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 PDF.
Page Count: 446

DownloadTEXAS  INSTRUMENTS Calculator Manual L0806875
Open PDF In BrowserView PDF
TEXAS
|NSTIRUMENTS

TI-83
GRAPHING
CALCULATOR

GUIDEBOOK

TI-GRAPH
Constant

LINK, Calculator-Based
Memory,

Instruments

Windows

Laboratory,

CBL, CBL 2, Calculator-Based

Power Down, APD, and EOS are trademarks

Ranger,
of Texas

Incorporated.

IBM is a registered
Macintosh

Automatic

trademark

is a registered
is a registered

© 1996, 2000, 200I

of International

trademark
trademark

Texas

Business

of Apple Computer,
of Microsoft

Instruments

Machines
Inc.

Corporation.

Incorporated.

Corporation.

CBR,

Important

Texas

Instrtu-nents

ilnplied,

including

inerchantability

makes
but
and

no warranty,

not lilnited
fitness

either

to any

for a particular

progralns
or book rnateriais
solely on an "as-is" basis.

and

expressed

implied

rnakes

purpose,
such

or

warranties

of

regarding

inateriais

any

availaMe

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.

US FCC
Information
Concerning
Radio Frequency
Interference

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

•

Increase

the separation

•

Connect the equipment into an outlet on a circuit
fl_m that to which the receiver is connected.

•

Consult the dealer or an experienced
technician for help.

between

antenna.
the equiplnent

and receiver.
different

radio/television

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:
Do This First!

TI-83 Keyboard
..........................................
TI-83 Menus .............................................

2
4

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 ................

F)

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 ....................
Setting the Display Contrast
.............................
The Display ..............................................
Entering Expressions
and Instructions
...................
TI-83 Edit Keys ..........................................

6
7
8
9
10
11
12
13
15
16
17

1-2
1-3
1-4
1-6
1-8

Setting Modes
...........................................
Using TI-83 Variable Names
.............................
Storing Variable Values ..................................
Recalling Variable Values ................................
ENTRY (Last Entry) Storage A_'ea ........................
Ans (Last Pmswer) Storage Pa'ea .........................
TI-83 Menus .............................................
VARS and VARS Y-VARS Menus .........................

1-9
1-13
1-14
1-15
1-16
1-18
1-19
1-21

Equation Operating
System (EOS TM) .....................
Error Conditions
.........................................

1-22
1-24

Introduction

iii

Chapter 2:
Math, Angle, and
Test Operations

Getting Started: Coin Flip ................................
Keyboard Math Operations
..............................
MATH Operations
........................................
Using tile Equation
Solver ...............................
MATH NUM (Numbe 0 Operations
........................
Entering and Using Complex Nmnbers ...................
MATH CPX (Complex)
OperatMns
.......................
MATH PRB (Probability)
Operations
.....................
ANGLE Operations
.......................................
TEST (Relational)
Operations
............................
TEST LOGIC (Boolean)
Operations
......................

Chapter 3:
Function

Getting Started: Graphing a Circle .......................
Defining Graphs
.........................................
Setting the Graph Modes .................................
Defining Funetions
......................................

Graphing

Graphing

Chapter 5:
Polar Graphing

iv

Introduction

3-2
3-3
3-4
3-5

Seleeting and Deseleeting
Punetions
.....................
Setting Graph Styles for Flmetions
.......................
Setting the Viewing Window \Tariahles ...................
Setting the Graph Format ................................

3-7
3-9
3-11
3-13

Displaying
Exploring
Exploring
Exploring

3-15
3-17
3-18
3-20

Graphs
.......................................
Graphs with the Free-Moving
Cursor ..........
Graphs with TRACE ...........................
Graphs with the ZOOM Instructions
...........

Using ZOOM MEMORY ..................................
Using the CALC (Calculate)
Operations
..................

Chapter 4:
Parametric

2-2
2-3
2-5
2-8
2-13
2-16
2-18
2-20
2-23
2-25
2-26

3-23
3-25

Getting Started: Path of a Ball ...........................
Defining and Displaying
Parametric
Graphs ..............
Exploring Parametrie
Graphs ............................

4-2
4-4
4-7

Getting Started: Polar Rose ..............................
Defining and Displaying
Polar Graphs
...................
ExNodng
Polar Graphs ..................................

5-2
5-3
5-6

Chapter

6:

Getting Started: Forest and Trees ........................
Defining and Displaying
Sequence
Graphs ...............
Selecting Axes Combinations
............................
Exploring
Sequence Graphs ..............................
Graphing Web Plots ......................................
Using Web Plots to Illustrate
Convergence
...............
Graphing Phase Plots ....................................
Comparing
TI-83 and TI-82 Sequence Variables ..........
Keystroke
Differences
Between
TI-83 and TI-82 .........

Chapter
Tables

7:

Getting Started: Roots of a Function
.....................
Setting Up the Table .....................................
Defining the Dependent
Variables ........................
I)isplaying
the Table .....................................

7-2
7-3
7-4
7-5

Chapter
DRAW

8:

Getting

8-2

Sequence
Graphing

Operations

Started:

Drawing

a Tangent

Line .................

Using the DRAW Menu ...................................
Clearing Drawings
.......................................
Drawing Line Segments
..................................

8-3
8-4
8-5

Drawing Horizontal
and Vertical Lines ...................
Drawing Tangent Lines ..................................
Drawing Functions
and Inverses
.........................
Shading Areas on a Graph
...............................
Drawing Circles ..........................................
Placing Text on a Graph .................................
UsHlg Pen to Draw on a Graph ...........................
Drawing PoHlts on a Graph ..............................
Drawing Pixels
..........................................
StorH N Graph Pictures (Pic) .............................
Recalling Graph Pictures
(Pic) ...........................
StorHlg Graph Databases
(GDB) .........................
Recalling Graph Dadabases
(GDB) .......................

Chapter 9:
Split Screen

(;-2
6-3
6-8
(;-9
6-11
6-12
6-13
6-15
6-16

Getting Started: Exploring
the Unit Circle ................
Using Split Screen
.......................................
Horiz (Horizontal)
Split Screen ...........................
G-T (Graph-Table)
Split Screen ..........................
TI-83 Pixels in Horiz aim G-T Modes .....................

Introduction

8-6
8-8
8-9
8-10
8-11
8-12
8-13
8-14
8-16
8-17
8-18
8-19
8-20

9-2
9-3
9-4
9-5
9-6

v

Chapter 10:
Matrices

Getting Started: Systems of Linear Equations
............
Defining a Matrix ........................................
Viewing and Editing Matrix Elements
....................
Using Matrices with Expressions
........................
I)isplaying
and Copying Matrices
........................
Using Math Functions
with Matrices
.....................
Using the MATRX MATH Operations
.....................

10-2
10-3
10-4
10-7
10-8
10-9
10-12

Chapter 11:
Lists

Getting Started: Generating
a Sequence
..................
Naming Lists .............................................
Storing and Displaying
Lists .............................
Entering List Names .....................................
Attaching
Formulas
to List Names .......................
Using Lists in Expressions
...............................
LIST OPS Menu ..........................................
LIST MATH Menu ........................................

11-2
11-3
11-4
11-6
11-7
11-9
11-10
11-17

Chapter 12:
Statistics

Getting Started: Pendulum
Lengihs and Periods
Setting up Statistical Palalyses ...........................

Chapter 13:
Inferential
Statistics and
Distributions

vi

Introduction

.........

12-2
12-10

Using the Stat List Editor ................................
Attaching
Formulas
to List Names .......................
I)etaehi_lg Fornmlas
from List Names ....................
Switching
Stat List Editor Contexts
......................
Stat List Editor Contexts .................................
STAT EDIT Menu ........................................

12-11
12-14
12-16
12-17
12-18
12-20

Regression
Model Features
..............................
STAT CALC Menu ........................................
Statistical Variables ......................................

12-22
12-24
12-29

Statistical
Statistical
Statistical

12-30
12-31
12-37

Analysis
Plotting
Plotting

in a Program
.........................
.......................................
in a Program
.........................

Getting Started: Mean Height of a Population
hfferential
Star Editors ...................................
8TAT TESTS Menu ......................................

............

13-2
13-6
13-9

Inferential
Statistics
Input Descriptions
..................
Test and Interval Output Variables .......................
Distribution
Functions
...................................

13-26
13-28
13-29

Distribution

13-35

Shading

.....................................

Chapter 14:
Financial
Functions

Getting Started: Finzmeing a Car. ........................
Getting Started: (;omputing
Compound
Interest ..........
Using tile TVM Solver ....................................
Using tile Financial
Functions
...........................
Calculating
Time Value of Money (TVM) .................
Calculating
(;ash Flows ..................................
Calculating
Amortization
................................
Calculating
Interest Conversion
..........................
Finding I)ays between [)ates_)ef'nm N Payment Method .....
Using tile TVM Variables .................................

14-2
14-3
14-4
14-5
14-6
14-8
14-9
14-12
l '4-13
14-14

Chapter 15:
CATALOG,
Strings,
Hyperbolic
Functions

Browsing tile TI-83 CATALOG ...........................
Entering and Using Strings ...............................
Storing Strings to String Variables .......................
String Functions and Instructions in the CATALOG ......
Hyperbolic Functions in the CATALOG ..................

17)-2
15-g
1:)-4
1.5-6
15-10

Chapter 16:
Programming

Getting Started: Volume of a Cylinder ....................
Creating and Deleting Progrmns
.........................
Entering Command
Lines and Executing
Programs
Editing Programs
........................................
Copying and Renmning
Programs
........................
PRGM CTL (Control)
Instructions
.......................
PRGM I/O (Input/Output)
Instructions
...................
('ailing Other Programs
as Subroutines
..................

Chapter 17:
Applications

16-2
16-4
......

16-5
16-6
16-7
16-8
16-16
16-22

Comparing Test Results Using Box Plots ................
Graphing Pieeewise Punetions ...........................
Graphing Inequalities ....................................
Solving a System of Nonlinear Equations ................
Using a Program to ( reate the Sierpinski Triangle .......
Graphing Cobweb Attractors ............................
Using a Program to Guess the Coefficients ...............
Graphing the Unit Circle and Trigonometric (;m_es ......
Finding the Area between Curves ........................
Using Parametric Equations: Ferris Wheel Problem ......
Demonstrating the Fundamental Theorem of Calculus...
Computing Areas of Regular N-Sided Polygons ..........
Computing and Graphing Mortgage Payments ...........

17-2
17-4
17-5
17-6
17-7
17-8
17-9
17-10
17-11
17-12
17-14
17-16
17-18

Introduction

vii

Chapter 18:
Memory
Management

{'heeLing Awailable MemolTy".............................
Deleting Items from MemoKy" ............................
Clearing Entries and List Elements ......................
Resetting the TI-8:3 ......................................

18-2
18-3
18-4
18-5

Chapter 19:
Communication
Link

Getting Started: Sending Variables
.......................
TI-83 LINK ...............................................

19-2
19-3

Selecting Items to Send ..................................
Receiving Items ..........................................
Transmitting
Items .......................................
Transmitting
Lists to a TI-82 .............................
Transmitting
from a TI-82 to a TI-83 .....................
Backing Up MemoKy" .....................................

19-4
19-5
19-6
19-8
19-9
1%10

Appendix A:
Tables and
Reference
Information

TabD

Menu Map ...............................................
Vm'iables
................................................
Statistical Formulas
.....................................
Financial Fommlas
......................................

A-39
A-49
A-50
A-.M

Appendix B:
General
Information

BatteKy" Information
......................................
In Case of Difficulty
.....................................
En'or Conditions
.........................................

B-2
B-4
B-5

of Functions

Accuracy hfformation
Support and Service
Win'rarity Information

Index

viii

Introduction

and Instructions

.....................

....................................
Infommtion
.........................
....................................

A-2

B-10
B-12
B-13

GettingStarted:
Do This First!
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

\

X=:I..5:B;!:=I_fiB

13
15
16
17

T1=83

INSTRUMENTS

/

2
4
5
6
7
8
9
10
11
12

\.

_Y=_;i:.90_;i:_lfi

=

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Getting

Started

1

TI-83 Keyboard

Generally,
keys,

the keybom'd

advanced

Keyboard

is dwided

function

Zones

keys,

Graphing
Editing

Graphing

Editing

allow

calculator
scientific

Keys

Scientific
Calculator Keys

Started

keys

Scientific
standard

Keys

these

access

function
functions.

FuncffonKeys

Getting

keys

Advanced
advanced

Advanced

2

into

and scientific

zones:

graphing

calculator

keys,

the interactive

graphing

you to edit expressions
keys

display

keys access
calculator.

editing

keys.

menus

features.

and values.
that

access

the capabilities

the

of a

Using the
Color-Coded
Keyboard

The

keys

locate

on the TI-83

are color-coded

to help you easily

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.

Using the K_
and @
Keys

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
the key. When you

of each key is printed
press the green @

in green above
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 A is 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
to access items from its menus,

will need

[5+9|

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
screen where you m'e working
displayed
again.

5+9_

Moving
Solne

from
keys

One

access

Menu
nlore

a menu,
usually

the
is

or letter

item is highlighted.
beyond
the screen,
replaces
the colon

than

one

lnenu.

CPX

PRB[

CPX

PRB

4:_(
5:_
6:¢Min(
74€Max(

When

next to the current

round(

5:int(
_sl_[
6:Min(
74.max(

menu

If the menu continues
a down arrow ( _ )
( : ) 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
number
or letter
• Press the key or
number
or letter

Leaving

lnove the cursor
to the
of the item; press [g_.
key combination
fia" the
next to the item.

a Menu without

Making

You can leave a lnenu without
selection
in ally of three ways.

4

PRB

an Item from a Menu

The number

• Press
where
• Press
screen.
• Press

CPX

to Another

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

NUM
Pao
:*Dec

[

Getting

Started

lnenu

4:?Part(
5:int(
5:Min(
74Max(

3tiPar.t(
4:?Part(
5:int(
6:Min(
7:max(
MRTH _
8:fOR(
i_lEIgcd(

a Selection

lnaking

a

@
to return to the screen
you were.
[2_] [QUIT] to t_tum
to the home
a key for another

round(
3:iPart(

or screen.

15+9_

I

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.

FOR]
to

1,

Press

turn

on the calculator.

2,

Press and release [_,
[MEM] (above []).

and then press

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.

RRM...
3:Clear Entries
4:ClrRllLists
5:Reset...

The MEMORY menu is displayed.
3.

Press 5 to select 5:Reset.
The RESET menu is displayed.

4,

_MeMoru..,
a. DeCaults...

Press 1 to select 1:All Memory,
The RESET MEMORY menu is displayed.
Resettin9
memoru
erases all data
and PrograMs.

5,

Press

2 to 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.

|

MeM

oleared

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.

Getting

Started

5

Entering

a Calculation:

Use the quadratic

fornmla

to solve

the quadratic

with the

equation

and 2X 2 - X + 3 = 0, Begin
3 _
@
the coefficient

The Quadratic

[n] (above 1_])
of the X 2 tenn.

Press
store

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.

to

[]

@

[B] []

[A]_

_

[<] @

[B]

[c] []17113[] 2

@
[A] [] to enter the expression
one of the solutions
for the quadratic
formula,

for

- b+
2a
Press _
equation

to find one solution
3X 2 + 5X + 2 = 0.

for the

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

3X 2 + 5X + 2 = 0

3÷R: 5÷B: 2÷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,

D [] 4_

equations

3X 2 + 5X + 2 = 0,

1,

Press[]

Formula

÷R: 5÷B: 2÷C

2

Converting

to a Fraction:

You can show the solution
1. Press [_

The Quadratic

Formula

as a fl'action.

to display the MATH lnenu.
Pao
NUN
eo

CPX

PRB

3:_
4:_#(
5: *#
6:¢Min(
7¢€Ma× (
Press 1 to select 1:)Frac froln the MATH

(-B+#(BZ-4RC))/(
2R)
%6666666667

lnenu,

When you press 1, AnsJ,Frac is displayed
the home screen. Arts is a variable that
contains the last calculated answer.

Press 1_
fl'action.

to convert

on

the result to a

Rns*Fr, ac|

(-B+4-(BZ-4RC)
2R)

To save keystrokes, you can recall the last expression
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,
2a
5,

you entered,

)/(

and then

I-B+E(BZ-4RC))/(
R)
-.6666666667
Rns*Fpac
-2/3
(-B+E(BZ-4RC))/(
2R)|

Press [] to nlove the cursor
onto the + sign
in the fornmla,
Press [] to edit the
quadratic-fornmla
expression
to become:

2R)
-.6666666667
Rns_Frac
(-B-.r(BZ-4RC))/(

-2/31

2a
6,

Press 1_
the quadratic

to find the other solution
for
equation
3X 2 + 5X + 2 = 0.

-1

_R)

Getting

Started

7

Displaying

Now

solve

mode,

Complex

the equation

the TI-83

Results:

The Quadratic

2X 2 - X + 3 = 0. When

displays

complex

Formula

you set a+bi complex

number

results.

Press 1_
[] [] [] [] [] [] (6 times),
and
then press [] to position
the cursor
over
a+bi. Press @
to select a+bi coinplexnumber
mode.

2,

Press [_ [QU*T]
the home screen,
cleat" it.
Press 2 _

@

_E])
to return to
and then press @
to

(above

[A] @

[: ] []

z G-T

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.
Press [_
[ENTRY] to recM1 the store
instruction,
and then press [_
[ENTRY]
again to recall the quadratic-fornmla
expression,

eR:-leB:3aC

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

3

3

2o
Press @
to find one solution
equation
2X 2 - X + 3 = 0.

for the

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

i25-I.

Press [2_ [ENTRY]repeatedly
quadratic-fornmla
expression

until this
is displayed:

2a
Press @
the quadratic

to find the other solution
for
equation:
2X 2 - X + 3 = 0.

198957881t

(-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

Take

a Function:

a 20 enl. x 25 enl. sheet

Box with Lid

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
volunle
of the box.
From

the diagram:

Substituting:

that

describes

the

2X + A = 20
2X + 2B = 25
V=ABX

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[]
volume

20[] 2 _
[] [] 25[]
2[]
[] _
[_
to define the
function
as Y1 in terms of X.

lets you enter X quickly, without
having to press @.
The highlighted
sign indicates
that Y1 is selected.

_

x

PloL:L

Plot;'

B

PICL3

","?t =I
\y._=
xY_=
"_y_=
,..y_=
,,y_=
xY?=

\'14tB<20-2X)

-X)X
_Yz=l

<25/2

,..y_=
=
xYfi=

Getting

Started

9

Defining

a Table of Values:

Box with Lid

The table feature of the TI-83 displays numeric
You can use a table of values fl'om the function
an answer to the problem,
1, Press [2_ [TBLSET] (a|)ove
_)
display the TABLE SETUP menu,

to

Tb IStart=O
aTbl=l
Indent:

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 _)
the table,
Notice

that

the nlaxilnuln

(box's volunm) occurs
between
3 and 5.

