A-35

° (degrees notation), 2-3, A-34

/(division), 2-3, A-37

=(equal-to relational test), 2-25,

A-35

! (factorial), 2-21, A-34

0(graph style, animate), 3-9

'. (graph style, (lot), 3-9

".. (graph style, line), 3-9

> (greater than), 2-25, A-35

> (greater than or equal to), 2-25,

A-35

• . o

-1 (mx.erse), 2-3, 8-9, 10-10, A-36

< (less than), 2-25, A-35

< (less than or equal to), 2-25, A-36

{ } (list indicator), 11-4

[] (matrix indicator), 10-7

(minutes notation), 2-23, A-38

* (multiplication), 2-3, A-37

(negation), 1-23, 2-4, A-37

(not equal to), 2-25, A-35

() (parentheses), 1-23

(pi), 2-4

[] (pixel mark), 8-15, 12-34

+ (pixel mark), 8-15, 12-34

(pixel mark), 8-15, 12-34

_::> (plot type, box), 12-33

2m= (plot type, histogram), 12-32

_:>'_" (plot type, modified box), 12-32

__ (plot type, normal probability),

12-33

^ (power), ~-3, A-36, A-37

10"( (power often), 2-#,A-37

×/ (root), 2-6, A-35

(seconds notation), 2-23, A-38

2(square), 2-3, A-36

_( (square root), 2-3, A-37

--> Store, 1-1]-_, A-28

.... (string indicator), 15-3

(subtraction), 2-3, A-38

-A-

a+bl (rectangular complex mode),

1-12, 2-16, A-3

above graph style(N), 3-9

abs( (absolute value), 2-13, 2-19,

10-10,A-2

accuracy information

computational and graphing, B-10

graphing, 3-17

function limits and results, B-11

addition (+), 2-3, A-38

alpha cursor, 1-5

alpha key, 3

alpha-lock, 1-8

alternative hypothesis, 13-7

amortization

hal( (amortization balanee), 14-9,

A-3

calculating schedules, 1]-t-9

fornmla, A-56

Elnt( (sum of interest),14-9, A-12

EPrn( (sum of principal), lJ.t-9, A-19

and (Boolean operator), 2-26, A-2

angle(, 2-19, A-2

ANGLE menu, 2-23

angle modes, 1-11

animate graph style (_), 3-9

ANOVA( (one-way variance analysis),

13-25, A-2

fornmla, A-51

Ans (last answer), 1-18, A-2

APD TM (Automatic Power Down__), 1-2

applications. ,fee examples,

applications

areeosine (cos < 0, 2-3

aresine (sin<0, 2-3

aretangent (tan "10, 2-3

augment(, 10-1J-t, 11-15,A-3

Automatic Power Down _xt(AP[Y_), 1-2

automatic regression equation, 12-22

automatic residual list (RESID), 12-22

axes fommt, sequence graphing, 6-8

axes, displaying (AxesOn, AxesOff),

3-14, A-3

AxesOff, 3-14t, A-3

AxesOn, 3-14t, A-3

Index-1

-B-

backing up calculator memmTy, 19-4,

19-10

bal( (amortization balance), 14-9, A-3

batteries, 1-2, B-2

below- graph style (6), 3-9

binomcdf(, 13-33, A-3

binompdf(, 13-33, A-3

Boolean logie, 2-26

box pixel mark ([]), 8-15, 12-34

Boxplot plot type (_), 12-33

busy indicator, 1-4

-C-

CALCULATE metal, 3-25

Calculate output option, 13-6, 13-8

cash flow"

calculating, 14-8

fornmla, A-57

irr( (internal rate of return), 14-8,

A-13

npv( (net present value), 14-8, A-17

CATALOG, 15-2

CBL 2/CBL System, 16-21, 19-3, A-IO

CBR, 16-21, 19-3, A-IO

Check RAM (memol_y screen), 18-2

old-square cdf 0_2cdf0,13-31, A-3

old-square pdf (z2pdf(), 13-31, A-4

eld-squm'e test (z2-Test), 13-22, A-4

Circle( (draw" circle), & l 1, A-4

Clear Entries, 1&4 ,A-4

clearing

entries (Clear Entries), 18-4, A-4

all lists (ClrAIIkists), 1&4, A-4

draw3ng (ClrDraw), 8-4, A-4

home screen (ClrHome), 16-20, A-4

list (Clrkist), 12-20, A-4

table (ClrTable), 16-20, A-4

ClrAIIkists (dear all lists), 1&4, A-4

ClrDraw (clear drawing), &4, A-4

ClrHome (clear home screen), 16-20,

A-4

Clrkist (elear list), 12-20, A-4

ClrTable (elear table), 16-20, A-4

coefficients of determination (r 2, R2),

12-23

colon separator (:), 6, 16-5

combinations (nCr), 2-21, A-16

- C (continued) -

complex

modes (a+bl, re^01), 1-12, 2-16, A-3,

A-22

numbers, 1-12, 2-16, 2-18, A-22

compounding-periods-per-year variable

(c/Y), 14-4, 14-14

coneatenation (+), 15-6, A-38

confidenee intervals, 13-8, 13-16 -

13-21

conj((conjugate), 2-18, A-4

Connected (plotting mode), 1-11, A-4

contrast (display), 1-3

convergence, sequence graphing, 6-12

conversions

)Dec (to deeimal), 2-5, A-5

_DMS (to degree_minute_ seeonds),

2-24, A-7

_Eff (to effeetwe interest rate),

14-12, A-7

Equ_String( (equation-to-string

conversion), 15-7, A-8

_Frac (to fraction conversion), 2-5,

A-IO

kist_matr( (list-to-matrix

conversion), 10-14, 11-15, A-14

MatrHist((matrix-to-list conversion),

10-14, 11-16, A-15

)Nora (to nominal interest rate

conversion), 14-12, A-16

)Polar (to polar eonversion), 2-19,

A-19

PH_x(, P)Ry( (polar-to-reetangular

conversion), 2-24, A-21

_Rect (to rectangular conversion),

2-19, A-22

R_Pr(, R_Pe( (reetangular-to-polm"

conversion), 2-24, A-23

String)Equ( (string-to-equation

conversion), 15-8, A-29

CoordOff, 3-14, A-5

CoordOn, 3-14, A-5

correlation eoefficient (r), 12-23, 12-25

to 12-27

cos((cosine), 2-3, A-5

cos'l((areeosine), 2-3, A-5

cosh( (hyperbolic cosine), 15-10, A-5

Index-2

- D (continued)-

cosh'l( (hyperbolic arceosine), 15-10,

A-5

cosine (cos(), 2-3, A-5

cross pixel mark (+), 8-15, 12-34

cube (3), 2-6, A-35

cube root (3_(), 2-6, A-35

CubicReg (cubic regression), 12-26,

A-5

cubic regression (CubicReg), 12-26,

A-5

eunmlative sum (cumSumO, 10-15,

11-12, A-5

cumSum( (cumulative sum), 10-15,

11-12, A-5

cursors, 1-5, 1-8

C/Y (compounding-periods-per-year

variable), 124-Y4,124-124

- D-

Data input option, 13-6, 13-7

days between dates (dbd0, 14-13, A-5,

A-58

dbd( (days between dates), 14-13, A-5,

A-58

_Dec (to decimal conversion), 2-5, A-5

decimal mode (float or fixed), 1-10

decrement and skip (DS<(), 16-14, A-7

definite integral, 2-7, 3-28, 4-8, 5-6

Degree angle mode, 1-11, 2-23, A-6

degrees notation (°), 2-3, A-3J4

DELETE FROM menu, 18-3

delete vm'iable contents (DelVar),

16-15, A-6

DeWar (delete vm'iable contents),

16-15, A-6

DependAsk, 7-3, 7-5, A-6

DependAuto, 7-3, 7-5, A-6

derivative. See numerical derivative

det((determinant), 10-12, A-6

determinant (det0, 10-12, A-6

DiagnostieOff, 12-23, A-6

DiagnostieOn, 12-23, A-6

diagnostics display mode(r, r2, R2),

12-23

differentiation, 2-8, 3-28, 4-8, 5-6

-D (continued) -

dimensioning a list or matrix, 10-12,

10-13, 11-11, A-6

dim((dimension), 10-12, 11-11, A-6

->dim( (assign dimension), 10-13,

11-11, A-6

Disp (display), 16-18, A-6

DispGraph (display graph), 16-19, A-7

display contrast, 1-3

display cursors, 1-5

DispTable (display table), 16-19, A- 7

DISTR (distributions memO, 13-29

DISTR DRAW (distributions drawing

menu), 13-35

distribution functions

binomedf(, 13-33, A-3

binompdf(, 13-33, A-3

z2cdf(, 13-31, A-3

z2pdf(, 13-31, A-4

Fcdf(, 13-32, A-8

Fpdf(, 13-32, A- 9

geometcdf(, 13-34, A- I O

geometpdf(, 13-34, A-11

invNorm(, 13-30, A-12

normalcdf(, 13-30, A-1 7

normalpdf(, 13-29, A-17

poissoncdf(, 13-324, A-99

poissonpdf(, 13-33, A-19

tcdf(, 13-31, A-29

tpdf(, 13-30, A-29

distribution shadh]g instructions

Shadex2(, 13-36, A-26

ShadeF(, 13-36, A-27

ShadeNorm(, 13-35, A-27

Shade_t(, 13-36, A-27

dhqsion (/), 2-3, A-37

[)MS (degrees/minutes/seconds entity"

notation), 2-23, A-38

_DMS (to degreegminutes/seconds),

2-224, A- 7

dot graph style ('..), 3-9

dot pixel Inark (.), 8-15, 12-324

Dot (plotting mode), 1-11, A-7

DrawF (draw- a function), &9, A-7

Index-3

- D (continued)-

drawing on agraph

circles (Circle(), 8-11

flmetions and inverses (DrawF,

Drawlnv), 8-9

lines (Horizontal, Line(, Vertical),

8-6, 8-7

line segments (Line(), 8-5

pixels (PxI-Change, Pxl-Off, Pxl-On,

pxI-Test), 8-16

points (Pt-Change, Pt-Off, Pt-On),

8-14

tangents (Tangent), 8-8

text (Text), 8-12

using Pen, 8-13

Drawlnv (draw" inverse), 8-9, A-7

DRAW menu, 8-3

DRAW instructions, 8-3 -8-16

[)raw- output option, 13-6 -13--8

DRAW POINTS menu, 8-14

DRAW STO (draw" store menu), 8-17

dr/d0 operation on a graph, 5-6

DS<( (decrement and skip), 16-14, A-7

DuplicateName menu, 19-5

dx/dt operation on a graph, 3-28, 4-8

dy/dx operation on a graph, 3-28, 4-8,

5-6

-E-

e(constant), 2-4

e^((exponential), 2-4, A- 7

E (exponent), 1-7, 1-10, A-7

edit keys table, 1-8

t.Eff( (to effective interest rate), 14-12,

A-7

Else, 16-10

End, 16-12, A-8

Eng (engineering notation mode), 1-10,

A-8

entry cm'sor, 1-5

ENTRY (last entry key), 1-16

EOS TM (Equation Operating System),

1-22

eqn (equation variable), 2-8, 2-12

equal-to relational test (=), 2-25, A-35

Equation Operating System (EOSTM),

1-22

Equation Solver, 2-8

equations with nmltiple roots, 2-12

-E(continued) -

Equi_String( (equation-to-string

conversion), 15-7, A-8

errors

diagnosing and correcting, 1-24

messages, B-5

example _-applieations

m'ea between cm_es, 17-11

m'eas of regular n-sided polygons,

17-16

box plots, 17-2

cobweb attractors, 17-8

fundamental theorem of calculus,

17-14

guess the coefficients, 17-9

inequalities, 17-5

mortgage payments 17-18

parametric equations: ferris wheel

problem, 1 7-12

pieeewise functions, 1 7-4

Sierpinski triangle, 1 7- 7

solving a system of nonlinear

equations, 17-6

unit circle and trig curves, 17-10

examples_--Getting Started

box w_th lid 9 to 16

defining a, 9

defining a table of values, 10

finding calculated maxinmm, 16

setting the viewlng window, 12

tracing the graph, 13

zooming in on the graph, 15

zooming in on the table, 11

coin flip, 2-2

compound interest, 14-3

drawing a tangent line, 8-2

financing a era', 14-2

forest and trees, 6-2

generating a sequence, 11-2

graphing a circle, 3-2

mean height of a population, 13-2

path of a ball, J-t-2

pendulum lengths and periods, 12-2

polar rose, 5-2

Index-4

-E (continued) -

exalnp]es_--Getting Started (continued)