TABLE
SETUP
Depend:
X

to display
I

value
when

inforlnation about a function.
defined on page 9 to estimate

for Y1

X is about

91
o

1
Z

207
3_6
_99
hOB

6

3t_

4,

X=O
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_

Getting

V1
_t2

F
B

231
lhh

10

0

X=12

[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.)

10

X
E

Started

TblStart=6
_Tbl=l
IndPn÷: P._
TRBLE SETUP
Depend:

_.
Rsk

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 X for lnaxilnuln
volunle

Y1.

2, Press[2_
3.

[TABLE],

X

Notice that tile nlaxinluln value for Y1 is
410.26, which occurs at X=3.7. Therefore,
nlaxinmln

TABLE
SETUP
Depend:

Press [] and [] to scroll the table.

the

TblStart=3
_Tbl=. 1
IndPnt: r=Rg_t_

occurs

where

3.6 is copied to the cursor

location.

3. Press @
and then the letter of the variable
you want to store the value.

to which

4. Press [gg_O. If you entered an expression, it is
evaluated. The value is stored to the variable.

[5+8_'3÷Q
Displaying a
Variable Value

To display- the value of a vm'iable, enter the name on a
blank line on the home screen, and then press IgOr.

I°

1-14

Operating

517[

the

5171

TI-83

Recalling

Using Recall
(RCL)

Variable

Values

To recall

and copy

location,

follow

variable

these

contents

steps.

to the current

To leave

1. Press [2_] ERCL]. Rcl and the edit
the bottom
line of the screen.
Enter

the name

of the variable

are displayed

on

in any of five ways.

Press

•

Press [g_ [LIST], and then
or press [g_ [Ln].

•

Press

•

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
program
(in the program

_,

variable

bottom

and then

cursor

cursor
@.

•

The

@

RCk, press

the letter

and then select

name

the name

the name

select
editor

you selected

line and the cursor

of the variable.

select

of the matrix.

the name
only).

is displayed

of the list,

of the

on the

disappeat\s.

100+
Rol 0
Press IENTEEI.The variable
contents
are inserted
the cursor
w_s located
befot_ you began these

1100+517I

where
steps.

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)

Using ENTRY
(Last Entry)

Storage

Area

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 [] 7

F_a] [ENTRY]

Accessing a
Previous Entry

5+7

5 +711

12

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.

2_B
I_
I_A
[_

[ENTRY]

2+B
1÷1::1
2+BI

12

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]

1-16

Operating

the

TI-83

2eB
1+RII

Reexecuting the
Previous Entry

After

you

have pasted

the last

entt'y to the home

and edited it (if you chose to edit it), you can
entry-. To execute
the last ent_T, press [_T_].

screen

execute

the

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_°
_
@
@N[]I_@N

Multiple Entry
Values on a Line

N

O+N
N+I÷N:NZ

0

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
instructions
separated
by colons
are
cursor locatkm.
You can edit any of
execute
all of them when you press

expressions
and
p_sted
to the current
the entries,
and then
[_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¥]
[]

F_t_q

7 [_

[INS] []

95

8÷R:_RZ
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

I

Ans (Last Answer)

Using Ans in an
Expression

When

Storage

an expression

Area

is evaluated

successfully-

home screen (Jr from a program,
answer to a storage
at_a called
be a real or complex
number,
a
When you turn off the TI-83, the

fronl

the

the TI-83 stores the
Ans (last answer).
Ans nlay
list, a lnatrix,
or a string.
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 []

Continuing an
Expression

Storing Answers

_

[ANS]

1.7.4.2
147/Rn_

14[

7

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

_gDg[N_ffl

Rns*9.9

To store an answer, store Ans to a variable
evMuate another expression.

2.5
24.75

before you

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.

1-18

Operating

I_ [_]s []

xSZ

N3D3

78.53981634
Rns*3.o
I

__v

Rns+U 259.1813939
259.1813939

the

TI-83

TI-83 Menus

Using a TI-83
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
or [] until that
location within
displayed with

other menu listed on the top line, press []
menu name is highlighted. The cursor
the initial menu is irrelewmt. The menu is
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.

Scrolling a 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

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
and then press [E6T_.

the cursor

After you select an item from
displays
the previous
screen,

to the item

a menu,

the TI-83

you want,
typically

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

Leaving a Menu
without
Making a
Selection

1-20

Operating

:_27.

You can leave
four ways.

a menu

without

making

a selection

•

Press

[_]

[QUIT] to return

•

Press

@

to return

•

Press a key or key- combination
such as [M_
or [_
[LIST].

for a different

menu,

•

Press a key or key combination
such as [] or _
[TABLE],

for a different

screen,

the

TI-83

to the home

in any- of

to the prexdous

screen.
screen.

VARS and VARS Y-VARS

VARS Menu

You can

enter

Menus

the

in an expression

haines

of functions

or store

to them

and systeln

varial>les

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

VARS Y VARS
i: Window...
2 : Zoom.,.
3: GDB...

one

secondaYy

lnenu,

X/Y, T/O, and U/VNV variables
ZX/ZY, ZT/ZO, and ZU wuiables
Graph database
vmiables
Picture variables

4:Picture.,.
5:Statistics.,.
6: Table...

XY, Z, EQ, TEST, and
TABLE vmiables

7: String..,

Selecting a
Variable from the
VARS Menu or
VARS Y-VARS
Menu

than

PTS 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:

Yn functions

Function...

2: Parametric...
3:Polar...

X_?,T,Y'rtT functions
rn functions

4:On/Off...

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
follow these steps.
1. Display

fronl

the VARS or VARS Y-VARS menu,

the VARS or VARS Y-VARS menu.

•

Press

[_

to display

•

Press

_

[] to display

the VARS menu.
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.
secondm:y-

menu

A

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
CUrSOr

a variable
location.

name

from

the menu.

Operating

It is pasted

the

TI-83

to the

1-21

Equation

Order of
Evaluation

Operating

System

(EOS

TM)

The Equation Operating System (EOS
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.
TM)

EOS evaluates

the functions

in an expression

in this order:

1

Single-argument
argument,
such

2

Functions
that are entered
after the argument,
such _ks2, -1, 1, o, r, and conversions

3

Powers

4

Pernmtations

5

Multiplication,
division

6

Addition

7

Relational

8

Logic operator

9

Logic operators

Within a priority
right.

functions
that precede
as ¢(, sin(, or log(

and roots,
(nPr)

such

as 2^5 or 5x¢32

and combinations

implied

the

nmltiplication,

(nOr)
and

and subtraction
functions,

such

_

> or <

and
or and xor

level, EOS evaluates

functions

fronl left to

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

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).

Parentheses

All calculations
inside a pair of pm'entheses
first. For example,
in the expression
4(1+2),
evaluates
the portion
inside the pm'entheses,
nmltiplies
the answer,
3, by 4.

4(1+2)
4.1+2

are completed
EOS first
1+2, and then

I_

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.

Negation

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,

For example,
[ _se parentheses

-2z
(-2) z

ale ewduated

-X 2, evaluates
to square

_
_

before

to a negative
a negative

negation.

number

(or 0).

number.

12->R
-AZ

42

( -A ) z

-4

Note:Use the[] key forsubtraction
and 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
Error

an

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
message as a menu title,
ERR:DOMAIN. Appendix
possible reasons for tile

an error, it returns an etTor
such _ts ERR:SYNTAX or
B describes each error type and
etTor.

ERR: S_,"NTRX
_a[IQuit
2: Goto

I

•
•

I

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 syntax erroroccurs in the contentsof a Y= functionduring
program execution, thenthe Goto option returnsto the Y= editor, not
to the program.
Correcting
Error

an

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
refer to Appendix B.
4. Correct

1-24

Operating

the

TI-83

the expression.

the error,

Math,Angle,
Operations and Test
Contents

Getting Started: Coin Flip ................................
Keyboard Math Operations
..............................
MATH Operations
........................................
Using the Equation
Solver ...............................
MATH NUM (Number)
Operations
........................
Entering and Using Complex Nmnbers ...................
MATH CPX (Complex)
Operations
.......................
MATH PRB (Probability)
Operations
.....................
ANGLE Operations
.......................................
TEST (Relational)
Operations
............................
TEST LOGIC (Boolean)
Operations
......................

'_

TEXAS

2-2
2-3
2-5
2-8
2-13
2-16
2-18
2-20
2-23
2-24
2-26

T1=83

iNSTRUMENTS

Q^3+PZ-125=O
-Q=4.6415888336...
P=5
bound={-50,50}
-le_t-rt=O

J
STAT

PLOT

TBLSET

FORMAT

Math,

CALC

Angle,

TABLE

and

Test

Operations

2-1

Getting

Getting

Started:

Started

Coin Flip

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 [] 5 to enter the probability of
heads. Press []. Press 40 to enter the
number of sinmlations.
Press D2.

3.

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.

_andBin(10,.5,40

{5574663_.

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).

Rgs_L_
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.

2-2

10,. 5,40

_andBin(

Math,

Angle,

and Test

Operations

4 6 6 3 ...

andBin( 10,. 5, 40
5 5 7 4 6 6 3 ,..

..£._._L_6 5 7 5 ...

Keyboard

Math Operations

Using Lists with
Math Operations

Math operations that are valid ff)r lists 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,

+ (Addition),
- (Subtraction),
* (Multiplication),
/ (Division)

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

Trigonometric
Functions

valueA
valueA

- valueB
/ valueB

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
tetut]ls

interpretation.
-.9880316241;

sin(value)

For example,
sin(a0) in Radian mode
in Degree mode it returns
.5.
cos(value)

tan(value)

You can use the inverse
trig functions
arccosine,
[g_] [c05-t];
and arctangent,
real nmnbers,
expressions,
and lists.
mode setting affects interpretation.
sin -1(value)

(aresine,
[g_] [StN-1];
[g_] [TAN-t])with
The current
angle

cos -1(value)

tan -1(value)

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

^ (Power),
2 (Square),
,[( (Square Root)

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

-1

(inverse)

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

You can use log( (logarithln,
FO_), 10^( (power
of 10, [_
[10x]), and In( (natural
log, @) with real or eolnplex

log(,
10^(,
In(

nulnbers,

expressions,

log(value)

e^( (Exponential)

and lists,
lO^{power)

In(value)

e^( (exponential,
[2_ [ex]) returns
the constant
a power.
You can use e^( with real or complex
expressions,
and lists.

e raised
numbers,

to

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 e to the cursor location. In
calculations, the TI-83 uses 2.718281828459 for e.

e (Constant)

e

2.718281828

- (negation, D) returns the negative of value. You can use with real or complex numbers, expressions,
lists, and
matrices.

- (Negation)

-value

EOS rules (Chapter 1) determine when negation is
evaluated. For example, -A2 t_turns a negative nulnber,
because squaring is evaluated before negation. Use
parentheses
to square a negated number, as in (-A)2,
2+R:
2z, ( {-RZ,
-2)z} ( -R>a, {-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)

(Pi, [g_ [_]) is stored
calculations,
the TI-83
Ix

2-4

Math,

Angle,

and

3.1415926541

Test

Operations

as a constant
in the
uses 3.1415926535898

TI-83, In
for _.

MATH Operations

MATH Menu

To display the MATH menu, press [MKTgl.
MATH NUMCPX PRB
1 : _Fra c
Displays
2:_Dec
3:3
4:3_(
5: x#
6: fMin(
7: fMax(
8:nDeriv(
9: fnlnt(
O: Solver.,.

_Frac,
_Dec

the answer

as a fraction.

Displays
the answer
as a decimal.
Calculates
the cube.
Calculates
the cube root.
Calculates
the x t;_root.
Finds
Finds

the nlininmln
the nlaxinlunl

of a function.
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,
following
value.
value

and matrices.

You

can only use _Dec

_Dec

I/2+I/3_Frac o/61
Ans_Deo
.8333333333

Math,

Angle,

and

Test

Operations

2-5

3(Cube),
3_r( (Cube

3 (cube)

Root)

returns

or complex
nmtrices.

the cube

numbers,

of value.

expressions,

You can use 3 with
lists,

real

and square

value 3
3_( (cube root) returns
the cube root of value.
3_( with
real or complex
numbers,
expressions,

You can use
and lists.

3_(value)

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

64 125}
3 4 5}

_J'(Rns){2

x_ (Root)

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

fMin(,
fMax(

2

fMin( (function
retun_ the value

and fMax( (function
the local ndninmm

nlininlunl)

at which

nlaxinlunl)

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
iE-5),

by tolerance

(if not specified,

the default

is

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,-:_
•

2-6

Math,

Angle,

and

1.570797171

Test

Operations

nDeriv(

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
which approximates
the numerical
derivative
slope of the secant
line through
these points.

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

f'(x) =

2e

As e becomes
nlore accurate.
nDer

method,
value as the

iv(RA3,

smaller,

the approxinmtion

usually- becomes

R, 5,.

01 )
75,0001
nDeriv(R^3o
R, 5,.
0001

)

75

You can use nOeriv( once
method
used to calculate
false derivative

fnlnt(

value

in expression.
Because
of the
nDeriv(, the TI-83 can return a

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

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

Entering an
Expression in the
Equation Solver

Solver,

one of two screens

•

The equation
editor (see step 1 picture
below)
is
displayed
when the equation
wu'iable
eqn is empty,

•

The interactive
2-9) is displayed

solver editor
(see step 3 picture
on page
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
equation
editor.
EQUATION
e_n: 0=|
2, Enter

the MATH menu

the expression

in any of three

•

Enter the expression
solver,

directly

•

Paste
lnenu

•

Press [_
[act_], p_kste a Y= variable
VANS Y-VANS lnenu,
and press [_,
expression
is pasted
to the equation

a Y= vmiable
name from
to the equation
solver,

is stored

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

|

Math,

Angle,

to display-

and Test

the

SOLVER

The expression
enter it.

2-8

is displayed.

Operations

ways,

into

the equation

the VANS Y-VANS

to the variable

name from
The
solver.
eqn as you

the

3, Press _
displayed.

or [_. The interactive

solver editor is

1%35 -1 5=8
P=8
bound={
•
•

•
•

-1 E99, 1...

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 use the solverto solve an equationsuch as K=.SMV2, enter
eqn:0=K-.SMV 2 inthe equationeditor.
Entering and
Editing Variable
Values

When you enter or edit a value for a variable in the
interactive solver editor, the new value is stored in
nlenlol_yto 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
e_n:
8=V., +7SSL_)ER

I

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

equation

has been

using

stored

the equation

to eqn, follow

solver
these

after

an

steps.

1. Select 0:Solver from the MATH menu to display the
interactive
solver editor, if not already
displayed.

I% ;P -125=°P=o
L.
bound={-1E99,

2. Enter

Ol" edit tile value

of each

known

variable.

variables,
except the unknown
variable,
nmst
value. To move the cm\sor to the next wuiable,

All
contain
press

INto or _.

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

3. Enter

-1 E99,

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=4I
z- 125=0
bound={
-I E99,

1...

(upper+
The

2-10

Math,

Angle,

and

default

Test

guess

is calculated

Operations

as

lower)
2

a

4. Editbound={lower,upper},
lower and
bounds

between

which

the TI-83

upper are the
searches
for a solution.

This is optional,
but it may help find the solution
quickly. The default is bound={- 1E99,1E99}.

more

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

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.

Equations with
Multiple Roots

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.

Further Solutions

After you solve for a varialfle,
solutions
from the interactive

you can continue
to explore
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].

Controlling
the
Solution for
Solver

or 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

Using solve( on
the Home Screen
or from a
Program

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)

MATH NUM Menu

To display

Operations

the

MATH NUM menu,

MATH NUM CPX PRB
i : ab s (
2: round(

Al_solute
Round

3 : i Part (

Integer

4:
5:
6:
7:

Fractional
part
Greatest
integer
Mininmln
value
Maxinlunl
value

f Pa r t (
i nt(
mi n (
max (

8 : ] cm(
9 :gcd (

abs(

press

[Z],

_

value
part

Legist eonlnlon
nmltiple
Greatest
eonnnon
divisor

abs( (absolute
value)
returns
complex
(modulus)
numbers,
matrices.

the absolute
expressions,

value of real
lists, and

or

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(

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.
rou nd(value [,#decimals

])
123456789012÷C
I
1.23456789E111

round

(x, 4) 3. 1416

C-round(C)
!21
123456789012-Iz3
456789000

Math,

Angle,

and Test

Operations

12

2-13

iPart( (integer

iPart(,
fPart(

or complex

part)
numbers,

returns

the integer

expressions,

lists,

part

or parts

of ++al

and matrices.

iPart(value)
fPart( (fra('tional
real or complex

paxt) returns
the fractional
part or p_u'ts of
numbe_,
expressions,
lists, and lnatrices.

fPart(value)

int(

iPart

(-23.45)

-23

f Part

( -23.45)._ 45

int( (greatest
integer)
returns
the largest integer
_m

4,
ERR-'NONRERL
ilBQuit
2: Goto

RNS

i

i

Entering
Complex
Numbers

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.

Note about
Radian versus
Degree Mode

Radian mode is reconnnended
for conlplex number
calculations. Internally-, the TI-83 converts all entered
values to radians, but it does not convert values for
exponential, logarithmic, or hyperbolic functions.

trig

In degree mode, complex identities such as
e ^ (i0) = cos(0) + i sin(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) + i sin(45) is treated internally as
e ^ (i45) = cos(_/4) + i sin(x/4). Complex identities are
always tree in radian mode.

2-16

Math,

Angle,

and

Test

Operations

Interpreting
Complex
Results

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^( ....
RectangularComplex
Mode

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 i is 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).

Polar-Complex
Mode

real component(÷

or -)imaginary

14+2t

4+2t

cornponenti

I

Polar-complex mode recognizes and displays a complex
number in the form re ^ 0/, where r is the nmgnitude, e is the
b_e of the natm'al log, 0 is the angle, and i is a constant equM
in(-I)
3.141592654e^

( I...

To enter a complex number
of r (magnitude),
press [_
enter the value of 0 (angle),
then press D.

in polar ff)nn, enter the value
[ex] (exponential
function),
press [_ [i] (constant),
and

ma_dtudeea(anglei)
10e._(n/3t)
10e"(I.04719755...