quadratic formula

converting to a fraction, g

displaying eomplex results, 8

entering a calculation, 6

roots of a, 7-2

sendHlg variables, 19-2

solving a system of linear equations,

10-2

unit circle, 9-2

volume of a cylinder, 16-2

examples_-nliseellaneous

convergence, 6-12

daylight hours in Alaska, 12-28

calculating outstanding loan

balances, lJ-t-l O

predator-prey model, 6-13

exponential regression (ExpReg),

12-26, A-8

expr( (string-to-expression conversion),

15-7, A-8

ExpReg (exponential regression),

12-26, A-8

expression, 1-6

converting front string (expr(), 15- 7,

A-8

turning on and off (lllxprOn,

lllxprOff), 3-1].t ,A-8

lllxprOff (expression off), 3-1].t, A-8

lllxprOn (expression on), 3-1].t, A-8

- F-

ff(x)dx operation on a graph, 3-28

factorial (!), 2-21, A-3]._

fandly of eut_es, 3-16

Fcdf(, 13-32, A-8

Fill(, 10-13, A-8

FINANCE CALC menu, 14-5

FINANCE VARS menu, 1]-t-1]-t

financial functions

amortization schedules, 10.-9

cash flows, 14-8

days between dates, 14-13

interest rate conversions, 14-12

payment method, 14-13

time value of money (TVM), 14-6

- F (continued) -

Fix (fJxed-deeimal mode), 1-10, A-8

fixed-deeimal mode (Fix), 1-10, A-8

Float (floating-decimal mode), 1-10,

A-8

floating-decimal mode (Float), 1-10,

A-8

fMax( (function maximum), 2-6, A-9

fMin( (function ndnimum), 2-6, A-9

fnlnt( (function integral), 2-7, A-9

FnOff (function off), 3-8, A-9

FnOn (function on), 3-8, A-9

For(, 16-10, k-9

format settings, 3-13, 6-8

formulas

amortization, A-56

ANOVA, A-51

cash flow, A-57

days between dates, A-58

factorial, 2-21

interest rate conversions, A-57

logistic regression, A-50

sine regression, A-50

time value of money, A-5].t

two-sample T-Test, A-52

two-sample ttest, A-53

fPart( (fractional part), 2-1& 10-11, A-9

Fpdf(, 13-32, A-9

)Frac (to fraction), 2-5, A-IO

free-moving cursor, 3-17

frequency, 12-2].t

Full (full-screen mode), 1-12, A-IO

full-screen mode (Full), 1-12, A-IO

Func (function graphing mode), 1-11,

A-IO

function, definition of, 1-7

function graphing, 3-1 to 3-28

accuracy, 3-17

CALC (calculate menu), 3-25

defining and displaying, 3-3

defining in the Y= editor, 3-5

defining on the home screen, in a

program, 3-6

deselecting, 3- 7

displaying, 3-3, 3-11, 3-15

evaluating, 3- 6

family of cmxres, 3-16

format settings, 3-13

Index-5

-F (continued) -

Ftmction graphing (continued)

free-moving cursor, 3-17

graph styles, 3-9

maximunl of (fMax0, 2-6, A-9

minimmn of (fMin0, 2-6, A-9

modes, 1-11, 3-4,A-10

moving the cursor to a value, 3-19

overlaying functions on a graph,

3-16

panning, 3-19

pausing or stopping a graph, 3-15

Quick Zoom, 3-19

selecting, 3-7, 3-8, A- 9

shading, 3-10

Snmrt Graph, 3-15

tracing, 3-18

window variables, 3-11, 3-12

Y= editor, 3-5

_ewing window, 3-11

AX and AY window variables, 3-12

ZOOM menu, 3-20

ZOOM MEMORY menu, 3-23

function integral (fnlnt0, 2-7, A-9

functions and instructions table, A-2 to

A-2

future vahle, 14-5, 14-7, l J-t-lJ-t

present value, 14-5, 14-7, 1J-t-l}-t

FV (future-value vm'iable), 1J4-J4, 1J4-1J4

-G -

gcd( (greatest common divisor), 2-15,

A-IO

GDB (graph database), 8-19

geometcdf(, 13-34, A- I O

geometpdf(, 13-34, A- I O

Get( (get data from CBL 2/CBL or

CBR), 16-21, A-IO

GetCalc( (get data from TI-83), 16-21,

A-IO

getKey, 16-20, A-IO

Getting Started, 1to 18. See also

examples, Getting Started

Goto, 16-13, A-IO

-G (continued) -

graph database (GDB), 8-19

graphing modes, 1-11

graphing-order modes, 1-12

GraphStyle(, 16-15, A-11

graph styles, 3-9

graph-table split-screen mode (G-T),

1-12, 9-5, A-11

greater than (>), 2-25, A-35

greater than or equal to (>), 2-25, A-35

greatest common divisor (gcd0, 2-15,

A-IO

greatest integer (intO, 2-14, 10-11,

A-12

GridOff, 3-14, A-11

GridOn, 3-14, A-11

G-T (graph-table split-screen mode),

1-12, 9-5, A-11

- H -

Histogram plot type (2m_), 12-32

home screen, l-J4

Horiz (horizontal split-screen mode),

1-12, 9-4, A-11

hyperbolic functions, 15-10

Horizontal (draw- line), &6 - 8-7, A-11

hypothesis tests, 13-10 -13"-15

i(complex number constant), 2-17

1%(annual interest rate variable), 14-4,

14-14

identity(, 10-13, A-11

if instructions

If, 16-9, A-11

If-Then, 16-9, A-11

If-Then-Else, 16-10, A-11

imag( (imaginmTy" pm't ), 2-18, A-11

imaginary part (imagO, 2-18, A-11

implied nmltiplieation, 1-23

increment and skip (IS>(), 16-13, A-13

IndpntAsk, 7-3, A-12

IndpntAuto, 7-3, A-12

independent variable, 7-3, A-12

inferential stat editors, 13-6

Index-6

-I (continued) -

inferential statistics. See also stat tests;

confidence intervals

alternative hypotheses, 13- 7

bypassing editors, 13-8

calculating test results (Calculate),

13-8

confidence interval calculations,

13-8, 13-16 -13-21

data input or stats input, 13-7

entering argument values, 13- 7

graphing test results (Draw), 13-8

input descriptions table, 13-26

pooled option, 13-8

STAT TESTS menu, 13-9

test and interval output variables,

13-28

Input, 16-16, 16-17, A-12

insert cursor, 1-5

inString( (in string), 15-7, A-12

instruction, definition of, 1-7

int( (greatest integer), 2-1#, 10-11,

A-12

Elnt( (sum of interest), 1#-9, A-12

integer part (iPart0, 2-1#, 10-11, A-12

integral. See nmnerical integral

interest rate conversions

eMeulating, 14-12

_Eff( (compute effective interest

rate), 14-12, A-7

formula, A-57

_Nom( (compute nondnal interest

rate), 1#-12, A-16

internal rate of return (irr(), 1#-8, A-13

intersect operation on a graph, 3-27

inverse (-1), 2-3, 8-9, 10-10, A-36

inverse eunmlative normal distribution

(invNorm0, 13-30, A-12

inverse trig functions, 2-3

invNorm( (inverse eunmlative normal

distribution), 13-30, A-12

iPart( (integer part), 2-14, 10-11, A-12

irr( (internal rate of return), 14-8, A-13

I$>( (increment and skip), 16-13, A-13

-K-

keyboard

layout, 2, 3

ninth operations, 2-3

key-code diagrmn, 16-20

- L-

L(user-created list nmne symbol),

11-16, A-13

LabelOff, 3-14, A-13

LabelOn, 3-14, A-13

labels

graph, 3-14, A-13

program, 16-13, A-13

Last Entry, 1-16

Lbl (label), 16-13, A-13

Icm( (least common multiple), 2-15,

A-13

least common nmltiple (Icm(), 2-15,

A-13

length( of string, 15-8, A-13

less than (<), 2-25, A-35

less than or equal to (<), 2-25, A-36

line graph style C'), 3-9

Line( (draw line), 8-5, A-13

line segments, drawing, &5

lines, drawing, 8-6, &7

linking

receMng items, 19-5

to a CBL 2/CBL System or CBR, 19-3

to a PC or Macintosh, 19-3

to a TI-82, 19-3, 19-8

transndtting items, 19- 6

two TI-83 units, 19-3

LINK RECEIVE menu, 19-5

LINK SEND menu, 19-4

kinReg(a+bx) (linear regression),

12-26, A-14

LinReg(ax+b) (linear regression),

12-25, A-14

LinRegTTest (linear regression ttest),

13-2#, A-14

AList(, 11-12, A-14

LIST MATH menu, 11-17

List_matr( (lists-to-matrix conversion),

10-14, 11-15, A-14

LIST NAMES menu, 11-6

LIST OPS menu, 11-10

Index-7

-L(continued) -

lists, 11-1 to 11-18

aeeessing an element, 11-5

attaehing fornmlas, 11-7, 12-14

clearing all elements, 12-12, 12-20

eopying, 11-5

creating, 11-3, 12-12

deleting from memory, 11-5, 18-3

detaching fommlas, 11-8, 12-16

dimension, 11-4, 11-11

entering list names, 11-6, 12-11

indicator ({ }), 11-4.

naming lists, 11-3

storing and displaJAng, 11-4.

transmitting to and from TI-82, 19-4

using in expressions, 11-9

using to graph a family of curves,

3-16, 11-5

using to select data points from a

plot, 11-13

using ,_th math functions, 11-9

using _th ninth operations, 2-3

In(, 2-4, A-14

LnReg (logarithmic regression), 12-26,

A-14

log(, 2-4, A-14

logic (Boolean) operators, 2-26

Logistic (regression), 12-27, A-15

logistic regression fornmla, A-50

- M -

MATH CPX (eomplex menu), 2-18

MATH menu, 2-5

MATH NUM (number menu), 2-13

math operations, keyboard, 2-3

MATH PRB (probability menu), 2-20

MatrHist( (nmtrix-to-list conversion),

10-14, 11-16, A-15

matrices, 10-1 to 10-16

accessing elements, 10-8

copying, 10-8

defined, 10-3

deleting from memory, 10-4

dimensions, 10-3, 10-12, 10-13

displaying a nmtrix, 10-8

displaying matrix elements, 10-4

editing matrix elements, 10-6

-M (continued) -

matriees, (eontinued)

indicator ([ ]), 10-7

inverse (-1), 10-10

math functions, 10-9 to 10-11

matrix math functions (det(, T, dim(,

Fill(, identity(, randM(, augment(,

MatrHist(, List_matr(, cumSumO,

10-12 to 10-16

reDreneing in expressions, 10- 7

relational operations, 10-11

row operations(ref(, rref(, rowSwap(,

row+(, *row(, *row+(), 10-15

selecting, 10-3

xqewing, 10-5

MATRX EDIT menu, 10-3

MATRX MATH menu, 10-12

MATRX NAMES menu, 10-7

max((maximum), 2-15, 11-17, A-15

maximum of a funetion (fMax0, 2-6,

A-9

maximum operation on a graph, 3-27

mean(, 11-17, A-15

median(, 11-17, A-15

Meal-Meal (median-median), 12-25,

A-15

inenlolTy"