Math,

Angle,

and

Test

Operations

2-17

MATH CPX (Complex)

MATH CPX Menu

To display

Operations

the

MATH CPX menu,

press

[_

[] [],

MATH NUM CPX PRB

Returns
Returns
Returns
Returns
Returns
Displays
Displays

1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:_Rect
7:_Polar

con j(

the
the
the
the
the
the
the

complex conjugate,
real part.
imaginary part,
polar angle.
magnitude (modulus),
result in rectangular
form,
result in polar form,

conj((conjugate) returns the complex conjugate
complex number or list of complex numbers,

of a

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
or list of complex nmnbers,

real(

number

real(a+bi) returns a,
real(f'e^(0i)) returns _"*cos(O).
r.eal(3+4t)

imag(

3[

real (3e_'(4t
>>
-I.968938863

imag( (imaginary
part) returns
the imagining(nonreal)
of a complex
number
or list of complex
numbers.
imag(a+bi) t_tunls
b.
imag(re^(Oi)) returns
_'_sin(O),

Iimag(3+4t )

2-18

Math, Angle,

and Test

Operations

41

imag(3e^(4t
>-2.
270407486
>

part

angle(

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
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 0 and < 1. To generate
a list of randomnumbers,
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 seedvalue also 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

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
5 nCe
nPe 2
2
(2_2_i;
{2,3> nPP
_ 6}
! (Factorial)

! (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

Math,

in the syntax

Angle,

and

description

Test

above.)

Operations

2-21

randlnt( (random

randlnt(

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
dlnt(1,6)

1,{26, 3)i5}

randInt(

randNorm(

G

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(

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)
randBin(7,.

3
4, 10)

{3 3 2 5 1 2 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

To display

the ANGLE menu,

menu displays
Radian/Degree
interpretation

press [_

[ANGLE]. The ANGLE

angle indicatot\_
and instruetions.
mode setting
affects the TI-S3's
of ANGLE menu entries.

The

ANGLE
1: °
3: r

Degree
notation
DMS minute notation
Radian notation

4: ,DMS

Displays

as degree/lninute/seeond

5: R,Pr(

Returns
Returns
Returns
Returns

r, given X and Y
0, given X and Y
x, given R and 0
y, given R and 0

2:'

6:

R_PO(

7: P_Rx(
8: PmRy(

DMS Entry
Notation

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,

the angle nlode is not set to Degree,
the TI-83 call interpret
the atgulnent
and seconds.

23 seconds.

If

you nmst use ° so that
as degrees,
minutes,

Radian mode

Degree mode

I

sin(30° 1'23")

I

sin(30° 1'23")
-. 98421299951

sin(30 °l 23 o)

.5003484441

° (Degree)

•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)

r (Radians)

designates

an angle

regardless
of the cmTent angle
mode, you can use r to convert

or list of angles

as radians,

mode setting.
In Degree
radians
to degrees.

value r
Degree mode
sin

(<_/4.')

r )

• 7071067812
sin(

{0,

,/2}

_)
%w.J

1}

(x/4> r
45
_DMS

_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.x and y can
be lists.

R_Pr (,
R_,Pe (,
P_-Rx(,
P*Ry(

R*Pr(x,y),

R*PO(x,y)
I

R*Pr(-1,O)

e,eo( }

,05

! I

Note: Radian mode is set

14i5926541

PI_Rx( converts
polar coordinates
to rectangular
coordinates
and returns
x. PI*Ry( converts
polar
coordinates
to reetangulm"
coordinates
and returns
0 can be lists.

y. r and

P*Rx(r,_,P*Ry(v,_
P*Rx(I,x)
-10

P*R_(I,x)

2-24

Math,

Angle,

and

Test

Operations

Note: Radian mode is set.

TEST (Relational)

TEST Menu

>_ ->,
<,_<

Operations

To display

the TEST menu,

[_

This operator...
TEST LOGIC

Returns

1: =
2: _
3: >

Equal
Not equal to
Greater
than

4: >
5: <

Greater
than
Less than

6: <

Less than

[TEST].

1 (true)

if,..

or equal

or equal

to

to

Relational
operators
compare
valueA
and valueB
and
return
1 if the test is true or 0 if the test is false, valueA
valueB
can be real numbet_,
expressions,
and _ only, valueA
and valueB
also can
complex
numbers.
If valueA
and valueB
nmst have the same dimensions.
Relational
program

operators
are often
flow and in graphing

function

over

valueA
valueA
valueA

specific

=valueB
>value B
valueB
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 a Program

To define
begin

a function

on a blank

fronl

the home

line and follow

1. Press
@

@
[,], enter
[-1 again.

2. Press

_.

Select
cursor

5. Press

or a prograln,

steps.

the expression,

3. Press _
[] 1 to select
VARS Y-VARS menu,
4.

screen

these

1:Function

and then

press

fl'om the

the function
name, which p_stes the name to the
location
on the home screen or program
editor.
_

to complete

"expression

the instruction.

" _ Yn

I"X z''÷Vt

Donel

"J',JtI_IX
2PI':'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.

Evaluating Y=
Functions in
Expressions

You can

calculate

specified

value

Yn(value)
Yn({valuel

the value

,value2,value3,

Pl*tlB. Pl*{2
P10t)
\V1
2Xs-2X+6

,,..z=
xV_-=

3-6

Function

Graphing

of a Y= function

of X. A list of values

. . .,value
I

I

returns

Yn at a
a list.

n})

Y1 (0)

6

'_1
._6({0,
4.2 1,2,3,4}
3.6 5.4 ) ...

Selecting

and Deselecting

Selecting and
Deselecting a
Function

You can
functkm

Functions

select and deselect
(turn on and turn off) a
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
these steps.
1. Press

[]

a function

to display

2. Move the cursor
deselect.

in the Y= editor,

follow

the Y= editor.

to the function

3, Press [] to place the cursor

you want

to select

on the functkm's

4. Press [gg_g] to change the selection

or

= sign.

status.

When you enter or edit a function, it is selected
automatically.
When you clem' a function, it is deselected.
Turning On or
Turning Off a Stat
Plot in the Y=
Editor

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_

_

",YI =. 2X 3-2X+6
\Vz= -Yt

J

-'1---,_
I

,_.y_=2X+XZ

j

\Y_=
",us =
",'¢_=

J

-W=

I

Plott

isturnedon.

Plot2 and Plot3 are turned off

/

Function

Graphing

3-7

Selecting and
Deselecting
Functions from

To select or deselect a function fronl the home screen or a
program, begin on a blank line and follow these steps.

the Home Screen

1. Press _

or a Program

2. Select 4:On/Off to display the ON/OFF secondary

[] to display- the VANS Y-VANS menu.
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,
with eonunas.

separate

•

To turn on or turn off all functions,
number after FnOn or FnOff,

do not enter a

FnOn [function#function#,.,,
FnOff[function# function#

function
function

....

them

n]
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

3-8

Function

Graphing

:FnOn

Dlo3e

I Pl<,tl

Plo_Z

Plot._

",Y1 B. 2X_-2X+6
_,Y;_= -Y1
",YsBXZ
xy_=
xY_=
\Y_=
,,y_=

Setting

Graph Styles for Functions

Graph Style
Icons in the Y=
Editor

This

table

describes

the

graph

graphing.
Use the styles
to be graphed
together,
solid line, Y2 as a dotted

styles

available

for function

to visually
differentiate
functions
For example,
you can set Y1 as a
line, and Y3 as a thick line,

Icon Style

Description

"..

Line

A solid line connects
plotted
points;
the default
in Connected
mode

"i

Thick

A thick

'_.i

Above

Shading

covers

the area

a*bove

ik

Below

Shading

covet\_

the area

below

'1!

Path

A circular
the graph

cursor
traces the
and draws a path

(!

Aidmate

A circular
the graph

cursor
without

".

Dot

A snlall dot represents
each plotted
this is the default
in Dot mode

solid

line connects

plotted

this is
points

the graph
the graph

leading

edge

of

traces
the leading
drawing
a path

edge

of

point;

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.

Setting the Graph
Style

To set the graph

style

for a function,
the Y= editor.

1. Press

[]

to display

2. Press

[]

and [] to nlove

follow

the cut\sor

these

steps.

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
styles. The seven styles
which
5. Press

they are listed
[],

to rotate through
the graph
rotate in the same order in

in the table

[], or [] when

you have

above.
selected

a style.

PlotJ. F'1ot;_P1ot:_
",Y1B8sin(X)
_YzB8cos(X)
\Y_=
xY_=
\Y_=
xy_=

xy_=

Function

Graphing

3-9

Shading Above
and Below

When

you select

TI-83

rotates

•

Vertical
graph

_mor 1;. for two or more

through
lines

four

shade

shading

the first

the

function

with

a '_.1or b.

style.

•

Horizontal

lines

•

Negatively

sloping

•

Positively

•

The rotation
returns
to vertical
lines for the fifth '_.ior i;.
function,
repeating
the order described
above.

sloping

VClmn shaded

Note:

shade

the second.

diagonal

lines

diagonal

are_Ls intersect,

When _1or h_,is selected

lines

shade
shade

for a Y= function

the third.
the fom'th.

the patterns

curves, such as Yl={1,2,3}X,
the four shading
each member of the family of curves.

Setting a Graph
Style from a
Program

functions,

patterns.

overlap.

that graphs
patterns

a family

of

rotate for

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,

1 = ". (line)
4 = 1'.-.(below)
(animate)

as shown

below.

2 = '_i(thick)
8 = ':) (path)
7 = ". (dot)

3 = ,m(above)
6 = (!

GraphStyle(fanction#,graphstyle#)
For example,
when this program
is executed
GraphStyle(1,3) sets Y1 to '_](above),

: OisPGr'aPh

3-10

Function

Graphing

in Func mode,

Setting

the Viewing

The TI-83 Viewing
Window

Window

Variables

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.
WINDOW
Xmin=-lO
XMax=lO
Xscl=l
Ymin=-lO
Ymax=lO
Yscl=l
XPes=l

_Ymax

Xsc_

Xmax /
_--Yscl
Ymir_ N

Displaying the
Window
Variables

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
only. The default is 1.
•
•

(1 through

At Xres=l, functions are evaluated
pixel on the x-axis.
At Xres=8, functions are evaluated
eighth pixel along the x-axis.

8) for function

graphs

and graphed

at each

and graphed

at every

Tip: SmalIXres valuesimprovegraph resolutionbut may causethe
TI-83 to draw graphs more slowly.
Changing a
Window Variable
Value

To change a window variable
editor, follow these steps.

value fronl the window

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,
TI-83 ewduates it. The new value is stored.

the

Note: Xmin.J
Fit_t

ll=0

cul_ve?

€

*

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 freemoving cursor, press [], [], [], or [].

Function

Graphing

3-27

dy/dx

dy/dx

(numerical

(slope)

derivative)

of a function

finds

at a point,

To find a function's

slope

1, Select 6:dy/dx from
graph is displayed.

the numerical

with

at a point,

the

follow

CALCULATE

2, Press [] or [] to select the function
to find the numerical
derivative.
3, Press [] or [] (or enter a value)
which to calculate
the deriwttive,
The

cursor

is on the solution

derivative

e= 1E-3,
these

menu.

steps,

The current

for which

you want

to select the X value at
and then press [_TE_.

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

ff(x)dx

[].

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.
2,

Press [] or [] to move the cm\sor to the function
which you want to calculate
the integral.

for

3, 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?

_= - 1 • _II

I,

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

4
Contents

Parametric
Graphing
Getting Started: Path of a Ball ...........................
Defining and Displaying Parametrie Graphs ..............
Exploring Parametric Graphs ............................

_

TEXAS

4-2
4-4
4-7

TF83

INSTRUMENTS

/

J
STAT

PLOT

TBLSET

FORMAT

CALC

TABLE

Parametric

Graphing

4-1

Getting

Getting

Started:

Started

Path of a Ball

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
has horizontal and vertical components.
Horizontal:
Vertical:
The vertical

X1 (t)=tv0cos(0)
Y1 (t)=tv0sin(0)and horizontal

Vertical vector:
Horizontal vector:
Gravity constant:

vectors

of the bali's motion also will be graphed.

X2(t)=0

Y2(t)=Yl(t)

X3(t)=Xl(t)

Y3(t)=0

g=9,8 m/see 2

Press @. Press 30 _
[_
[ANGLE] I (to select °) [] [_
XITin terms of T.

4.

26 [_
to define

_
28 [_ [ANGLE]1 [] []
[] _
to define YIT.

The vertical component
by X2Tand Y2T.

vector

is defined

Press 0 [ggY_ to define X2T.

Press [_
[] to display the VARS Y-VARS
menu, Press 2 to display the PARAMETRIC
secondmT nlenu, Press 2 [gN?_7to define
Y2T,

4-2

Parametric

Graphing

of time

1 ,
g gt 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 30 _
9.8 [] 2 _

of the ball as a function

The horizontal component
defined by X3Tand Y3T,

vector

is

PI,:,I:t

Press [gAg_ [] 2, and then press 1 [gNTgglto
define X3T.Press 0 [gNT_ to define Y3T.

PI,:,L>

PlOI:3

91T B30Tsin (25 ° )
-9.8/2TZ
xXzT Be

VaT B'¢1T

",X_T BX1T
V St 1_10
\X_T

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
Tmax=5

Xmin=-10
Xmax=100

Ymin=-5
Ymax=15

Tstep=,l

Xscl=50

Yscl=10

Press [g_ [FORMAT] [] [] [] [] F_
AxesOff, which turns off the axes.

=

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

to set

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.

1 1. Press _
to obtain numerical results
and answer the questions at the beginning
of this section.

glT=3OTcg¢_;(_

Y1T=30TSin(_:_

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.

Parametric

Graphing

4-3

Defining

and Displaying

Parametric

Graphs

TI-83 Graphing
Mode Similarities

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.

Setting
Parametric
Graphing Mode

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.

Displaying the
Parametric Y=
Editor

After selecting Par graphing
_arametric Y= editor.

mode, press [] to display the

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 X and 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.

Selecting a
Graph Style

4-4

Parametric

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.

Graphing

Defining and
Editing
Parametric
Equations

To define

or edit

a parametric

equation,

•

Press

•

Press@

the steps

in

_.
[T].

Two components,
X and Y, define a single
equation.
You nmst define both of them.

Selecting and
Deselecting
Parametric
Equations

follow

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
T in
either of two ways.

parametric

The TI-83 graphs only the selected
parametric
equations.
In the Y= editor, a parametric
equation
is selected
when
= signs of both the X and Y components
are highlighted.
You may select any or all of the equations
XIT and YIT
through

the

X6T and Y6T.

To change the selection
status, move the cursor
onto the =
sign of either the X or Y colnponent
and press [gNYE_. The
status of both the X and Y components
is changed.

Setting Window
Variables

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 T v'Mue to evaluate
Largest T value 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,
change the T window variables.

Parametric

you may want to

Graphing

4-5

Setting the Graph
Format

To display-

the

current

graph

format

Displaying a
Graph

When you press _,
the TI-83 plots the selected
parametric equations, It evaluates the X and Y components
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,

You can

•

•

perform

these

actions

Access functions
by using
component
of the equation
*.5

graphs (Chapter

fronl

the home

3).

screen

or a

Store

•

Select

parametric

Store

1

values

360÷Tnax

Graphing

equations.

"÷Yi TD°neT
"÷Xl
Done

or deselect

FR0t'f"

•

the name of the X or Y
as a vm'iable.

-,
94. r0916375

"cos(T)
"sin(T)

Parametric

[_

program.

NiT

4-6

press

X, Y, and T m'e updated.

Snlart Graph applies to parametric
Window
Variables and
Y-VARS Menus

settings,

[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,

\XzT="Xl
Bsin(T)yzT=Vin°tIT
T Bcos(T)nOtz
nots

parametric

equations,

Done

Pl0tl =cos(T)
,otz
,,t,
",XlT
YiT=sin(T)
xXzT=
YZT=

directly

to window

360

variables.

I
I

I

Exploring

Free-Moving
Cursor

Parametric

The

Graphs

free-lnoving

cursor

in Par graphing

In RectGC format,
nloving
X and Y; if CoordOn format
displayed.
In PolarGC format,
format is selected,

TRACE

works

the

salne

as

the cursor
updates
the values
is selected,
X and Y are

of

in Func graphing.

X, Y, R, and 0 are updated;
R and 0 m'e displayed.

if CoordOn

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 T are updated; if CoordOn
format is selected, R, 0, and T are displayed. The X and Y
(or R and 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
(Chapter 3).

in Par graphing;

Parametric

panning

is not

Graphing

4-7

Moving the Trace
Cursor to Any
Valid T Value

To move

the trace

cursor

to any valid

current
function,
enter the
first digit, a T= prompt
and
displayed
in the bottom-left
enter an expression
at the
valid for the current
_ewing
colnpleted
the ent_% press

T value

on the

number,
When you enter the
the number
you entered
are
corner of the screen.
You can
T= prompt,
The wdue nmst be
window,
When you have
[K_Y_ to lnove the cursor.

PIoI:I PloL2 Plot_
_.X1 T _sir,(T)
YtT_T
XIT=S;n(T)

XIT=_;ifl(T)

T=2
ZOOM

_,Ii

(

_IT=T

T=T

}

T=;_

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

4-8

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.

Parametric

Graphing

Polar
Graphing
Contents

Getting Started: Polar Rose ..............................
Defining and Displaying
Polar Graphs
...................
Exploring Polar Graphs ..................................

TEXAS

5-2
5-3
5-6

T1=83

INSTRUMENTS

J
STAT

PLOT

TBLSET

FORMAT

CALC

TABLE

Polar

Graphing

5-1

Getting

Getting

Started:

Started

Polar Rose

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.

Plot:t

Plot2

Plot3

_rl B8sin(2.50)
\r_:=
i_.r_ =

Press [] to display- the polar Y= editor.
Press 8 NTN2.6 _
[] [g_gO to define

%rfi=

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
value of 0max to 4x.

5,

Press _
the graph.

the

5 to select 5:ZSquare and plot

Repeat steps 2 through 5 with new values
for the variables A and B in the polar
equation rl=Asin(B0). Observe how the new
values 'affect the graph.

5-2

Polar

Graphing

WINDOW
Omin=O
OMaX=4X
Ostee=,1308996...
XMin=-lO
Xmax=lO
XSCI=I
_VMin=-lO

Defining

and Displaying

steps

Polar Graphs

TI-83 Graphing
Mode Similarities

The

for defining

a polar

graph

are similar

Setting Polar
Graphing Mode

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.

Displaying the
Polar Y= Editor

After selecting
Pol graphing
_olar Y= editor.

for defining
a function
graph. Chapter
are familiar
with Chapter
3: Function
details aspects
of polar graphing
that
graphing.