backing up, 19-10

checking available, 18-2

clearing all list elements from, 18-4

elem'tng entries from, 18-4

deleting items from, 18-3

insufficient during transmission,

19-5

resetting defaults, 18-6

resetting memory, 18-5

MEMORY menu, 18-2

Menu( (define menu), 16-14, A-15

menus, 4, 1-19

defining (Menu(), 16-14, A-15

nmp, A-39

scrolling, 1-19

min( (minhmm0, 2-15, 11-17, A-16

minimum operation on a graph, 3-27

minimum of a function (fMin0, 2-6, A-9

minutes notation ('), 2-23, A-38

ModBoxplot plot type (4>.), 12-32

Index-8

-M (continued) -

modified box [)lot type (o..), 12-32

mode settings, 1-9

a+bl (complex rectangular), 1-12,

2-16, A-3

re^Of (complex polar), 1-12, 2-16,

A-22

Connected (ploning), 1-11, A-4

Degree (angle), 1-11, 2-24, A-6

Dot (plotting), 1-11, A-7

Eng (notation), 1-10, A-8

Fix (decimal), 1-10, A-8

Float (decimal), 1-10, A-8

Full (screen), 1-12, A-IO

Func (graphing), 1-11, A-IO

G-T (screen), 1-12, A-11

Horiz (screen), 1-12, A-11

Normal (notation), 1-10, A-16

Par/Param (graphing), 1-11, A-18

Pol/Polar (graphing), 1-11, A-19

Radian (angle), 1-11, 2-24, A-21

Real, 1-12, A-22

Sci (notation), 1-10, A-25

Seq (graphing), 1-11, A-26

Sequential (graphing order), 1-12,

A-26

Simul (graphing order), 1-12, A-27

modified box [)lot type (o..), 12-32

multiple entries on a line, 1-6

multiplication (*), 2-3, A-37

multiplieative inverse, 2-3

-N-

N(number of payment periods

variable), 14-4, 14-14

nCr (number of combinations), 2-21,

A-16

nDeriv( (numerical derivative), 2-7,

A-16

negation (-), 1-23, 2-4, A-37

_Nom( (to nominal interest rate), 14-12,

A-16

nonrecursive sequences, 6-5

normal distribution probability

(normalcdf(), 13-30, A-17

Normal notation mode, 1-10, A-16

normal probability plot type (__),

12-33

-N (continued) -

normalcdf( (normal distribution

probability), 13-30, A-17

normalpdf( (probability density

function), 13-29, A-17

NormProbPIot plot type ([__), 12-33

not( (Boolean operator), 2-26, A-17

not equal to (_), 2-25, A-35

nPr (pernmtations), 2-21, A-17

npv( (net present value), 14-8, A-17

numerical derivative, 2- 7, 3-28, 4-8,

5-6

numerical integral, 2- 7, 3-28

- O-

one-proportion zconfidence inte_ral

(1-PropZInt), 13-20, A-20

one-proportion ztest (1-PropZTest),

13-14, A-20

one-sample tconfidence inte_al

(Tlnterval), 13-17, A-30

one-variable statistics (1-Var Stats),

12-25, A-31

or (Boolean) operator, 2-26, A-17

order of evaluating equations, 1-22

Output(, 9-6, 16-19, A-18

panning, 3-19

Par/Param (pm'ametrie graphing

mode), 1-9, 1-11, A-18

parametric equations, 4-5

parametric graphing

CA/C (calculate operations on a

graph), 4-8

defi_ling and editing, 4-4

free-moving cursor, 4- 7

graph format, 4-6

graph styles, 4-4

moving the cursor to a value, 4-8

selecting and deseleeting, 4-5

setting parametric mode, 4-4

tracing, 4- 7

window variables, 4-5

Y= editor, 4-4

zoom operations, 4-8

parentheses, 1-23

path (_.))graph style, 3-9

Index-9

-P (continued) -

Pause, 16-12, A-18

pausing a graph, 3-15

Pen, 8-13

pernmtations (nPr), 2-21, A-17

phase plots, 6-13

Pi (_), 2-4

Pic (pictures), 8-17, 8-18

pictures (Pic), 8-17, 8-18

pixel, 8-16

pixels in Horiz/G-T modes, 8-16, 9-6

Plot4 (, 12-34, A-18

Plot2(, 12-34, A-18

Plot3(, 12-34, A-18

PlotsOff, 12-35, A-18

PlotsOn, 12-35, A-18

plotting modes, 1-11

plotting stat data, 12-31

PMT (payment amount variable), 14-4,

14-14

Pmt_Bgn (payment beghming

variable), 14-13, A-19

Pmt_End (payment end variable),

14-13,A-19

poissoncdf(, 13-324, A-19

poissonpdf(, 13-33, A-19

Pol/Polar (polar graphing mode), 1-9,

1-11,A-19

polar equations, 5-4

polar form, complex numbers, 2-17

*Polar (to polar), 2-19, A-19

polar graphing

CALC (calculate operations on a

graph), 5-6

defining and displaying, 5-3

equations, 5-4

free-moxqngcursor, 5-6

graph format, 5-5

graph styles, 5-3

moving the cursor to a value, 5-6

selecting and deselecting, 5-4,

mode (Pol/Polar), 1-9, 1-11, 5-3,

A-19

tracing, 5-6

window variables, 5-]-_

Y= editor, 5-3

ZOOM operations, 5-6

PolarG¢ (polm" graphing coordinates),

3-13, A-19

-P (continued) -

pooled option, 13-6, 13-8

power (^), 2-3, A-36, A-37

power of ten (10^0, 2-& A-37

present vahle, 1].t-5, 1].b7, 14-1].t

prexqous entlT (Last Entry), 1-16

PRGM CTL (program control menu),

16-8

PRGM EDIT menu, 16-7

PRGM EXEC menu, 16-7

P RGM I/O (Input/Output menu), 16-16

prgm (program name), 16-15, A-19

PRGM NEW menu, 16-0.

ZPrn( (sum of principal), 12.t-9, A-19

probability, 2-20

probability density" function

(normalpdfO, 13-29, A-17

prod((product), 11-18, A-19

programming

copying and renaming, 16-7

creating new-, 16J._

defined, 16J.t

deleting, 16J-_

deleting command lines, 16-6

editing, 16-6

entering command lines, 16-5

executing, 16-5

instructions, 16-9 -16-21

inserting command lines, 16-6

name (prgm), 16-15, A-19

renaming, 16- 7

stopping, 16-5

subroutines, 16-22

Prompt, 16-18, A-19

1-PropZlnt (one-proportion

zconfidence interval), 13-20,

A-20

1-PropZTest (one-proportion ztest),

13-1].t, A-20

2-PropZlnt (two-proportion

zconfidence interval), 13-21,

A-20

2-PropZTest (two-proportion ztest),

13-15, A-20

P)'Rx(, P)'Ry( (polar-to-rectangular

conversions), 2-24, A-21

Pt-Change(, 8-15, A-20

Pt-Off(, 8-15, A-20

Pt-On(, 8-10, A-20

Index-lO

-P (continued) -

PV (present value variable), lJ4-J4,

114-114

p-value, 13-28

PwrReg (power regression), 12-27,

A-20

Pxl-Change(, 8-16, A- 21

PxI-Off(, 8-16, A-21

PxI-On(, 8-16, A-21

pxI-Test(, 8-16, A-21

PlY (nunlber-of-payment-periods-per-

year variable), lJ4-J4, lJ4-1J4

QuadReg (quadratic regression),

12-25, A-21

QuartReg (quartic regression), 12-26

Quick Zoom, 3-19, A-21

-R-

r (radian notation), 2-2/4, A-3J4

r (correlation coefficient), 12-23

r2, R2 (coefficients of determination),

12-23

Radian angle mode, 1-11, 2-2J4, A-21

radian notation (r), 2-24, A-34

rand (random number), 2-20, A-21

randBin( @andom binomial), 2-22,

A-21

randlnt( (random integer), 2-22, A-22

randM( (random matrix), 10-13, A-22

randNorm( (random Normal), 2-22,

A-22

random seed, 2-20, 2-22

RCL (recall), 1-15, 11-9

re^Oi (polm" complex mode), 1-12,

2-16, A-22

Real mode, 1-12, A-22

real( (real part), 2-18, A-22

RecalIGDB, 8-20, A-22

RecallPic, 8-18, A-22

_Rect (to rectangulm'), 2-19, A-22

rectangular form, complex numbers,

2-17

RectGC (rectangular graphing

coordinates), 3-13, A-22

recursive sequences, 6-6

ref( (row-echelon form), 10-15, A-22

-R (continued) -

RegEQ (regression equation vm'iable),

12-22, 12-29

regression model

automatic regression equation,

12-22

automatic residual list feature,

12-22

diagnostics display mode, 12-23

models, 12-25

relational operations, 2-25, 10-11

Repeat, 16-11, A-23

RESET menu, 18-5

resetting

defaults, 18-6

memmTy', 5, 18-5

resklual list (RESID), 12-22

Return, 16-15, A-23

root (x?), 2-6, A-35

root of a function, 3-26

round(, 2-13, 10-10, A-23

row+(, 10-16, A-23

*row(, 10-16, A-23

*row+(, 10-16, A-23

rowSwap(, 10-16, A-23

RH=r(, I_P0( (reetangular-to-polm"