PI,:,I:I PloL2
\rl=
\i-- 2---M-_ 3:=
\1,-, tl =
\1.'. _ =
\p6=

mode,

to the steps

5 assumes
that you
Graphing.
Chapter
5
differ from function

press

[]

to display-

the

Plot3

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).
Selecting
Styles

Graph

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

To define

or edit

a polar

equation,

follow

the steps

•

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 M1 of the equations.
To change the selection status, nlove the cursor
= sign, and then press [_.

Setting Window
Variables

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,
change the 0 window variables.

Polar

onto the

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,..

5-4

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.

Graphing

you may want to

Setting the Graph
Format

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.

Displaying a
Graph

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,

Window
Variables and
Y-VARS Menus

X, Y, R, and 0 are updated.

Slnart Graph applies to polm" graphs

(Chapter

You

the

can

perfornl

these

actions

fronl

honle

3).

screen

or

a

program.
•

Access functions
wuiable

by using the name of the equation

rl +r.z
•

8

Store polar equations,

"51_1"÷1"i

•

•

as a

Done

\r?:=\rll_5OPl°tl
P10t_:

Select or deselect

polar equations.

FnOff

Done

1

Plott
xr
I =50PIotZ Plot_

Store values directly to window
IO+Orqih

Plot3

I

I

I

variables.

OI

Polar

Graphing

5-5

Exploring

Polar Graphs

ffee-mo_ing

cursor

in Pol graphing

Free-Moving
Cursor

The

works

the same

as

TRACE

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 Func graphing.
In RectGC fonnat,
moving tile cursor
updates
the values of X and Y; if CoordOn format is
selected,
X and Y are displayed.
In PolarGC format,
X, Y, R,
and 0 are updated;
if CoordOn format is selected,
R and 0
m'e 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, R and 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
not (Chapter 3).

in Pol graphing

mode; panning

is

Moving the Trace
Cursor to Any
Valid e Value

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

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

5-6

CALC operations
in Pol graphing
work the sanle
graphing.
The CALCULATE nlenu items available
graphing
are 1:value, 2:dy/dx, and 3:dr/d0.

Polar

Graphing

as in Func
in Pol

Sequence
Graphing
Contents

Getting Started: Forest and Trees ........................
Defining and Displaying
Sequence
Graphs ...............
Selecting Axes ('ombinations
............................
Exploring
Sequence Graphs ..............................
Graphing Web Plots ......................................
Using Web Plots to Illustrate
Convergence
...............
Graphing Phase Plots ....................................
Comparing
TI-83 and TI-82 Sequence Variables ..........
Keystroke
Differences
Between
TI-83 and TI-82 .........

'_

TEXAS

6-2
6-3
6-8
6-9
6-11
6-12
6-13
6-1.5
6-16

T1=83

iNSTRUMENTS

u= -.Bu(7_-:1.)+3.6
-,_

I=

-%

l

........
>'_=:L5
X=l.F_61172

I'

....

"_
"%_
i'=1._ _:61172

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Sequence

Graphing

6-1

Getting

Getting

Started:

Started

Forest and Trees

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.

Soi Eng
0123456789
Degree
ar Pol

Press [_ [FORMAT] and select Time axes
format and ExprOnformat if neeessatT.

3.

Press @. If the graph-style icon is not ".
(dot), press [] [], press [g_-gRquntil ". is
displayed, and then press [] [].

4.

Press [_
[] a to 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.

MW

UW

PI_I

PI_tZ

Plot3

_Min=l
'..u(_bBiPart(.Bu(
_-I)+1000)
u(_Min)B4000

".v(_)=
v(_Min)=
".u(_)=

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
Xscl=10

Ymax=6000
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 n is plotted on the x-axis), and Y
(tree count) are displayed at the bottom.
When will the forest stabilize? With how
many trees?
6-2

UM

PolaPGC
CoopdO_
GridOn
RxesO_
LabelOn

Sequence

Graphing

lu=iPart(.Bu(_-l)+lOO0)

I

Defining

and Displaying

Sequence

Graphs

TI-83 Graphing
Mode Similarities

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.

Setting Sequence
Graphing Mode

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

After selecting
Y= editor.

Seq mode,

press

[]

to display-

the sequence

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
n value 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,which requires an initialvalue.
Selecting
Styles

Graph

Selecting and
Deselecting
Sequence
Functions

The icons to the left of u(n), v(n), and w(n)
graph style of each sequence
(Chapter
3).
$eq mode is ". (dot), which shows discrete
"..(line), and "i (thick)
styles m'e available
graphing.
Graph styles m'e ignored
in Web

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
move the
then press
sequence

6-4

Sequence

represent
the
The default
in
values. Dot,
for sequence
format.

Graphing

the selection status of a sequence function,
cut\sor onto the = sign of the function name, and
[g_.
The status is changed for both the
function u{n) and its initial value u(nMin).

Defining and
Editing a
Sequence
Function

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
in either of two ways.
•
•

vmiable

Press _.
Press [g67][CATALOG][N].

You can enter the function

name from the keyboard.

•
•

To enter the function
To enter the function

name u, press [gh_][u] (above [_).
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, n is always a series of consecutive integers, starting
at zero or any positive integer.
Nonrecursive
Sequences

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

2, 4, 6, 8,10,

equation

above

returns

the sequence

. . . 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

In a reem\Mve

Sequences

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,
u(5) without

sequence,

the nth term

in the sequence
first calculating

plo1:1 PloL2 pl,:a:_:
_Min=l
"..u(_)B2*u(n-1
)

in the sequence

is

below you cannot
calculate
u(1), u(2), u(3), and u(4).

I

I

u(.n[_in)B1

Using an initial value u(nMin) = 1, the sequence
returns
1, 2, 4, 8, 16,...

above

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
since they reference
•

require
an initial
undefined
terms.

If each term in the sequence
pre_dous
term, as in u(n-1),
value for the first tenn.
PloLi

plol:._

[-2)
u(r_Min)B{l,O

term

6-6

Sequence

Graphing

value

sequence
is defined in relation
to the
the previous
term, as in u(n-2), you
values for the first two terms. Enter
a list enclosed
in braees
({ }) with
the values.

Plot3

nMin=l
I..u(n)Bu(n-1

The

is defined in relation
to the
you nmst specify an initial

1 )+5

If each term in the
term that precedes
nmst specify- initial
the initial values as
commas
separating
PloI:2

or values,

Plot3

nMin=l
..u (n) B. 8u (n0
u(nMin)B100

Plot't

value

of the first

)+u(n
}
term

is 1 for the sequence

is 0 and the value
u(n).

of the second

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 n value to ev'gduate
Largest n value to evaluate
First term number to be plotted
Incremental n value (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 n wdue to evaluate, nMin also is
displayed in the sequence Y= editor, nMax is the largest
value to evaluate. Sequences are evaluated at u(nMin),
u(nMin+l), u(nMin+2), ... , u(nMax).

n

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
n wdue 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

To display-

the

current

graph

Time Web uv
vw uw
RectGC
PolarGC
CoordOn
CoordOff
GridOff
GridOn
AxesOn
AxesOff
LabelOff
LabelOn
ExprOn

Setting Axes
Format

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,

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
uv
vw
uw

x-axis

y-axis

n

u(n), v(n),w(n)

u(n-1), v(n-1),w(n-1)

u(n), v(n),w(n)

u(n)
v(n)
u(n)

v(n)
w(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).

Displaying a
Sequence Graph

To plot the selected sequence functions, press _.
graph is plotted, the TI-83 updates X, Y, and n.
Snlart Graph applies to sequence

6-8

Sequence

Graphing

graphs

(Chapter

As a
3).

Exploring

Sequence

Free-Moving
Cursor

The

TRACE

The

Graphs

free-moving

cursor

in Seq graphing

works

the same

as

in Func graphing.
In RectGC fonnat,
nloving tile cursor
updates
the values of X and Y; if CoordOn format is
selected,
X and Y are displayed.
In PolarGC fornlat,
X, Y, R,
and 0 are updated;
if CoordOn format is selected,
R and 0
m'e displayed.

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 n during 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

Moving the Trace
Cursor to Any
Valid n Value

To nlove the trace cursor to any valid n vMue 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=_:

""

Sequence

Graphing

}1=5"I_

?=3

6-9

ZOOM

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 1 through 7 are the ZOOM MEMORY variables for Seq
graphing.

CALC

The only CALC operation

Evaluating u, v,
and w

is value.

When Time axes format is selected,
u(n) value) for a specified n value.

•

When Web axes format is selected, value draws the web
and displays Y (the u(n) value) for a specified n value,

•

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),

value displays Y (the

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]),
is optional; default is 1.
"nz"+u:u(3)
u({1,3,5,7,9})
{i 9 25 49
u(1,9,2)
{1 9 25 49

Sequence

in Seq graphing

•

•
•
•

6-10

available

Graphing

9
81}
81}

nstep

Graphing

Web Plots

Web axes

To select

Valid Functions
for Web Plots

V_l_en Web axes format is selected,
a sequence
graph properly
or will generate
an error.

Displaying the
Graph Screen

format,

press

[FORMAT] []

Graphing a Web
Plot

[_

[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.

•

It must
(u(n-1)

be recursive
with
but not u(n-2)).

•

It cannot

reference

n directly.

•

It cannot

reference

any defined

only one recursion

In Web format, press _
The TI-83:
•

Draws

•

Plots
the
independent

will not

sequence

level

except

itself.

to display the graph screen.

a y=x reference

line

selected
sequences
variable.

in AxesOn
with

format.

u(n-1)

as the

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.

Drawing

the Web

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
PlotStart=l).
2. It lnoves

vertically

3. It lnoves

horizontally

4. It repeats
continue

this vertical
to press [].

at the initial

(up or down)

value

u(nMin)

(when

to the sequence.

to the y=x reference
and horizontal

Sequence

line.

movenlent

Graphing

as you

6-11

Using Web Plots to Illustrate

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.

Example:
Convergence

u(_Min)B{-4}

"-.v(n)=
_Min=lPl_l
PloL_

v(nMin)=

PloL_

)+

".uO?)=
2.

Press

[_

3. Press

[_
nMin=l
nMax=25
PlotStart=l

[FORMAT] _

to set Time axes

and set the variables
Xmin=0
Xmax=25
Xscl=l

ff)rmat,

as shown below.
Ymin=-10
Ymax=l 0
Yscl=l

PlotStep=l

4. Press [g_

5, Press [_
6. Press [_
Xmin=-10
7.

Press [g_

to graph the sequence.

[FORMAT]and select the Web axes setting.
and change the variables
Xmax=10

below.

to graph the sequence.

8. 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 n value 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

N'--_.?_:EII?2

6-12

Sequence

Graphing

t.-*

I?=1,?_:El172

Graphing

Phase Plots

Graphing with uv, The phase-plot m,ces settings uv, vw, and uw show
vw, and uw
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 [_.

Example:
Predator-Prey
Model

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
M
K
W

=
=
=
=

number of rabbits
rabbit population growth rate without wolves
rabbit population death rate with wolves
number of wolves

G
D
n
Rn

=
=
=
=

wolf population growth rate with rabbits
wolf population death rate without rabbits
time (in months)
Rn_I(I+M-KWn_I)

W,

= W,_I(I+GRn_I-D

(.05)
(.001)
(.0002)
(.03)

)

1, Press [] in Seq mode to display the sequence Y= editor.
Define the sequences and initial wdues for Rn and Wn as
shown below. Enter the sequence Rn as u(n) and enter
the sequence Wn as 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] _

3, Press _
nMin=O
nMax=400
PlotStart=l

to select

and set the variables
Xmin=O
Xmax=400
Xscl=100

Time axes format,
as shown below.
Ymin=O
Ymax=300
Yscl=100

PlotStep=l
4, Press

[ghT_]

to graph

the

sequence,

5, Press _
[] to individually trace the number
rabbits (u(n)) and wolves (v(n)) over time (n),
Tip: Press a number,

6,

Press [g_]
format,

7. Press

_
below.
Xmin=84
Xmax=237
Xscl=50

Press _.
the number

[FORMAT]

and then press _

[]

[]

and change

of

to jump to a specific

n

to select uv axes

_

these

variables

as shown

Ymin=25
Ymax=75
Yscl=lO

Trace both the number of rabbits (X) and
of wolves (Y) through 400 generations,
Note: When you press [_,
the
equation for u is displayed in the

top-left corner. Press [] or [] to
see the equation for v.
I g=160.LIB_.=:B y=6;',66;'BLI9

6-14

Sequence

Graphing

Comparing

Sequences and
Window
Variables

TI-83 and TI-82 Sequence

Refer

to the table

shows TI-83
well as their

if you are familim"

sequences
and sequence
TI-82 counterparts.

with

the TI-82.

window

It

vm'iables,

as

TI-82

TI-83
In the

Variables

Y= editor:

u(n)

Un

u(nMin)

U nStart

v(n)

Vn

v(nMin)

VnStart

w(n)

not

available

w(nMin)

not

available

In the window

(window

variable)

(window

vm'iable)

editor:

nMin

nStart

nMax

nMax

PlotStart

nMin

PlotStep

not

available

Sequence

Graphing

6-15

Keystroke

Differences

Between

to the table

TI-83 and TI-82

Sequence

Re%r

Keystroke
Changes

conlpares
TI-83 sequence-name
sy_tax
and variable
sy_tax
with TI-82 sequence-name
syntax
and variable
syntax.

if you are familiar

with

the TI-82.

It

TI183 / TI-82

On TI183, press:

On TI-82,

n/ n

_

_

[,]

u(n) / Un

_

_

[Y-VARS] []

[u]

press:

[]

D_D
v(n)
/ vn

_

w(n)

_

[i

r_ [¥-VARS][] []

[w]

not

available

D_D
D_D

u(n-1)lUn-1

_

[u]

_

[Un-l]

v(n-1)/vn-1

I_

[v]

I_

[vn-_]

w(n-1)

_

[w]

not

available

D_DmD
I]]_E]mD
[]_•mD

6-16

Sequence

Graphing

Tables
Contents

Getting Started: Roots of a Function
.....................
Setting Up the Table .....................................
Defining the Dependent
Variables ........................
Displaying the Table .....................................

'_

TEXAS

T1=83

iNSTRUMENTS

X
0
1
2

Y_
0
"1
h
21
_
11_

h
5

7-2
7-3
7-4
7-5

Y2
0
"_
0
15
hE
10_

X= -1
J
STAT

PLOT

TBLSET

FORMAT

CALC

TABLE

Tables

7-1

Getting

Getting

Started:

Started

Roots of a Function

is a fast-paced

introduction.

Read

Evaluate
the function
Y = X :_- 2X at each integer
many sign changes
occur, and at what X values?

1.

2.

the chapter
between

for details.

-10 and

Press _
[] [] [] FENY_to set Func
graphing mode.

Press @. Press _
Then press [] 2 _
function Y1=X3- 2X.

_
3 to select 3
to enter the

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 [_
screen.

[TABLE]to display the table

Plol:l

Press [] until you see the sign changes in
the value of Y1. How many sign changes
occur, and at what X values?

TABLE SETUP
TbIStart= -10
_Tbl=l
Indent: _
Ask

Depend:

X

_

Y_

"9
"B
"?
"6

"7tl
"h96
"329
"_.Oh

"_:

"Jig

"h

"gtl

X
"2
"1
0
1

X=3

Tables

Pl_l:_

P1*{_

-.Y1BX x-2X
,,yz=
b.Y_=
•,.y _ =
\Yg=
".YG=
\YT=

X= -10

7-2

10. How

YI
"h
1
0
"t
h

Ask

Setting

Up the Table

TABLE SETUP
Screen

TodisplaytheTABLESETUPscreen,
TblStart=O
_Tbl=lSETUP
TRBLE
IndPnt:
Depend: i

TblStart, ATbl

press[_[TBLSET].

Rsk
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
variable.

step)

defines

the increment

for the independent

Note: In Seq mode, both TblStart and ATbl must be integers.

Indpnt: Auto,
Indpnt: Ask,
Depend: Auto,
Depend: Ask

Setting Up the
Table from the
Home Screen or
a Program

Selections

Table Characteristics

Indpnt: Auto
Depend: Auto

Values are displayed
automatically
the independent-variable
colunm
dependent-variable
colunms.

Indpnt: Ask
Depend: Auto

The table is empty; when you enter a value
for the independent
variable,
all
corresponding
dependent-variable
values
are cah:ulated
and displayed
automatically.

Indpnt: Auto
Depend: Ask

Values are displayed
autonmtically
for the
independent
variable;
to generate
a value
for a dependent
variable,
move the cursor
to that cell and press [E_.

Indpnt: Ask
Depend: Ask

The table is empty; enter values for the
independent
variable;
to generate
a value
for a dependent
variable,
move the cm:sor
to that cell and press [EN_,

in both
and in all

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
independent-variable
values in the cmTent

is a list of
table.

When you press [2_ [TBLSET] in the program
editor,
can select IndpntAuto, IndpntAsk,
DependAuto, and
DependAsk.

Tables

you

7-3

Defining

the Dependent

Variables

Defining
Dependent
Variables from
the Y= 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).

Editing
Dependent
Variables from
the Table Editor

To edit a selected
these steps.

Y= function

fronl the table editor, follow

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.

5G
20't

Vt BX_-2X
3, Press [ggT_. The cursor
the function.
X

moves to the bottonl
X

ml

o
I
.-,

o
"t
it
2t
_6
I15
20_

LI
_;
I_

71BII_-2X

line. Edit

m

o
t

o
"1

6

20_

V1BX:-4X

Press [ggT_ or []. The new values are calculated. The
table and the Y= function are updated automatically.

X

"3
Y1

Yt =O
Note:
defines

7-4

Tables

You also can use this feature
a dependent

variable

without

to view the function
having

that

to leave the table.

Displaying

the Table

The Table

To display-

the table,

press

[_q

[TABLE].

Current cell
Independentvariable values

to

X

_ 1 4,
_

in the first
column

lZ
13

-h?.eB -_:Z.BE
-_Z.I_6 -6Z.eE

11

"hh.86

9"_

"_

"_'.gB

1_

1

1h

Yz
-_9.iz

Dependentvariable values in

"_:h.86

"G6.98
"E.q.Z

16
"6h._:B "?h,59
Y1 = -39, 173120459

_.
--

--

the second and
third columns

T
Current cell's full value
Note: The table abbreviates the values, if necessary.

Independent
Dependent
Variables

and

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
Variable

Dependent
Variable

Func (function)

X

Y1 through
Y0

Par (parametric)

T

X1T/Y1T through
X6T/Y6T

Pol (polar)

0

rl through

Seq (sequence)

n

u(n), v(n), and w(n)

Yg, and

r6

From the home screen, select the CIrTable instruction
the CATALOG. To clear the table, press [ggY_.

fronl

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
IndependentVariable 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
dependentvariable
values also are displayed.
All dependent-variable
values may not be displayed
if Depend: Ask is selected.

X

YI

Yz

1
z

"t
4

"_
¢

4
5
6

_6
115
204

4B
105
192

X=O

X
1
.3

YI
"t
4
21

Yz
I "_
io
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
Dependent
Variables

Other

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.

X
"_
"2
"1
O
1
Z

Yz

Y_

"6
"6
"4
_
G
:L=I

":LB
"10
"LI
O
2
;L

Y_= -28
Tip:
that
and
For
the

7-6

Tables

To simultaneously
display on the table two dependent
variables
are not defined as consecutive
Y= functions,
go to the Y= editor
deselect the Y= functions between the two you want to display.
example, to simultaneously
display Y4 and Y7 on the table, go to
Y= editor and deselect Y5 and Y6.

8
Contents

Dnrs Wuction
s
Getting Started: Drawing a Tangent Line .................
Using the DRAW Menu ...................................
Clearh]g Dra,_lngs
.......................................
Drawing Line Segments
..................................
Drawing Horizontal
and Vertical Lines ...................
Drawing Tangent Lines ..................................
Drawing Functions
and hwerses
.........................
Shading Areas on a Graph
...............................
Drawing ('ircles ..........................................
Plaeing Text on a Graph .................................
Using Pen m Draw on a Graph ...........................
Drawing Points on a Graph ..............................
Drawing Pixels
..........................................
Storing Graph Pictures (Pies) ............................
Recalling Graph Pictures
(Pics) ..........................
Storing Graph Databases
(GDBs) ........................
Recalling Graph Databases (GDBs) ......................

4_ TEXAS INSTnUMENTS

STAT

PLOT

TBLSET

FORMAT

8-2
8-3
8-4
8-5
8-(;
8-8
8-9
8-10
8-11
8-12
8-1:3
8-14
8-16
8-17
8-18
8-19
8-20

T1=83

CALC

T._,B L E

DRAW Instructions

8-1

Getting

Getting

Started:

Started

Drawing

is a fast-paced

a Tangent

introduction.

Suppose you want to find the equation
function Y = sinX.

Read the chapter

of the tangent

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.

Line

Press _
7 to select 7:ZTrig, which
graphs the equation in the ZOOlll Trig
window.

Press [g_ [DRAW] 6 to select 6:Tangent(.
The tangent instruction is initiated.

line at X = _2

P1,'.,tl

Plot_

/-7--,.

"..>"

[4] 2[]

[] 2.

Pl(,t3

/-7_

/-7\

".,_i_1

?=0

/2"-..

-,_i_1

4=,r(2)/211

8-2

DRAW Instructions

-,,_i__
_

tl=sih((X)

_.--..

Press [ggg_. The tangent line is drawn; the
X value and the tangent-line equation are
displayed on the graph.

".L/

tl==in(:4)

1{=0
Press_

for the

".Y1Bsin(X)
%yz=
",Yx=
-.y_=
-,y_=
,,y_=
xY_'=

/-7_.

4.

for details.

_

[//

",2/

Using the DRAW Menu

DRAW Menu

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 : C1 rDraw
Clears
2: Line(
3: Horizontal
4: Vertical
5: Tangent(
6: DrawF

elements.

a line segment
between
a horizontal
line.
a vertical
line.

8: Drawlnv
9: Circle(
O: Text(

Draws text on a graph
Activates
the free-form

A: Pen

The DRAW instructions
draw on top
before you use the DRAW instructions,
you want

2 points,

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.

7: Shade(

Before Drawing
on a Graph

all drawn

Draws
Draws
Draws

to perform

one or more

•

Change

the mode

•

Change

•

Enter

or edit functions

•

Select

or deselect

•

Change

•

Turn

stat

•

Clear

existing

the fornlat

of graphs.
consider

settings

tool.

Therefore,
whether

of the following

on the mode

actions,

screen,

on the format

screen.

in the Y= editor,

functions

the window

plots

settings

screen.
drawing

variable

in the Y= editor.
values.

on or off.
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.

Drawing on a
Graph

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
instructions
to identify
instructions

use most

DRAW menu

and DRAW POINTS

menu

to draw directly
on a graph, using the cursor
the coordinates.
You also can execute
these
from the home screen or from within a

progranl.
If a graph is not displayed
DRAW menu instruction,
the home

when
screen

you select a
is displayed.

DRAW Instructions

8-3

Clearing

Drawings

Clearing
Drawings When
a Graph Is
Displayed

All points,

Clearing
Drawings from
the Home Screen
or a Program

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

instructkms

lines,

and shading

drawn

on a graph

with

DRAW

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,

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:Beforeyou cleardrawings,you can store them withStorePic
(page 8-17).

8-4

DRAW Instructions

Drawing

Line Segments

Drawing a Line
Segment Directly
on a Graph

To draw

is displayed,

follow

2. Place the cursor
on the point where you want
segment
to begin, and then press [_E_.

the line

these

a line segment

when

a graph

steps.

1. Select

2:Line( from

the DRAW menu.

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,
To cancel
Line(, press @.

Drawing a Line
Segment from
the Home Screen
or a Program

repeat

steps

2 and 3.

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,

To erase
Line(2,

0, 6, 9)11

a line segment,
3, 4, 6, 0)11

enter

Line(X1,Y1,X2,Y2,0)
/,

DRAW Instructions

8-5

Drawing

Horizontal

Drawing a Line
Directly on a
Graph

and Vertical

Lines

To draw

a horizontal

or vertical

displayed,

follow

steps.

1, Select

these

3:Horizontal

line is displayed

line when

or 4:Vertical
that

nloves

from

[_

To continue
To cancel

8-6

DRAW Instructions

to draw

drawing

is

the DRAW menu.

as you nlove

2. Place the cm'sor on the y-coordinate
lines) or x-coordinate
(for vertical
you want the drawn
line to pass.
3. Press

a graph

the cursor.

(for horizontal
lines) through
which

the line on the graph.

lines, repeat steps

2 and 3.

Horizontal or Vertical, press @,

A

Drawing a Line
from the Home
Screen or a
Program

Horizontal

(horizontal

line)

y can be an expression

but

draws

a horizontal

line at Y=y.

not a list.

Horizontal y
Vertical (vertical
line) draws
an expression
but not a list,
Vertical

line,

tile TI-83

to draw

more

separate

each

instruction

Ho_-izor,÷_al

t_al

line at X=x, x can be

_"

To instruct
vertical

a vertical

than

one horizontal
with

a colon

or
( : ).

7: Vet

4: Vertical

......................

DRAW Instructions

8-7

Drawing

Tangent

Drawing
a Tangent Line
Directly
on a Graph

Lines

To draw
these

a tangent

line when

a graph

is displayed,

follow

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
to see fewer digits displayed for X and the equation for Y.

Drawing
a Tangent Line
from the Home
Screen or
a Program

Tangent( (tangent
line) draws a line tangent
to expression
in terms of X, such as Y1 or X2, at point X=value.
X can be
an expression,
expression
is interpreted
as being in Func
nlode,

Tangent(expression,value)
Tangent

8-8

if you want

DRAW Instructions

('gi, 3)|

Drawing

Drawing a
Function

Functions

and Inverses

DrawF (draw

function)

draws

expression

at a function

in

terms of X on 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

Drawing an
Inverse of a
Function

use a list in exp'_vssion

......

./_-.._ .(_.

to draw a family

.....

of curves.

Drawlnv (draw inverse) draws the inverse of expression by
plotting X values on the y-axis and Y values 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 family of curves.

DRAW Instructions

8-9

Shading

Areas

Shading a Graph

on 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

pattern= 1
pattern= 2
pattern= 3
pattern=4
patres

specifies

patterns.

vertical (default)
horizontal
negative--slope
45 °
positive--slope
45 °
one of eight shading

patres= 1
patres=2
patres=3
patres=4
patres=5
patres=6
patres=7
patres=8

shades
shades
shades
shades
shades
shades
shades
shades

resolutions.

every pixel (default)
evetF- second pixel
every third pixel
eve_- fourth pixel
every fifth pixel
eve_Ty-sixth pixel
evetsz seventh pixel
every eighth pixel

Shade(lowerfanc,uppe_:func[._left._right,patte_,patres])

Shade(X_-8X,

8-10

DRAW Instructions

X-2),

.......

____...;.:(

Drawing

Circles

Drawing a Circle
Directly on a
Graph

To draw
cursor,
1, Select
2, Place
draw.

a circle
follow

directly

these

9:Circle(

on a displayed

graph

using

the

steps,
fronl

the

DRAW menu.

the cursor
at the center
Press [NTEN.

of the circle

you want

3. Move the cursor
to a point on the circumference.
[ggTE_ to draw the circle on the graph.

to

Press

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
cancel Circle(, press

Drawing a Circle
from the Home
Screen or a
Program

circles,
@.

repeat

Circle( draws a circle with center
values can be expressions.

steps

2 and 3, To

(X,Y) and radius.

These

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

To place
follow

text
these

1, Select
2, Place

on a graph

when

the graph

is displayed,

steps,

0:Text(

from

the cursor

the

where

DRAW menu.
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

Placing Text on a
Graph from the
Home Screen or
a Program

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

Split Screen

8-12

..... ......

)|

On a Horiz split screen, the nlaxinlunl
On a G-T split screen,
the nlaxinlunl
and the nlaxinlunl
value for column

DRAW Instructions

I

?'I=._:X_-_:X+G

value for row is 25,
value for ro_t_)is 45,
is 46,

Using Pen to Draw on a Graph

Pen draws

directly

Pen from

the home

on a graph
screen

To draw

on a displayed

1. Select

A:Pen from

only, You cannot

graph,

follow

these

[_

to turn

steps.

the DRAW menu,
where you want
on the pen,

3. Move the cursor.
As you move the cursor,
the graph, shading
one pixel at a time,
4. Press

execute

or a progranL

2. Place the cursor
on the point
drawing.
Press [_
to turn

to begin

you

draw

on

off the pen,

For example,
Pen was used to create the arrow
the local minimunl
of the selected
function.

.....

Using Pen to
Draw on a Graph

pointing

to

E.,dL

I
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
Menu

To display- the DRAW POINTS menu, press [_a] [DRAW] [_.
The TI-83's interpretation
of these instructions
depends
whether
you accessed
this nlenu froth the home screen
the program
editor or directly
froth a graph.
DRAW POINTS

ST0

i : Pt On(
2: Pt Off(
3:
4:
5:
6:

Drawing Points
Directly on a
Graph with
Pt-On(

Turns

on apoint.

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,

Pt Change(
Pxl On(
Pxl Off(
Pxl Change(

7: pxl

Test(

To draw a point on a graph, follow these steps.
1, Select 1 :Pt-On( from the DRAW POINTS menu,
2. Move the cursor
the point.

to the position

where you want to draw

3. Press [ggY_ to draw the )oint.

o

R:Ll,_6e0mgl

y:LI.BM]?O.:I?

To continue drawing points, repeat
cancel Pt-On(, press @.

8-14

on
or

DRAW Instructions

steps 2 and 3. To

Erasing Points
with Pt-Off(

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
3. Press

_

you want

points,

repeat

steps

2 and 3. To cancel

To change (toggle on or off) a point on a graph, %llow
these steps.
1. Select 3:Pt-Change( (point change)
POINTS menu.
2. Move the cursor
3. Press I_

from the DRAW

to the point you want to change.

to change the point's

To continue changing points, t_peat
cancel Pt-Change(, press @.
Drawing Points
from the Home
Screen or a
Program

to erase.

to ertkse the point.

To continue
ertLsing
Pt-Off(, press @.

Changing Points
with Pt-Change(

to the point

on/off status.
steps 2 and 3. To

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)

Pt-On(x,y[,mark])
Pt-Off(x,y[ ,mark
Pt-Change(x,y)

2 = [] (box)

3 = + (cross)

])

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;

Turning On and
Off Pixels with
Pxl-On( and
Pxl-Off(

jq

PxI-On( (pixel on) turns
where row is an integer
integer

between

PxI-Off( turns
and off.

on the pixel at (row,column),
between
0 and 62 and column

is an

0 and 94.
the pixel

off. Pxl-Change(

toggles

the pixel

on

Pxl-On(row,column)
Pxl-Off(row,column)
Pxl-Change(_'ow,column)

Using pxI-Test(

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)

Split Screen

On a Horiz split screen, the maxinmm
value for row
for PxI-On(, PxI-Off(, Pxl-Change(, and pxI-Test(.

is 30

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(,

8-16

DRAW Instructions

and pxI-Test(.

Storing

Graph Pictures

DRAW STO Menu

(Pics)

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

Storing a Graph
Picture

Stores
Recalls
Stores
Recalls

the current picture.
a saved picture.
the current graph datal)ase.
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 select a variable from the PICTURE
secondarymenu (_
4). The variable is pasted next to
8torePic.
3. Press [ggTE_ to display- the current
picture.

graph and store the

DRAW Instructions

8-17

Recalling

Graph Pictures

Recalling a
Graph Picture

To recall

a graph

(Pics)

picture,

1. Select 2:RecallPic
is pasted

ffonl

to the current

follow

these steps,

the DRAW STO menu,
cursor

RecallPic

location,

Enter the number
(from 1 to 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
picture
superimposed
on it,

graph

with

the

Note: Pictures are drawings. You cannot trace a curve that is part of a
picture.

Deleting a Graph
Picture

8-18

To delete graph pictures
from
MEMORY DELETE FROM menu

DRAW Instructions

memo[3z,
(Chapter

use the
18).

Storing

Graph Databases

What Is 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
each
Graph style for each Y= function

GDBs do not

Storing a Graph
Database

(GDBs)

To store

a graph

is pasted

StoreGDB

from

to the current

the number

to which
example,
GDB7,

drawn

database,

3:StoreGDB

1, Select

2. Enter

contain

(from

items

or stat

follow
the

these

plot

of

definitions.

steps.

DRAW STO menu.

cursor

status

StoreGDB

location,

1 to 9, or 0) of the GDB variable

you want to store the graph database.
For
if you enter 7, the TI-83 will store the GDB to

7

Note: You also can select a variable from the GDB secondary
menu ([_
3). The variable is pasted next to $toreGDB.
3, Press 1_
specified

to store the current
GDB variable.

database

to the

DRAW Instructions

8-19

Recalling

Graph Databases

Recalling a
Graph Database

(GDBs)

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 1 to 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 select a variable from the GDB secondary
menu (_
3). The variable is pastednext to 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.
Deleting a Graph
Database

8-20

To delete a GDB fronl nlemo_T, use the MEMORY DELETE
FROM menu (Chapter 18).

DRAW Instructions

Screen
Split
Contents

Getting Started: Exploring
tile Unit Circle ................
Using Split Screen
.......................................
Horiz (Horizontal)
Split Screen
..........................
G-T (Graph-Table)
Split Screen ..........................
TI-83 Pixels in Horiz and G-T Mode ......................

'_

TEXAS

T1=83

INSTRUMENTS

','t==in_)J

oX

_'.', l

.._,75 1.2,_3

_,

X=.BO:_h7:_O h
?=.7190761B

9-2
9-3
9-4
9-5
9-6

I oY 1

1.07

1.1177_:

2.337

.97:_9

1.605

.ggg4

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Split

Screen

9-1

Getting

Getting

Started:

Started

Exploring

is a fast-paced

the Unit Circle

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 []
graphing
[ggg_] to
[]

to display" the Y= editor for Par
mode. Press [g6_ _
[]
store cos(T) to XIT, Press [gF_
_
to store sin(T) to YIT.

Press _
editor. Enter
variables.
Train=0
Tmax=360
Tstep=l 5

to display the window
these values for the window
Xmin=-2.3
Xmax=2.3
Xscl=l

Ymin=-2.5
Ymax=2.fi
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 1 and 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.

9-2

Split Screen

li X1,
i

V1T
0

.g
.Bfl6
.zsne ._ss_
T=_O
g:.BSfi02B_

0

1

Using Split Screen

Setting a SplitScreen 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
6-7 mode,
which that
the cursor
displayed.
the half in

press a key or key combination
in either Horiz or
the cursor is placed in the half of the display- for
key applies. For example, if you press _,
is placed in the half in which the graph is
If you press [g_ [TABLE],the cursor is placed in
which the table is displayed.

The TI-83 will remain in split-screen
change back to Full screen mode.

lnode until you

Split

Screen

9-3

Horiz (Horizontal)

Horiz Mode

Split Screen

In Horiz (horizontal)
split-screen lnode, a horizontal
splits tile screen into tc ) and bottom halves.

line

\ViBsin(X z)
,.YzBcos(XZ )
\Y._=
The top half displays the graph.
The bottom
•
•
•
•
•
Moving from Half
to Half in Horiz
Mode

half displays

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

Full Screens in
Horiz Mode

any of these editors.

half of tile split screen:

•

Press any key or key combination
home screen.

•
•
•
•

Press
Press
Press
Press

that displays the

[] (Y= editor).
[gT_ [g_
(stat list editor).
_
(window editor).
[2_ [TABLE](table editor).

All other screens are displayed
split-screen mode.

as full screens

in Horiz

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)

G-T Mode

Split Screen

In G-T (graph-table) split-screen
mode, a vertical
tile screen into left and right halves.
X

line splits

Y1

Io
,2:

X=Bgq.

The left half displays the graph.
The right half displays the table.
Moving from Half
to Half in G-T
Mode

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,
Using _
G-T Mode

in

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_

g=.B0ZtlTZ0h
Y=,7190761B

X

Vi

1.07 .B77_
1._7_7 ,97:'9
t,l_0g .999h

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 T is
displayed on the graph.

Full Screens in
G-T Mode

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

"*.
Horiz and G-T
Modes

(o,0.',

l

.(°._.h.)?l

€,30,0)

1

o0,9_)_,

_ X
lg
30
_g
60

TI-Sa
Pixels
in

"i
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(,
•

In Horiz mode,

•

In G-T mode,

row
row

nmst
nmst

and pxI-Test(:

be _<30; column

nmst

be _<50; column

nmst

be _<94.
be _<46.

Pxl-On(row,column)

DRAW Menu
Text( Instruction

For the

Text( instruction:

•

In Horiz mode,

•

In G-T mode,

row
row

nmst
nmst

be _<25; column

must

be _<45; column

nmst

be _<94.
be _<46.

Text(row,column,"text")

PRGM I/O Menu
Output(
Instruction

For the

Output(

•

In Horiz mode,

•

In G-T mode,

instruction:
row
row

Output(row,column,

Setting a
Split-Screen
Mode from the
Home Screen or
a Program

nmst
nmst

nmst
nmst

be _<16.
be _<16.