conversions), 2-2J4, A-23

rref( (reduced-row-echelon form),

10-15, A-23

-S -

2-SampFTest (two-sample g-Test),

13-23, A-2J4

2-SampTInt (two-sample tconfidence

illtel_ral), 13-19, A-24

2-SampTTest (two-sample ttest),

13-13, A-2J4, A-25

2-SampZlnt (two-sample zconfidence

inte_5,al), 13-18, A-25

2-SampZTest (two-sample ztest),

13-12, A-25

Scatter plot type (L_), 12-31

Sci (scientific notation mode), 1-10,

A-25

scientific notation, 1-7,1-10

screen modes, 1-12

second cursor (2nd), 1-5

second key (2nd), 3

Index- 11

-S (continued) -

seconds DMS notation ('), 2-23

Select(, 11-12, A-25

selecting

data points from a plot, 11-13

functions from the home screen or a

program, 3-8

functions in tile Y= editor, 3-7

items from nlenus, J4

stat plots from tile Y= editor, 3-7

Send( (send to (BL 2/('BL or CBR),

16-21, A-26

sending. See trtmsmitting

Seq (sequence graphing mode), 1-11,

A-26

seq((sequence), 11-12, A-26

sequence graphing

axes fommt, 6-8

CALC (calculate memO, 6-10

defining and displaying, 6-3

evaluati]lg, 6-10

free-mo_ng cursor, 6-9

graph fommt, 6-8

graph styles, 6-J4

moving the cursor to a value, 6-9

nonreeursive sequences, 6-5

phase plots, 6-13

recursive sequences, 6-6

setting sequence mode, 6-3

selecting and deseleeting, 6-4

TI-83 versus TI-82 table, 6-15

tracing, 6-9

web plots, 6-11

window variables, 6- 7

Y= editor, 6-J4

ZOOM (zoom menu), 6-10

Sequential (graphing order mode),

1-12, A-26

service infornmtion, B-12

setting

display contrast, 1-3

graph styles, 3-9

graph styles from a program, 3-10

modes, 1-9

modes from a program, 1-9

split-screen modes, 9-3

split-screen modes from a program,

9-6

tables from a program, 7-3

-S(continued) -

SetUpEditor, 12-21, A-26

shade above (7) graph style, 3-9

shade below- (6) graph style, 3-10

Shade(, 8-9, A-26

Shadexi(, 13-36, A-26

ShadeF(, 13-36, A-27

ShadeNorm(, 13-35, A-27

Shade_t(, 13-36, A-27

shading graph areas, 3-10, 8-10

Simul (simultaneous graphing order

mode), 1-12, A-27

sin((sine), 2-3, A-27

sin'1((m-csine), 2-3, A-27

sine (sin(), 2-3, A-27

sine regression formula, A-50

sinh( (hyperbolic sine), 15-10, A-27

sinh'l( (hyperbolic m'csine), 15-10,

A-27

SinReg (sinusoMal regression), 12-27,

A-28

Smart Graph, 3-15

solve(, 2-12, A-28

Solver, 2-8

solving for variables in tile equation

solver, 2-10, 2-11

SortA( (sort ascending), 11-10, 12-20,

A-28

SortD( (sort descending), 11-10, 12-20,

A-28

split-screen modes

G-T (graph-table) mode, 9-5

Horiz (horizontal) mode, 9-#

setting, 9-3, 9-6

split-screen values, 8-12, 8-16, 9-6

square (2), 2-3, A-36

square root (_(), 2-3, A-37

STAT CALC menu, 12-2J-t

STAT KDIT menu, 12-20

stat list editor

attaching formulas to list names,

12-1J.t

clearing elements from lists, 12-12

creating list names, 12-12

detaching fornmlas from list names,

12-16

displaying, 12-10

edit-elements context, 12-18

Index-12

-S (continued) -

star list editor (eonthmed)

editing elements of fornmla-

generated lists, 12-16

editing list elements, 12-13

enter-names context, 12-19

entering list names, 12-11

formula-generated list names, 12-15

remoxqng lists, 12-12

restoring list names L1-L& 12-12,

12-21

switching eontexts, 12-17

x_ew-elements eontext, 12-18

x_ew-names eontext, 12-19

STAT PLOTS metal, 12-34

stat tests and confidence intel_rals

ANOVA( (one-way analysis of

variance), 13-25

x2-Test (ehi-squm'e test), 13-22

LinRegTTest (linear regression

ttest), 13-24

1-PropZlnt (one-proportion

zconfidence interval), 13-20

1-PropZTest (one-proportion ztest),

13-14

2-PropZlnt (two-proportion

zeonfidence interval), 13-21

2-PropZTest (two-proportion ztest),

13-15

2-SampFTest (two-sample F-Test),

13-23

2-SampTInt (two-sample

teonfidenee interval), 13-19

2-SampTTest (two-sample ttest),

13-13

2-SampZlnt (two-sample

zeonfidenee interval), 13-18

2-SampZTest (two-sample ztest),

13-12

Tlnterval (one-sample teonfidenee

inte_x_al), 13-17

T-Test (one-sample ttest), 13-11

Zlnterval (one-sample zeonfidenee

inte_x_al), 13-16

Z-Test (one-sample ztest), 13-10

Stats input option, 13-6, 13-7

STAT TESTS menu, 13-9

statistieal distribution functions. See

distribution functions

-S (continued) -

statistieal plotting, 12-31

Boxplot (regular box plot), 12-33

defining, 12-34

from a program, 12-37

Histogram, 12-32

ModBoxplot (modified box plot),

12-32

NormProbPIot (normal probability

plot), 12-33

Scatter, 12-31

tracing, 12-36

turning on/off stat plots, 3-7, 12-35

x_e,slng window, 12-36

xyLine, 12-31

statistieal vm'iables table, 12-29

stdDev( (standard dexdation), 11-18,

A-28

Stop, 16-15, A-28

Store (-)), 1-14, A-28

StoreGDB, 8-19, A-28

StorePic, 8-17, A-29

storing

graph databases (GDBs), 8-19

graph pictures, 8-17

vmiable values, 1-14

String_Equ( (string-to-equation

conversions), 15-8, A-29

strings, 15-3 to 15-9

concatenation (÷), 15-6, A-38

converting, 15-7, 15-8

defined, 15-3

displaying contents, 15-5

entering, 15-3

functions in CATALOG, 15-6

indicator ("), 15-3

length (length(), 15-8, A-13

storing, 15-5

vmiables, 15-4

student-t distribution

probability (tcdf0, 13-31, A-29

probability density function (tpdf0,

13-30, A-30

sub((substring), 15-9, A-29

subroutines, 16-15, 16-22

subtraction (-), 2-3, A-38

sum((sumnmtion), 11-18, A-29

system variables, A-49

Index-13

-T-

TABLE SETUP screen, 7-3

tables, 7-1 to 7-6

description, 7-5

variables, 7-3 to 7-5

tan((tangent), 2-3, A-29

tan'l((aretangent), 2-3, A-29

tangent (tan(), 2-3, A-29

Tangent( (draw line), 8-8, A-29

tangent lines, drawi_lg, 8-8

tan h( (hyperbolic tangent), 15-10, A-29

tanh'l( (hyperbolic aretangent), 15-10,

A-29

ATbl (table step variable), 7-3

TblStart (table start variable), 7-3

tcdf( (student-t distribution

probability), 13-31, A-29

teelmieal support, B-12

TEST (relational menu), 2-25

TEST LOGIC (Boolean menu), 2-26

Text(

instruction, 8-12, 9-6, A-29

placing on a graph, 8-12

Then, 16-9, A-11

thick (_.) graph style, 3-9

TI-82

link differences, 19-9

transmitting to/from, 19-2-t, 19-8,

19-9

TI-83

features, 17, 18

keyboard, 2, 3

key code diagram, 16-20

Link. See linking

menu map, A-39

TI-GRAPH LINK, 19-3

Time axes format, 6-8, A-30

time value of money (TVM)

calculating, 12-t-6

C/Y vm'iable (nmnber of

compounding periods per year),

12`1-12`1

formulas, A-54

FV vm'iable (furore value), 12`1-12`1

I% variable (annual interest rate),

12.t-12.t

-T(continued) -

time value of money (eontinued)