"text")

To set Horiz or G-T from
1. Press [M0_] while
program
editor.

be _<4; column
be _<8; column

a program,

the cursor

follow

is on a blank

these

steps.

line in the

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
Contents

Matrices

Getting Started: Systems of Linear Equations
............
Defining a Matrix ........................................
Viewing and Editing Matrix Elements
....................
Using Matrices with Expressions
........................
Displaying and Copying Matrices
........................
Using Math Functions
with Matrices
.....................
Using the MATRX MATH Operations
.....................

'_

TEXAS

T1=83

iNSTRUMENTS

MRTRIX[R]

10-2
10-2
10-4
10-7
10-8
10-9
10-12

8 x4

r_

-_.:l.h_: 1:_

E "1
ro
r 0
E 1.B
r 0
[0

_:.1h11_
0
0
0
.8571h
0

0
0
BB
0
0
2

i, i=3.141592653
J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Matrices

10-1

Getting

Getting

Started:

Started

Systems

is a fast-paced

of Linear Equations

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 1 to select 1: [A],
2.

3.

Press 2 [_
4 [_
to define a 2x4
matrix. The rectangular
cursor indicates
the current element. Ellipses (...) indicate
additional eolunms beyond the screen.
Press 1 [_
to enter the first element.
The rectangular
cursor nloves to the
second colunm of the first row.

MATRIX[R]

[0

2 x4

0

1_1=0
MATRIX[R]

[0

0

2 x4

0

I_Z=0
4.

Press 2 [g_
3 [g_
3 [g_
to complete
the first mw for X + 2Y + 3Z = 3.

5.

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

IMRTRIX[A]

2 x4

rre?(|

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 [_
1 to 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
1Y+2Z=3

10-2

Matrices

so
so

X=-3+Z
Y=3-2Z

rref'([Al )
-31
[[1 18 213
]l

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

Before you can define or display
a matrix in the editor, you
first nmst select the matrix name. To do so, follow these
steps.
[] to display
the MATRX EDIT menu. The
of any previously
defined
lnatrices
are

1. Press _
dimensions
displayed.

MATH

[el
[D]
[El
[F]
[G]
2, Select
screen

the matrix you want
is displayed.

MATRIX[B]
ro

Accepting or
Changing Matrix
Dimensions

to define.

The MATRX EDIT

I xl
I

The dimensions
of the matrix
displayed
on the top line. The
are 1 xl, You nmst accept
or
time you edit a matrix,
When

(row x column)
are
dimensions
of a new matrix
change the dimensions
each
you select a matrix to define,

the cursor

dimension.

highlighLs
the row

the row

•

To accept

•

To change
the row dimension,
(up to 99), and then press [_.

dimension,

press
enter

[_.
the number

of rows

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

Displaying Matrix
Elements

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 MATRX EDIT 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.

"t

_:.tht6

MRTRIX[R]

0

8 0 x4

i

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

10-4

a Matrix

Matrices

To delete matrices fronl nlenlory,
FROM seconding- menu ((;hapter

use the MEMORY DELETE
18).

Viewing a Matrix

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.

":1,

}.:DI:I.I_

0

MRTRIX[R]

8 x4
2
I,I=3. 141592653

Viewing-Context
Keys

1

Key

Function

[] or []

Moves the rectangular
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
edit cursor on the bottom line.

@

Switches to editing context;
value on the bottoin line.

Any entry
character

Switches to editing context; clears the
value on the bottoln line; copies the
character to the bottom line.

[_

[ggn

[INS]

cursor

within the

the

clears the

Nothing

Nothing

Matrices

10-5

Editing a Matrix
Element

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
element you want to change.
3. Switch to editing context
an entw key-.

by pressing

to the lnatrix

[ggT_, @,

or

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,

[],

MRTRIX[RI

or []

to Inove

to another

element.

8 ×4

r :Ll_ntG ":kl_

13

[ 0
[ :t.B

0
0

BII
0

[ 0

.BgT:th

0

[0

0

3.1_I_

").1ill

MRTRIX[R]

1_

8 x4

i

3, i=2Xz+3|
Editing-Context
Keys

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

Any entrycharacter

Copies the character to the location
edit cursor on the bottom line.

[_

[INS]

[DE[]

10-6

Matrices

Activates

line.
of the

the insert cursor.

Deletes the character
on the bottonl line.

under the edit cursor

Using Matrices

Using a Matrix in
an Expression

with Expressions

To use a matrix in an expression,
following.
•
•
•

Entering a Matrix
in an Expression

you can do any of the

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
You also can enter a nlatrix directly
in an expression.
in an expression,

follow

these

editor.

To enter

a nlatrix

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
5. Repeat
6. Press

[2_] [] ] to indicate
steps

2 through

the end of a row.
4 to enter

[2_] [] ] to indicate

all of the rows.

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
executed.

are evaluated

when

the

enttsz is

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

Displaying a
Matrix

Matrices

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
%88oo65.00...I
i::47'.
0000
...3, 0000

Copying One
Matrix to Another

-69.04,
136,0...

To copy a matrix,
1. Press [_

follow these steps.
to display the MATRX NAMES 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 [_

Accessing a
Matrix Element

to copy the lnatrix to the new lnatrix

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
8 91
[B1(2,3)[3

10-8

Matrices

nalne.

2 0110

Using Math Functions

with Matrices

Using Math
Functions with
Matrices

You can use many

of the math

functions

on the TI-83

+ (Add), (Subtract), *
(Multiply)

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.

keybom'd,
tile MATH menu, tile MATH HUM
MATH TEST menu with matrices.
However,
nmst be appropriate.
Each of the functions
new matrix; the original matrL, c remains
the

matrixA
matrixA

+matrixB
- mat)_ixB

To nmltiply
dimension
matrixB.

matrixA

menu, and tile
the dimensions
below creates
a
same.

([_) two matrices
together,
the colunm
of matrixA
nlust match the row dimension

of

*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

- (Negation)

Negating
of evetN

a matrix
(D) returns
a matrix
element
is changed
(reversed),

in which

the sign

-matrix

-ira
[RI

-41

[[212; 41-211]

Matrices

10-9

abs( (absolute value, MATH NUM menu) returns a matrix
containing the absolute value of each element of matrix.

abs(

abs(mat_qx)

[°]

14,69'

abs([Cl_[2512369]14]

round(

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[m
2 ×2 1
[ 3,662

-I

(Inverse)

I,'15_

])

[[1.26
2.331
Pound([A],2)
[3.66 4.121

[ Jse the -1 function
([_
) to invert a matrix
valid), matrix
nmst be square.
The determinant
equal

]

("-1 is not
cannot

zero.

matrix-1

MRTRIX[R]
El
E_
_z

2 x2

]

l[m-,

[[-2
[1.5

1-.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&

Powers

matrix
matrix

2
3

matrix^power

[[37 54 ]
[81 1181

MRTRIX[R]_
_

10-10

Matrices

2 x2

]

[R]_,5
[R]_ [[1069
[2337

15581 i
34061

Relational

To compare

Operations

and _ (TEST menu), they must have the sanle dimensions,
=
and _ compare
mat_ixA
and mat_ixB
on an element-byelement
basis. The other relational
operations
are not valid
with matrices.

two

matrices

matri._'A=matrixB
returns
t_tums
0 if any comparison

using

the

relational

operations

1 if eveFy" comparison
is false.

=

is true;

matrixA_matrixB
t_tums 1 if at least one comparison
false; it returns 0 if no comparison is false,

it

is

[RI#[B]
[R]=[B]

iPart(, fPart(, int(

iPart( (integer part), fPart( (fractional
part), and
(greatest integer) are on the MATH NUM menu,
iPart( returns
a matrix
element
of matrix,

containing

the integer

int(

part

of each

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

[[1
3 1
[100 471
¢PaPt([D])
iPaPt([D1)
[[.25
.3331 i
[.5
.15 ]

Matrices

10-11

Using the MATRX

MATRX MATH
Menu

MATH Operations

To display
NAMES
i:

the

MATH

det(

MATRX MATH menu,
EDIT
Calculates

2: T

[_,

_

the determinant.

Transposes
the matrix,
Returns
the matrix dimensions.
Fills all elements
with a constant.

3: dim(
4: Fill(
5:identity(

Returns
Returns

6: randM(
7:augment(

the identity
matrix.
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.

8: Matr*list(
9: List*matr(
O: cumSum(
A: ref(
B: rref(

Swaps two rows of a matrix.
Adds two rows; stores
in the second
Multiplies
the row by a number.
Multiplies
the row, adds to the second

C: rowSwap(
D: row+(
E: *row(
F: *row+(

det(

press

det((determinant)
of a squm'e matrix.

returns

the determinant

row.
row.

(a real number)

det(matrix)

T

(Transpose)

T (transpose)
returns
a matrix
in which each element
colunm)
is swapped
with the corresponding
element
(colunm,
row) of matrix.
matrix

T

[R]

[R]T
11
[[1[32 2 311

Accessing Matrix
Dimensions with
dim(

dim((dimension)
({rows columns}

[3 11

returns
a list containing
) of mat_qz.

the dimensions

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(

3,111

10-12

Matrices

(row,

[_2,7,11[

-8,

{2 3}

dim([l>+Li:L1

3,111

Creating a Matrix
with dim(

Use dim( with _
dimensions
rows

to create
x columns

a new matrixname
of
with 0 _Lseach element.

{rows,columns}_dim(mat_xname)

{2,2}+di_([E])
[E]

Redimensioning a
Matrix with dim(

Fill(

[

I

I

[0 01
[0

011

Use dim( with _
to redimension
an existing
matrixname
to dimensions
rows x columns,
The elements
in the old matrixname
that m_ within the new dimensions
are not changed.
Matrix elements
deleted.

Additional
created
elements
are zeros.
that m'e outside
the new dimensions
are

{rows,columns}->

dim(matrixname)

Fill(storesv_uetoeve_

elementin

mat_xname.

Fill(v_ue,mat_xname)

FilI(5,[E])
[El

identity(

Done
[[5[5 5]
51]

identity( returns
the identity
dimension
colunms.

matrix

of dimension

rows

x

identity(dimension)

randM(

randM( (create
random
matrix)
returns
a rows x columns
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( appends matrixA to matrixB
as new colunms.
matrixA and mahqxB both nlust have tile sanle number of

augment(

[_)WS.

augment(mat) qxA,matrixB)
[ [5,61

[7,811+[BI

_a,.,gr,,ent([Rl,[B[
[1,21 [[1[3,41256]]+JR] ]
[3
Mats,list(

7 811

4

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

MatP_lis[4
5 611
"*
[[R]
[[1
It( 2 31
,Li,LI)
[Rl,LiDone

n)

Lz
i_

{I ii
{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 I
5 6111 "*

[a

Lt

{3 6}

Matr_list(
Lt )

Listymatr(

JR]Done
,3,

List)matr( (lists stored to matrL, c) fills matrixna,me colunm by
colunm with the elements fronl each list. If dimensions (ff MI
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(

10-14

Matrices

{1'2'3}+L_I

2 3}

{4'5'6]'+L_4

5

_

IX,

LB,[CI)

...

[C]

L_",

I

O°nel'

[[1

_

_ll]l

cumSum(

cumSum(

returns

cumulative

sums

of the elements

in

mat_'ix,
starting
with tlle first element.
Each element
cumulative
sum of the colunm
from top to bottom.

is the

cumSum(mat,_ix)

[0]

[[1151361412]]

°ur_Su'_([Dl_[9[46212]]]]

Row Operations

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(, rref(

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
echelon form
be greater

row-echelon
ff)rm) ret, umls the reduced
rowof a _al matrix', The number
of colunms
must

than

or equal

to the number

of rows,

rref(mat,_ix)

[7
[B]

[ [4

8 9]
5 6] ]

re?([B])
[[1
1.142857143_3
[0 1
...
rre?([B])
[[1
0 -1]
[0 1 2 ]]

Matrices

10-15

rowSwap(

rowSwap(

returns

a matrix,

It swaps

rowA

and rowB

of

matrix,
rowSwap(matrix,

rowA,rowB)
PowSwaP ( [F]

[F]

row+(

[2
[[2[6

,2,4>[

I

5 1 O]
_ 46
3
8 51
791]

row+( (row addition) returns a lnatnx.
rowB of matrix and stores the results

It adds rowA and
in rowB.

row+(mat_x,rowA,rowB)

[[2,5,7118,9,411
+[O]
[[2[8 5
9 71
41

* row(

row+{[D],l,2)[1012
514711111

*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+(

*row+(value,matrix,rowA,rowB)

*Pow+(3,
[[1

10-16

Matrices

[E], 1,2)
21 3511

I

11
Contents

Lists

Getting Started: Generating
a Sequence
..................
Naming Lists .............................................
Storing and Displaying
Lists .............................
Entering List Names .....................................
Attaching
Fornmlas
to List Names .......................
Using Lists in Expressions
...............................
LIST ©PS Menu ..........................................
LIST MATH Menu ........................................

'_

TEXAS

I I-2
11-3
11-4
11-6
11-7
11-9
11-10
11-17

T1=83

iNSTRUMENTS

cunSu_,( {1,2, 3, 4,
5} )
{1
6 18 15}

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Lists

11-1

Getting

Getting

Started:

Started

Generating

is a fast-paced

a Sequence

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] []
nlenu,

to display

MRTH

the LIST OPS

3:dim(
4:Fill(
5:se_(
8:cumSu_(
7$_List(
2.

Press 6 to select 6:seq(, which pastes
the current cursor location.

3. Press l [] @
[A] [] [] @
[] 8 [] 1 [] to enter the sequence.

seq( to

[A] [] l

4.

Press F_,
and then press [_ @
to
turn on alpha-lock. Press [s] [E] [Q], and
then press @
to turn off alpha-lock.
Press 1 to 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 FENTEm
to p_Bte LSEQ1 to the
current cursor location. (If SEQ1 is not item
1 on your LIST NAMES menu, move the
cursor to SEQ1 before you press F_.)

se_(I/RZ,R,1,8,1
i;S_

_IOPS

.1111111...

MRTH

7. Press [_
to display the MATH menu.
Press 1 to select 1:*Frac, which pastes *Frac
to the current cursor location.

Ise_(i/Ri,R,1,8,1
)+SEQI
{i .25 .1111111._
LSEQI*Frac

8.

_I

11-2

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.

Lists

1/4

1,'9 Ix16_.

Naming

Lists

Using TI-83 List
Names L1
through L6

The

TI-83

Creating a List
Name on the
Home Screen

To create

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
1 through
6 when you reset nlenlory,

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

@
[letter from
of the name.

4. Enter

zero to four

A to Z or 0] to enter

letters,

0, or numbers

the first

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{I
2 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

in the stat

four

places,

•

At the blame= prompt

•

At an Xlist:, Ylist:, or Data List: Dxnnpt
editor

•

At a List:, List1:, List2:, Freq:, Freql:, Freq2:, XList:, or
YList: prompt in the inferential
stat editors

•

On the home

screen using

You can create as many
has space to store.

list editor
in the stat

plot

SetUpEditor

list names

as your

TI-83

memo[3z

Lists

11-3

Storing

and Displaying

Storing Elements
to a List

You can
•

store

Use braces
{4+2t,

•
The

Lists

list elements
and _

in either

of two ways.

on the home

screen.

5-3t } _k G
{4+2t
_,-3t }

Use the stat
maxinmm

list editor

(Chapter

12).

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.

Displaying a List
on the Home
Screen

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
repeatedly
(or press and hold [])
all the list elements.

_IDRTR
{2. 154

11-4

Lists

{2 5 _0}
50,47
....

window.
to scroll

Press []
the list and view

Copying One List
to Another

To copy a list, store it to another

list.

LTEST÷TEST2
LTEST
{123:}}
{123

Accessing
Element

a List

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

Deleting a List
from Memory

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

Lists

3).

11-5

Entering

List Names

Using the
LIST NAMES
Menu

To display- the LIST NAMES menu, press [_
[LIST].
item is a user-created
list name. LIST NAMES menu

Each
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].

T

_

IOF'S

I

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
L1 through L6 directly from the keyboard (page 11-3).
When

you select

the list name
•

Entering a UserCreated List
Name Directly

from

the LIST NAMES menu,

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
•

a list name

is pasted

(I

2

3 4}

The L symbol 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

1. Press

[_

list nmne

[LIST] []

directly-,

follow

these

steps.

to display" the LIST OPS menu.

Select B:L, which pastes
L is not always
necessary

L to the current
(page 11-16).

NRMES
[_]_R MRTH
61"CMFISL, Ir'l (
7: _List(
8: Selec.t(
9: augrqent(
81List*F, ate(
R: Mate* 1 ist(

cursor

location.

Note: You also can paste L to the
current cursor location from the
CATALOG (Chapter I5).

=11,
3. Enter the characters

ILT123I

11-6

Lists

that conlprise

I

the list name.

Attaching

Formulas

Attaching a
Formula to a List
Name

to List Names

You call attach
element
attached

a formula

to a list name

is a result of the fornmla.
When
formula
nmst resolve
to a list.

V_llen anything
in the attached
which the fornmla
is attached

so that

each

executed,

list
the

formula
changes,
the list to
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,
to which the fornmla
is attached

all elements
are updated.

in the list

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
to -6, and then redisplays L3.

the first element in L3

I
{II 12 13}I
-6÷Li(1):Li
{-6 2 3}

W+IO+L4

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
L4
{Ii
Note:

12 13}
12 13}

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

To attach

Screen

1. Press @
[.], enter
a list), and press @

or in a

Program

home

a ff)rnmla

screen

from

to a list name

or from

a program,

a blank

follow

the formula
[-] again.

these

(which

line

on the

steps.
must

resolve

to

Note: When you include more than one list name in a formula,
each list must have the same dimension.
2,

Press

_.

3. Enter the name
the fornmla.

of the list to which

•

Press [_,
and then
through
ks.

•

Press [_
[LIST] and select a usm_created
from the LIST NAMES menu.

•

Enter a use_created
11-16).

Press

enter

you want

a TI-83

list name

to attach

list name

kl
list name

directly-

using

t (page

ITNt_RI.

{4, 8,
"5*LI

9}÷L_4
8 9}
'% 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.

Detaching a
Formula from
List

a

You can detach
(cleat')
any- of tht_e ways.

an attached

Lists

fron]

a list in

• Enter ""Olistname on the home screen.
•

Edit any element
attached.

•

Use the stat

of a list to which

list editor

Note: You also can use ClrList
from a list (Chapter 18).

11-8

fornmla

(Chapter

a fornmla

is

12).

or ClrAIIList

to detach a formula

Using

Lists in Expressions

Using a List in an
Expression

You can

use lists

in an expression

in any- of three

When you press [NY_,
any expression
each list element,
and a list is displayed.
•

Use L1-Ls or any user-created

ways.

is evaluated

list name

for

in an expression.

5 16}
20/L1
•

Enter

{10 4 2}
the list elements

20/{2,
•

directly

(step

1 on page

11-3).

5, 10}
{10 4 2}

Use [_
[RCL] to recall the contents
of the list into
expression
at the cursor
location
(Chapter
1).

Rcl Lt

an

"* {2,5,10}I{4
25 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
functions.
Other chapters
a list is valid. The function
element,

several values ff)r some math
and Appendix
A specify
whether
is evaluated
for each list

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

F'loti Plot_:
\VIBx,r(
{1, F'lot3
O, -I}

)

This returns an error.

Thisskips
graphsX*_(1)
but
X*_(-1).

and X*_(O),

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.
{5 5,7 6}
9}
{i, 2, 3}+{4,
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

6 7}

Lists

11-9

LIST OPS Menu

LIST OPS Menu

To display
NAMES OPS

the

LIST OPS menu,

[LIST]

[_.

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,

2:SortD(
3:dim(
4:Fill(
5:seq(
6:cumSum(
7:aList(
8:Select(
9:augment(
O:List_matr(
A:Matr_list(
B:L

SortD(

[_

MATH

1:SortA(

SortA(,

press

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
listnome and update the list in nlenloi_.
SortA(listname)

of

SortD(listname)

Sor.tR(L_ )
Done
L_
{4 5 6}

{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
SortD(k¢ylistname,deperwllistl[,depe_wllist2,...,depe_wllist

{5'6'4}÷L_5

6

{1,2,3},L_I

2

4}

S°rtR(k_'L_>Done
_

3}

n])
n])

{4 5 6}
{3 1 2}

Note: In the example, 5 is the first element in L4, and 1 is the first
element in L5. After SortA(L4,Ls),
5 becomes the second element
L4, and likewise, 1 becomes the second element of L5.

of

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

dim((dimension)
of list.

returns

the length

(number

of elements)

dim(list)
diM({1,3,5,7})

Using dim( to
Create a List

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
Lz

Using dim( to
Redimension a
List

You can
listnome
•

) {0 0 0_

use dim with
to dimension

The elements
new

in the old listname

dimension

•

Extra

•

Elements
dimension

[gg_] to redimension
an existing
length from 1 to 999.
that

are within

the

are not changed.

list elements

are filled

in the old list that
are deleted.

by 0.
are outside

the new

length_ d im(listname)
{4'8'6}÷L_4
4÷dim(L1
LI

Fill(

Fill( replaces

8

6

)
{4 8 6 0}

each

element

3÷diM(L1
L1

in listnome

with

) {4 8 6_

value.

Fill(value,listname)

{3'4'5}÷L_3

4 5}

FilI(8,L_)
Done
L_
{8 8 8}

Fill(4+3t,Li_one
Li
{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((sequence)

seq(

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,
{I

cumSum(

R, 1,11,3)
16

49

100}

cumSum( (cunmlative sunl)
returns the cunmlative
the elements in list, starting with the first element,
elements can be real or complex numbers.

sunls of
list

cumSum(list)
c.umSum( {i,2, 3,4,
5}){I 3 6 10 15}
AList(

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(

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(

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

{1,2, 3, 4, 5,6,7,8]
,9,9.5,10}+DIST
I
I{i 2 3 4 5 6 7 ...I
1{15, 15, 15, 13, ll,I
IEg,?,5,3,2,2)÷TIM
I
I{15 15 15 13 11...I

t
Using Select( to
Select Data
Points from a
Plot

the data

(Chapter

_DOnO_z
_1*t_
el.
TgPe: I If"_
_ i_ _
Xlist.:oIsm
YlisL:TIME
Mark: [] ÷ •

J

To select data points fronl a scatter
follow these steps.

3).
. °o
" .

.
° °
%.

plot or xyLine plot,

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.
I

ISeleot(L1,Cz)l

3. Press [g_-gm. The graph screen is displayed
Left Bound? in the bottom-left corner.

a

LeFtBound?

u

with

iI

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
)oint that you want as the left bound.

keFt BOLIhd?

plot

data

_ ua

Lists

11-13

6. Press [NER]. A _ indicator on the graph screen shows
the left bound. Right Bound? is displayed in the bottonlleft corner.
P i:BIST.,TIH{
o a a _
u
U
a
U
uua

RiZlht _OUnd?

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
i

aa_
a

Ri_htBound?

m u

a

"

o

u u"_

u

"

[] u

The x-values and y-values of the selected points
stored in xlistname
and ylistname.
A new stat
._:listname and ylistname
replaces the stat plot
which you selected data points. The list names
updated in the stat plot editor.

are
plot of
from
are

11 9 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

11-14

Lists

< "l_ight-bound

x-value

must

be true.

augment(

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(

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,

{l'2'3}+LX1

. . . ,list n,mat_xname)

2

3}

List*matt(

LB, 1C1 )

LX,

Lists

L'_J,

I

Oone[

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

[4
Matr_li_t(
,Lz,L_)

5 6111

--

....

Lz

[RI,L1
Done

,listnamen)

{2 5}
{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 [
5 6111 --

L1

{3 6}

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

LIST MATH Menu

min(,

max(

Menu

To display

the

LIST MATH menu,

press

[_

[LIST]

E],

NAMES OPS MATH
i: min(
Returns
2: max(
Returns
Returns
3: mean(
Returns
4: median(
Returns
5: sum(

nnninmm
element
of a list.
nl_ximum
element
of a list.
mean of a list,
median
of a list,
sum of elements
in a list.

6: prod(
7:stdDev(
8: variance(

product
of elements
in list,
standard
deviation
of a list,
the variance
of a list,

Returns
Returns
Returns

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(,

median(

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
_'_ed
ian ({i, 2, 3} )2

Lists

11-17

sum(, prod(

sum((sununation)

returns

the sunl

of the elements

start and end are optional;
they specify
a range
elements,
list elements
can be real or complex

in list,

of
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
sur_(L_ )

8

10}
26

su_KLI,3,5)

Sums and
Products
of
Numeric

You can

23

colnbine

2 5 8
)

10}

400800

Prod(Li,3,5)

sum( or prod( with

upper

Sequences

k_
{I
Prod(L1

seq( to obtain:

upper

expression(x)
x=lower

To evaluate

x=lower

Z 2 (N 1)fl'Oln N=I to 4:

sur_(se_ (2" (N- I ),
N, 1,4, I))

stdDev(,
variance(

15

stdDev( retrains the standard
deviation
of the element._
The default value forfreqlist
is 1, Eachfreqlist
element
counts the number
of consecutive
occurrences
of the
con'esponding

element

in list. Complex

in list.

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])
stdOev(

,3,

11-18

Lists

vadance(list[freqlist])

{i, 2, 5, -6

-2})
3. 937003937

variance(

-6,3,

-2})

{i,

2,5,
15.5

2
Contents

Statistics
Getting Started: Pendulum Lengihs and Periods .........
Setting Up Statistical Analyses ...........................
Using the Stat List Editor ................................
Attaching Fornmlas to List Names .......................
Detaching Formulas from List Names ....................
Switching Stat List Editor Contexts ......................
Stat List Editor Contexts .................................
STAT EDITMenu ........................................
Regression Model Features ..............................
STAT CALC Menu ........................................
Statistical Variables ......................................
Statistical Analysis in a Program .........................
Statistical Plotting .......................................
Statistical Plotting in a Program .........................

TEXAS

12-2
12-10
12-11
12-14
12-1(;
12-17
12-18
12-20
12-22
12-24
12-2(.)
12-30
12-31
12-37

TI-83

INSTRUMENTS

p Z:LI_RE:VIn
D

0
M
0

M
0
0

g=Nl.g

Y='.OZ7001

J
STAT

PLOT

TBLSET

FORMAT

CALC

TABLE

Statistics

12-1

Getting

Getting

Started:

Started

Pendulum

is a fast-paced

A group of students is
between the length of
pendulum). The group
then suspends it from
of 12 string lengths.*

Press [_DE] [] []
graphing
mode.

2.

Press [g_g]
SetUpEditor
screen.

introduction.

and Periods

Read the chapter

for details.

attempting to determine the lnathelnatical
relationship
a pendulum and its period (one complete swing of a
makes a simple pendulum froln string and washers and
tile ceiling. They record the pendulum's period for each

Length

1.

Lengths

(cm)

Time

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

(sec)

[] [g_gg] to set Func

5 to select 5:SetUpEditor.
is pasted
to the honm

Press [gfff_. This relnoves lists fronl stat
list editor colunms 1 through 20, and
then stores lists L1through L6 in
eolunms 1 through 6.

SetUeEditof

Done[

Note: Removinglists from the stat list editor doesnot
deletethem from memory.
3.

Press [gf_] 1 to 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.

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
Publications,
Inc., Dedham, MA. 1-800-322-MATH.
© 1992. Aft rights reserved.

12-2

Statistics

4. Press
6[]

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
to the first row in 1.2.

cursor

Press [] 61 _
to store the first time
measurement
(.51 sec) in 1.2. The

LI

.Z

L_:

1

.Z

L_:

Z

26,6
37.ti
L1(1_) =
Lt
26.6

t.0B

3LI.:_
3?.tl

t.Ztl
J..ZB

rectangulm"
cursor moves to the next
row, Repeat
this step to enter each of
the 12 time wdues in the table on

6.

page

12-2.

Press

[]

to display-

Plot1 PloLZ Plot:_
\V1 =11

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.

".Yz=
_.y_=
xy_=
"_y_=
xY_;=
\Y?=

Press [_
[STAT
PLOT]
1 to 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.

_peO Plo_2 P1o_:_

+-,._

liar-k:

. []

•

Press _
9 to select 9:ZoomStat
fronl
the ZOOM menu. The window
variables
are adjusted
automatically,
displayed.
This is a scatter
time-versus-length
data.

÷ +
÷

and plot 1 is
plot of the

÷

÷

++
+
+÷+
+

Statistics

12-3

Since
thescatter
plotoftime-versus-length
dataappears
tobeapproxhnately
linear,

fit a line to the data.

10. Press _
[] 4 to select
(linear
regression
nlodel)
CALC menu, kinReg(ax+b)
tile home screen.

11. Press [_
[L1]
[] 1 to display

4:LinReg(ax+b)
fronl the STAT
is pasted
to

LinReg(ax+b)

|

_
[L2] [_.
Press
the VARS Y-VARS

[]

FUNCTION secondmT
menu, and then
D_ss 1 to 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
regression
Residuals

on the home screen. The linear
equation
is stored in Y1,
are calculated
and stored

automatically
in the list name RESID,
which becomes
an item on the LIST
NAMES menu,

13. Press _.
The regression
scatter plot are displayed.

12-4

Statistics

line and the

LinReg
9=_x+b

a=.0230877122
b=.4296826236

Theregression
lineappears
tofit thecentral
portionofthescatter
plotwell.
However,
aresidual
plotmayprovide
moreinformation
about
thisfit.
14.Press
[g_g] 1 to select 1:Edit. The stat
list editor
Press
L3.

E2;
11

is displayed.

[] and [] to lnove

Press [_
displayed
shift right
prompt
is
alpha-lock

the cursor

onto

[INS]. An unnamed
colunm
is
in colunm
3; 1.3, k4, L5, and 1_6
one colunm.
The Name=
displayed
in the entry line, and
is on.

15. Press [2_ [LIST] to display
NAMES menu.

the

1_;
18
;:3.1
2h.h
NaMe=_

2;1
._8
,79
,8B
.99
1,01

LIST

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.

Lt

.2

&5

,B1

11
13.2

,l_B
.73

2h.h

1.01

1_:
1B
.2_:.1

17. Press IgOr. RESID is stored in colunm
of the stat list editor.
Press [] repeatedly
residuals.

to examine

the

_

.79
.EB
.99

3
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...

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] 2 to select 2:Plot2
from the STAT PLOTS menu. The stat
plot editor is displayed for plot 2.

19. Press [_T@]
plot 2.

to select

On, which

turns

on

Press [] FEffEEN
to 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 _
9 to 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

_

Statistics

Pl*t_

xY1 =. 02308771216
587X+. 4296826135
7287
xYz=
xY?=
xY_=
\Y_=

D
Eli=

Notice the pattern
of the residuals:
a group of negative
residuals,
of positive
residuals,
and then another
group of negative
residuals.

12-6

.

then

a group

Theresidual
patternindicates
acm5Tature
associated
withthisdatasetfor
whichthelinearmodeldidnotaccount.
Theresidual
plotemphasizes
a
downward
curvature,
soamodelthatcm_'es
downwiththedatawouldbe
moreaccurate.
Perhaps
afunction
suchassquare
rootwouldfit.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
2.

",Yz=
,.Y_=
_.y_=
-,y_=
_.y_=
\y;_=

23. Press _
9 to select 9:ZoomStat froin
the ZOOM menu. The window
variables

÷ +

÷

+

are adjusted
automatically,
and the
original
scatter
plot of time-versuslength data (plot 1) is displayed.

_+
÷
÷÷÷
÷

24. Press Fgg_ [] @
[A] to select
A:PwrReg from the STAT CALC menu.
PwrReg is pasted to the home screen.

PuPReg

L1,Lz,Yi|

Press [g_ [L1][] [g_ [L2][]. Press
[] 1 to display the VARS Y-VAR$
FUNCTION secondmT menu, and then
press 1 to 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,
26. Press _.
The regression
scatter plot are displayed.

PwrReg
_=a*x^b
a=.1922828621
b=.5224982852

line and the

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

Pl*tl

the Y= editor.

_

Pl*t3

19228286213

".,Y 1 ----.

Press

[] _

to deselect

552X%

Y1.

Press [] [NY_ to turn offplot
[] [ggY_ to turn on plot 2.

1. Press

Note: Step 19 defined plot 2 to plot residuals (RESID)
versus string length (11).

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.

5224982852

\y_=
\Y_=

D

[]

a

El

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.

12-8

Statistics

P ;':LI_F;E$'r

II/:_1.5

B

[]

Y:'.OZ?OOJ.

Nowthatyouhaveagoodmodelfortherelationship
between
lengthand
period,
youcanusethemodeltopredict
theperiodforagivenstringlength.
Toprediet
theperiods
forapendulum
withstringlengths
of20cmand50cm,
continue
withthesesteps.
30.Press
[_ [] 1todisplaytheVARS
Y-VARS
FUNCTION
seconda[w
menu,
and
thenpress1toselect
1:Y1.
Y1ispasted
tothehomescreen.
_1

31.Press
[]
20

20 [] to enter

a string

length

II

of

enl,

Press _
to calculate
the predicted
time of about 0.92 seconds.
Based on the residual
expect
the prediction
seconds
to be within
of the actual value.
32. Press

_

[ENTRY]

anMysis,
we would
of about 0.92
about 0.02 seconds

to recall

Press [] [] [] 6 to change
length to 51) enL

the Last EnbTy'.
the string

33. Press _
to calculate
the predicted
time of about 1.48 seconds.

I. 484736865
_11(50)(28!9198781364

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.
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

Data for statistieM

Setting Up a
Statistical
Analysis

To set up a statistical
chapter
for details.
1. Enter
2. Plot

is stored

4.

data

in lists,

which

you

stat list editor. The TI-83 h_ks
L1 through
L6, to which you
calculations.
Also, you call
you create (Chapter
11).

analysis,

the statistical

follow

into

these

steps.

one or more

Read

the

lists.

the data.

3. Calculate
Graph

the statistical

the regression

5. Graph

Displaying the
Stat List Editor

analyses

can create and edit using the
six list vadal_les
in lnelnory,
can store data ff_r statistical
store data to list names that

the residuals

vm'iables
equation

or fit a model

to the data

for the plotted

list ff)r the given

data.

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

L1
mmm

L_:

._

1

SortO(
ClrList
SetUeEditor
LI(I)=

The top line displays
list names.
L1 through
colunms
1 through
6 after a lnelnolT
reset.
the current

colunm

is displayed

L6 are stored
in
The number
of

in the top-right

The bottom
line is the entry line. All data entry
this line. The characteristics
of this line change
to the current
context
(page 12-17).

corner.
occurs
on
according

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 all 20 columns,you mustremove
a list name to makeroomfor an unnamedcolumn.
The Name= prompt
LI

L:;"

is displayed

and alpha-lock

is on.

1

qame=_
2. Enter a valid list name in any of four ways.
•

Select a name fl'onl file LIST NAMES menu (Chapter

•
•

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,Iamo=RBC

I

11).

I

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,
[]. The rectangular
cursor is displayed.
Note: If the
another stat
move to the
names shift

press

list name you entered in step 2 already was stored in
list editor column, then the list and its elements, if any,
current column from the previous column. Remaining
list
accordingly.

Statistics

12-11

Creating a Name
in the Stat List
Editor

To create

1,

a name

in the stat

list editor,

ff)llow

these

steps,

Follow step 1 on page 12-11 to display- the Name=
prompt.

2, Press

[letter from A to Z or 0] to enter the first letter of
the name. The first character cannot be a number.

3, Enter zero to four letters, O, or numbers
new user-created
list name. List names
five characters

to conlplete
the
can be one to

long.

Press [g_
or [] to store the list name in the current
colunm
of the stat list editor. The list name becomes
item

Removing a List
from the Stat List
Editor

on the

[_[ST NAMES menu

(Chapter

an

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).

Removing
Lists and

All

Restoring L1
through
L6

Clearing All
Elements from a
List

You

Use SetUpEdRor

•

Reset

all user-created

all memotT

•
•

•

lists

list names L1 through
of two ways.
with

no arguments

(Chapter

You can clear all elements

•

Statistics

remove

•

•

12-12

can

editor and restore
through
6 in either

from

the stat

list

L6 to colunms

(page

1

12-21).

18).

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).

Editing a List
Element

To edit

a list element,

follow

1. Move the rectangular
to edit.
2. Press

[_

to move

these

cursor

steps.

onto

the cursor

the element

to the entry

you want

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
you enter the ill,st character,
the current
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
delete, and then press [ff_] to delete the character.

To cancel any editing and restore
the rectangular
cursor,
press @
ABe

Lt

L2

the

value.
value

original
[_.

When
is

element

to
at

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.
L1

ttl_C

L_:

1

:LO

_C(_)=20
When
updated

you edit

a list element

in nlenloFy

ill the stat

list editor,

the list is

inunediately.

Statistics

12-13

Attaching

Formulas

Attaching a
Formula to a List
Name in Stat List
Editor

to List Names

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_,
4. Press @

andthen edit the formula.

[,,], enter the fornmla,

and press @

[,,].

Note: If you do not use quotationmarks,the T1-83calculatesand
displays the same initiallist of answers,but does not attach the
formula forfuture calculations.
I i:i_¢

"II]

tO

L;_

;;

....