Nvm'iable (number of payment

periods), 14-12-t

PMT vm'iable (payment amount),

14-14

PV variable (present value), 12`1-12`1

PlY vm'iable (number of payment

periods per yem'), 12`1-12-1

tvm_FV (future value), 12-1-7,A-31

tyro_l% (interest rate), 14-7, A-31

tvm_N (# payment periods), 12-1-7,

A-31

tvm_Pmt (payment amount), 14-6,

A-31

tvm_PV (present Vahle), 12`1-7, A-31

TVM Solver, 12-1-2-1

vm'iables, 12-1-14

Tlnterval (one-sample teonfidenee

interval), 13-17, A-30

tpdf( (student-t distribution probability

density funetion), 13-30, A-30

TRACE

eursor, 3-18

entering numbers during, 3-19, 4-8,

5-6, 6-9

expression display, 3-12`1,3-18

Trace instruction in a program, 3-19,

A-30

transmitting

error conditions, 19-6

from a TI-82 to a TI-83, 19-9

items to another unit, 19-6

lists to a TI-82, 19-2-1,19-8

stopping, 19- 6

to an additional TI-83, 19-7

T(transpose matrix), 10-12, A-34

transpose matrix (T), 10-12, A-34

trigonometric functions, 2-3

T-Test (one-sample t test), 13-11, A-30

Index-14

- T (continued) -

turlling Ol1and off

axes, 3-1J4

calculator, 1-2

coordinates, 3-14

expressions, 3-1J4

functions, 3- 7

grid, 3-1J4

labels, 3-1J4

pixels, 8-16

points, 8-1J4

stat plots, 3-7, 12-35

tvm_FV (future vane), lj4 -7, A-31

tyro_l% (interest rate), 114-7, A-31

tvm_N (# payment periods), 114-7, A-31

tvm_Pmt (payment amount), 114-6,

A-31

tvm_PV (present value), 114-7, A-31

two-proportion zconfidence inte_a_al

(2-PropZlnt), 13-21, A-20

two-proportion ztest (2-PropZTest),

13-15, A-20

two-sample F-Test formula, A-52

two-sample ttest formula, A-53

two-vm'iable statistics (2-Var Stats),

12-25, A-31

-U-

u sequence function, 6-3

user variables, A-49

uv/uvAxes (axes format), 6-8, A-31

uw/uwAxes (axes format), 6-8, A-31

-V-

vsequence function, 6-3

1-Var Stats (one-variable statistics),

12-25, A-31

2-Var Stats (two-variable statistics),

12-25, A-31

value operation on a graph, 3-25

-V (continued) -

vmialAes

complex, 1-13

displaying and storing values, 1-11t

equation solver, 2-10

graph databases, 1-13

graph pictures, 1-13

independent/dependent, 7-5

list, 1-13, 11-3

matrix, 1-13, 10-3

real, 1-13

recalling values, 1-15

solver editor, 2-9

statistical, 12-29

string, 15-].L15-5

test aim inte_xral output, 13-28

types, 1-13

user and system, 1-13, A J-t9

VARS and Y-VARS menus, 1-21

variance( (variance of a list), 11-18,

A-31

vm'ianee of a list (variance(), 11-18,

A-31

VARS menu

GDB, 1-21

Picture, 1-21

Statistics, 1-21

String, 1-21

Table, 1-21

Window, 1-21

Zoom, 1-21

Vertical (draw line), &6, A-31

_dewing window, 3-11

vw/uvAxes (axes format), 6-8

wsequence function, 6-3

warranty inforlnation, B-13

Web (axes format), 6-8, A-31

web plots, sequence graphing, 6-11

While, 16-11,A-32

window variables

function graphing, 3-11

parametric graphing, ]4-5

polar graphNg, 5-]4

sequence graphing, 6- 7

Index-15

-X-

XFact zoom factor, 3-2J4

x-intercept of a root, 3-26

xor (Boolean) exclusive or operator,

2-26, A-32

xmroot (_), 2-6

xyLine ([__) plot type, 12-31

AX window variable, 3-12

-y-

YFact zoom factor, 3-2J4

Y= editor

function graphing, 3-5

parametric graphing, J4-J4

polar graphing, 5-3

sequence graphing, 624

Y-VARS menu

Function, 1-21

Parametric, 1-21

Polar, 1-21

On/Off, 1-21

AY window variable, 3-12

-Z-

ZBox, 3-20, A-32

ZDecimal, 3-21, A-32

zero operation on a graph, 3-26

Zlnteger, 3-22, A-32

Zlnterval (one-sample zconfidence

intm_al), 13-16, A-32

zoom, 3-20 to 3-214

cursor, 3-20

factors, 3-2J4

function graphing, 3-20

parametric graphing, J4-8

polar graphing, 5-6

sequence graphing, 6-10

ZoomFit (zoom to fit function), 3-22,

A-33

Zoom In (zoom in), 3-21, A-32

ZOOM menu, 3-20

ZOOM MEMORY menu, 3-23

Zoom Out (zoom out), 3-21, A-32

ZoomRcl (recall stored window), 3-23,

A-33

ZoomStat (statistics zoom), 3-22, A-33

- Z (continued) -

ZoomSto (store zoom _lndow), 3-23,

A-33

ZPrevious (use previous window),

3-23, A-33

ZSquare (set square pixels), 3-21, A-33

ZStandard (use standard window),

3-22, A-33

Z-Test (one-sample ztest), 13-10, A-3]-_

ZTrig (trigonometric window), 3-22,

A-3J4

Index-16

_TEXAS INSTRUMENTS T1=83

STAT PLOT TBLSET FORMAT

CALC TABLE

QUiT INS

A-LOCK LiNK LiST

TEST A ANGLE E{ DRAW C

FINANCE D SIN -1 E COS -1 F

I EE J { K

exSL4 TL5 U

RCL X L1 Y L2 Z

DISTR

TAN -1 G 1T N

} L eIvI

L6 V _ W

L3 ® ME[V] f_

OFF CATALOG _ i :ANS ?ENTRY SOLVE

TEXAS INSTRUMENTS Calculator Manual L0806875

Navigation menu

Versions of this User Manual:

Views

Navigation