L20__ul_5__.
LFIEIC+IO"11

Note: Any user-created
list name referenced
preceded by an L symbol (Chapter 11 ).

in a formula

must be

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

tO
;;_:O00

u_1_=15

12-14

Statistics

$ j L>

_:0
_O::!.0

_:

Using the Stat
List Editor When
Formula-

When

Generated

(Chapter

Lists

Are Displayed

you edit

attached
element

ABC
I(,
2_:000
Z$

an element

of a list referenced

in an

fommla,
the TI-83 updates
the co_Tesponding
in the list to which the fornmla
is attached

11).
LI
$
t5
_:0
_:_:0i0
._0

._:

1

ItI_C

2_:000

LI

$

.2

1

>0
;:_: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
attached
are in view.

when

no lists with

formulas

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.

Handling Errors
Resulting from
Attached
Formulas

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
since the logarithm
of a negative
number
returns
complex
result,

than
a

O,

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

Detaching a
Formula from a
List Name

Formulas

You can detach
four ways,
•

•

•

•

List Names

(clear)

a formula fronl a list name in any of

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, M1 fornml_ts m'e detached from 'all
list names, and all lock symbols disappear. All list
nanles

Editing an
Element of a
FormulaGenerated List

from

renlain.

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

The

Stat List Editor
Contexts

stat

list editor

•

View-elements

•

View-nanles

has four
context

context

contexts,
•

Edit-elements

•

Enter-name

context
context

The star list editor is first displayed
in view-elements
context.
To switch through
the four contexts,
select
from the STAT EDIT menu and follow these steps,
Lt

_ L_

1

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,

2.

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 enhzyline, Press [] and [] to view more list elements.

3.

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.

4.

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,

20
2,55?
30
35

Z,SE7
2_
Z5

1:Edit

_c ={5, 10,25000...
LI
5

$ L2

i _5

i

......

I_5._ii_5,
_5

i 35

Asc :|5_10,25000...
_5C

2_5E?
_
_5

LI

$

L&

i 3_
i 35

LIc3)=25000010
AI_5
5

LI

$ L2

i _,5

......

2_5E7
25

i 35

LI(3)=|5000010

5
:i._
2,557
20
25

fist

_5
20
2.557
3_
35

_'1

5

i 15

2.5E7
_
25

_.5£?
i 30
i 35

_ L2

2

6,

Press

2.

7,

Press [], You are now back in _dew-elements

......

@,

You are now in view-naines

context.

Li =" LR_C+10"
_5C
5
:L_
2.5E7
2_
25

LI
im
i 20
i 2,557
i 30
i 35

$

L2

context.

......

LI(I)=15

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

5

t5

2._:E7
;'0

_0

$

._

2

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
line depends on the previous context.
When you switch
elements context,
is displayed. You
then press [] and
R_(:

LI

in the enttT

to edit-elements
context from xqewthe full value of the cmTent element
can edit the value of this element, and
[] to edit other list elements.

$ L_:

ABe

LI

$

2g010
_0

_g

_0

3E:

2g

_co)=25000

25

A_co_=|5000

When you switch to edit-elements
context fronl viewnames context, the full vMues of 'all elements 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.
g
t0
_000

IA_c:£5,

L1

1_;

$

k:;"

-,

Z0
Zg0t0

10, 25000._

L1

1

I0
Z_:000

_c

$

.2

1

ZO
7_010

=I5, 10, 25000...

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

In view-names
context,
and the list elements,
LI
5
10

15
_O

25
25

_O
_5

€

.2

the

entry

line displays

the list name

I

,Pc =15,10,25000_.
To remove
Remaining
deleted
To insert
Remaining

Enter-Name
Context

a list from the stat list editor, press [3_],
lists shift to the left one colunm.
The list is not

from

memow.

a name in the eutTent colunm,
press [_
eolunms
shift to the right one colunm,

In enter-name
context,
the Name= prompt
the entw line, and alpha-lock
is on.

[_NS],

is displayed

in

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
r.
10
_OOO
_O

.1
') i
1_r
_0
-_SOiO
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

STAT EDIT Menu

To display

the

STAT EDIT menu,

press

[_,

EDIT CALC TESTS
i: Edit..,
Displays the stat list editor.
2: SortA(
Sorts a list in ascending order.
3: SortD(
Sorts a list in descending order.
4: ClrList
Deletes all elements of a list.
5: SetUpEditor

Stores lists in the stat list editor.

Note: Chapter 13: Inferential Statistics describes the STAT TESTS
menu items.

SortA(,

SortD(

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
SortD(k_ylistname,depe_Mlistl[,depe_wllist2,...,depe_Mlist
{5 4 3}I
,{1,2,3}+L4
{5, 4,33 +L {i
_ 2 3} I
I
_ortR (L_, L4 >Done

n])
n])

{3 4 5}
{3 2

_
L_

I}

Note: SortA( and SortD( are the same as SortA( and SortD( on the
LIST OPS menu.

CIrList

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

display- one or more listnames
in the order that
specify-. You can specify
zero to 20 listnames.

to

you

SetUpEditor

[listnamel,listname2,...,listname

n]

SetUpEditor
names fron]

with one to 20 listnames
removes
the stat list editor and then stores

all list
listnames

the stat

list editor

colunms

in the specified

in

order,

beginningincoluinnl.
SetUPEditor
RESI
D,L_,L_,TIME,LOH
G,RI23
_E_ID

.00692

Done
L_

._

_ t

2

12

".001_ h
.OOBh _
",OOIB 6
",0106

t_
I_
16

RESZD 0.

nmst

be _>0, and at least

one

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

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

2-Var Stats

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

Med-Med (nmdian-n]edian)

(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).

fits the model

equation

y=ax+b

Med-Med[Xlis_ame,_is_ame_v_ist,regequ]
_=ax+b

_ed-Med

LinReg
(ax+b)

L_,L_,Yz

a=.875
Med-Med
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
(axZ+bx+c)

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
four points are requil_d.
CubicReg

Qua_Reg
(ax4+bx3+cx2+
dx+e)

[Xlistname,_istnamedCreqlist,regequ

At least

]

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 R 2. 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

LinReg
(a+bx)

regression.

[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 r2 and r.
LinReg(a+bx)

LnReg
(a+b In(x))

[Xlistname,_istnamedCreqlist,regequ

LnReg (logarithmic
regression)
y=a+b ln(x) to the data using

]

fits the model equation
a least-squares
fit and

transformed
values ln(x) and y. It displays
b; when DiagnosticOn
is set, it also displays
and r.

values for a and
values for r2

LnReg [Xlistname,YlistnamedCreqlist,regequ]

ExpReg
(ab x)

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 a and b; when
DiagnosticOn
is set, it also displays values for r2 and r.
ExpReg

12-26

Statistics

[Xlistname,YlistnamedCreqlist,regequ]

PwrReg (power l_gression) fits the model equation y=ax b to
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

(axb)

PwrReg [Xlistname,Ylistname_freqlist,regequ]
Logistic
c/(l+a*e

-bx)

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

SinReg
a sin(bx+c)+d

[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
will iterate

is the nlaxinlonl
number
of times the algorithm
to find a solution.
The value for iterations
can

be an integer
The algorithm

_>1 and _<16; if not specified,
nlay find a solution
before

the default is 3.
iterations
is

l_a('hed.
Typically,
lm'ger values for iterations
result in
longer execution
times and better accuracy
for SinReg,
and
vice versa.
A period
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.
A SinReg

example

is shown

on tile next

page.

Statistics

12-27

SinReg Example:
Daylight Hours in
Alaska for One
Year

Compute

the regression

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

model

for the number

[liar

of

Notz _lotx

orr

IT_Pe:_I..
_ _
-_

li<,listiE
16Jlist:Lz
Mark:

SinReg

of hours

one year.

° []

.

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 b is
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
vm'iables
m'e clem'ed.

Variables

the type

of analysis,

1-Var
Stats

2-Var
Stats

all statistical

Other

VARS
menu

mean of x values

_

_

XY

SUnl of x values

Ex

Ex

E

sunl of X2values

Yx2

Yx2

E

Sx

Sx

XY

_x

Gx

XY

n

n

XY

_

XY

2y

1;

sample

standard

population
nulnber

deviation

standard

of x

deviation

of x

of data points

mean of y values
sunl of y values
sunl

of y2 values

sample

standard

population

dexqation of y

standard

deviation

of y

sunl of X * y

'Fy2

y

Sy

XY

_y

XY

Zxy

Z

lninimuln

of x values

minX

minX

XY

lnaxilnuln

of x values

maxX

max)(

XY

lninimuln

of y values

minY

XY

lnaxilnum

of y values

maxY

1st quartile
median
3rd quartile
regression/fit
polynomial,
coefficients

coefficients
Logistic, and SinReg

correlation

coefficient

coefficient

of determination

regression

equation

sulnl:laI T points (Med-Med only)
Q1 and Q3

XY

Q1

PTS

Med

PTS

Q3

PTS
a, b

EQ

a, b, c,
d, e

EQ

r

EQ

r2, R2

EQ

RegEQ

EQ

xl, yl, x2,
y2, x3, y3

PTS

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

Entering Stat
Data

Analysis

in a Program

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),
: {1,2,3}÷LI
PROGRRM:
: {-I, -2, STRTS
-5}÷Lz

Statistical
Calculations

To perform
these steps,

a statistical

1, On a blank
calculation

]

calculatkm

from

a program,

line in the progrmn
editor,
select
from the $TAT CALC menu.

follow

the type of

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)

12-30

Statistics

LI

Statistical

Plotting

Steps for Plotting
Statistical Data in
Lists

You call plot
types of plots
modified box
plot. You can

statistical data that is stored in lists. The six
available m'e scatter plot, xyLine, histogram,
plot, regulm" box plot, and normal probability
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

(Scatter)

the graph.

Scatter plots plot the data
coordinate pairs, showing
( + ), or dot ( • ). Xlist and
You can use the same list

points fronl Xlist and Ylist as
each point as a box ( o ), cross
Ylist nmst be the sanle length.
for Xlist and Ylist,

"t]';i'Off

÷

T'_Pe:_m_,._
Xlist.;_t-Vli__L:Lz

÷

+÷
:+_

Mark: [] []

(xyLine)

÷

k____

÷

.........

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 plots

(Histogram)

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'€

i

;

X list,;"Ct
Fr.e_:

(ModBoxplot)

Ip_in=_B.4Bt30B

I

ModBoxplot
(modified
box plot)
like the regular box plot, except
Interquartile
Range beyond the
Range is defined
_s the difference
quartile
Q3 and the first quartile
plotted
individually
beyond
the
(5 or + or ,) you select. You can
are called outliers.
The prompt
ff)r outlier points
is the maximunl
point (maxX)
(minX). When outliers
exist,
display x=. When no outliers
prompts
for the end of each
and Q3 define the box (page

plots one-variable
data,
points that are 1.5 *
quartiles.
(The Interquartile
between
the third
Q1.) These points are
whisker,
using the Mark
trace these points,
which

is x=, except
when the outlier
or the minimunl
point
the end of each whisker
will
exist, minX and maxX are the
whisker.
O1, Med (median),
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

(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

2: P lot2...0n

le

3: Plot3...Of'f"
44,P 1otsOtPt"

(NormProbPIot)

,a ....

NormProbPIot (normal probability plot) plots each
observation X in Data List vel\sus the corresponding
quantile z of 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

X or Y

for the Data Axis setting.
•

If you select
the z-values

X, tile TI-83 plots
on the y-axis.

tile data

on tile x-axis

and

•

If you select
the z-values

Y, the TI-83 plots
on the x-axis.

the data

on the y-axis

and

[PandHorp_(35,
)÷L_

2,90
7

36

Plot1 p1OI:;_

m

0f'f"

T_Pe:
Data
Data
Mar'k:

P 3:Lh

-L_ b-_ 31_
_.- a]b I
Crst.--: L _
Axis:@
Y
= *

II

N=')E.E:1321E

?=.?hEIBB19

Statistics

12-33

Defining the
Plots

To define

a plot,

1, Press [_
displayed

follow

these

steps.

[STAT PLOT]. The STAT PLOTS menu
with the current
plot definitions,

2, Select the plot you want to use, The stat
displayed
for the plot you selected,

3, Press _
statistical

Select
options

Statistics

is

you select

On or Off,

the type of plot.
checked

Each

type prompts

for the

in this table.

Plot Type

XList

YList

Mark

Freq

Data
List

Data
Axis

_L_ Scatter

_

_i

_

rl

[]

[]

xyLine

_

121

_

[]

[]

[]

Zn_ Histogram

_

[]

[]

_

[]

[]

o,.

_

[]

_

_

[]

[]

_:_> Boxplot

_

[]

[]

_

[]

[]

[__

[]

[]

_

[]

_

lTI

ModBoxplot

NormProbPIot

Enter

12-34

editor

to select On if you want to plot the
data imnlediately.
The definition
is stored

whether
4,

plot

is

list names

or select

options

for the plot

•

Xlist (list name

containing

independent

•

Ylist (list name

containing

dependent

•

Mark (aor

•

Freq (frequency

•

Data List (list nanle for NormProbPIot)

•

Data Axis (axis

type,

data)
data)

+ or.)
list for Xlist elements;

on which

to plot

default

Data List)

is 1")

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.

_" _
Xlist:L1
Vlist:Lz
Mark: [] *

Turning On and
Turning Off Stat
Plots

L_

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

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.

Tracing a Stat
Plot

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

Defining a Stat
Plot in a Program

in a Program

To display a stat plot fronl a program,
then display the graph.

define the plot, and

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
Plot3( to the cursor location.

Plot1(, Plot2(, or

PROGRAM:PLOT
:{I,2,3,4}+LI
:{5,6,7,8}+Lz
:Plot2(I
Press[_[STATPLOT][_todisplaytheSTATTYPE
nlenu,

PLOTS _
._Soatter
z: x_Line

MARK

5:Bo>,'g
Iot
S:HorMProbPlot
Select
plot

the type of plot,

type

to the cm'sor

which

pastes

the name

of the

location.

PROGRAM:PLOT
:{1,2,3,4}+LI
:{5,6,7,8}+Lz
:Plot2(SoatterI

Statistics

12-37

5_

Press

[].

Enter

the list names,

separated

by eonunas.

6, Press [] [_
[STAT PLOT] [] to display the
STAT PLOT MARK menu. (This step is not necessaqyyou selected
3:Histogram
or 6:Boxplot
in step 4.)

Select the type of nlark (D or + or °) for each data
The selected
mm'k symbol is pasted to the cursor
location.
Press

[]

_

to complete

: {I02,3,4}÷LI
: {5, 6, 7,8}÷Lz
: Plot2(Soattet-,
PROGRAM: PLOT

Displaying a Stat
Plot from a
Program

To displayinstruction

(Chapter

line,

L

3),

::
DisParaF-h

Statistics

point.

a plot from a program,
use the DispGraph
(Chapter
16) or any of the ZOOM instructions

PROGRR_I: PLOT
: {1,2,3,4}÷LI
: ,.5,6, _, 8}+Lz
: Plot2(ScatteP,
I,Lz,=)

12-38

the command

if

L

PROGRRM:PLOT
:{1,2,3,4}÷Lt
:_506,7,8}÷Lz
:Plot2(ScatteP,L
I,Lz,.)
::_°°MStat

3
Contents

and Distributions
InferentialStatistics
Getting Started: Mean Height of a Population
Inferential
Star Editors ...................................
STAT TESTS Menu ......................................
Inferential

Statistics

Input

I)eseriptions

............

..................

13-2
13-6
13-9
13-26

Test and Interval Output Variables .......................
Distribution
Functions
...................................

13-28
13-29

Distribution

13-35

'_

Shading

TEXAS

.....................................

T1=83

iNSTRUMENTS

z=.ee:l.

I_=._?e:_
J

STATPLOT

TBLSET

FORMAT

Inferential

CALC

Statistics

TABLE

and

Distributions

13-1

Getting

Getting

Started:

Started

Mean Height of a Population

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 t distribution 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
169.43

168.33

159.55

(in cm.)

169.97

of Each

159.79

of 10 Women

181.42

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

171.17

162.64

1

167.15

159.53

.I

L_

I

.1

L;'

1

L_

3

HaMe==

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,

13-2

hfferential

Statistics

and

Distributions

HGHT

mmm

H6HT(1) =

HGHT
1_9.7B
171.17
16Y.tg

H6HT(11)=

.1

4.

Press [gY_ [] to display the STAT TESTS
menu, and then press [] until 8:Tlnterval is
highlighted.

EDIT CRLCIII_
2ST-Test,,
3:2-SamPZTest
4:2-Sar4eTTest_
7:ZIntervM,.,"[_tlTInterval...

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.

TlntervM
InPt:_
Stats
List:HGHT
Fre_:1
C-Level:.99
Calculate

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

Tlnterval
(159.74,173.94)
R=166.838
Sx=6.907879237
n=lO

the results.

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] [] 8 to 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.
8.

Press

[] 163 [] 8 [N?_

to store

Press

7 [] 1 [ggY_

Press

90 [NTgN to store

to store

163.8 to _.

7.1 to Sx.

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
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
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

Press [2_] [DISTR] to display
(distributions)
menu.

13-4

hfferential

Statistics

screen.

the DISTR

and

Distributions

DRAW
normalcd?(
3:invNorm(
4:tPd?(
5:tod¢(
6:XZpd?(
74XZod¢(

11.Press
3 to

invHorr_(.
1_ 6.35)

invNorm( to the home

paste

screen.

Press_
95_
.95 is the area,

lS5_
1_
6_ 35_
1G5.1 is p, and 6.35 is o.

The result is displayed
women
are taller than

on the home
175.5 cm.

I

screen;

Now graph and shade the top 5 percent

it shows

Ymin=-.02
Ymax=.08
Yscl=0

13. Press [_ [DISTR]
DRAW menu.

that

five percent

Xres=l

STR Llli'_l_
ShadeNoPm
3: ShadeX
4: ShadeF

14. Press
home
Press

_
to paste
screen.
[_

[ANS] []

ShadeNorm(

1 _

[EE l 99_

of the

gINDOg
XMin=145
Xmax=185
Xsol=5
YMin=-.82
YMax=.88
Yscl=O
XPes=1

to display the DISTR

[]

175.5448285

of the population.

12. Press [_
and set the window
variables to these values.
Xmin=145
Xmax=185
Xscl=5

95,165.

to the

165[_

1

D6[]asD.

(

z(
(

invHor.M(. 95,165.
1,6.35)
175. 5448285
ShadeNoPFKRns,
1E
99, 165. 1,6.35)I

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

low is the lower
bound.

bound,

the 95th percentile.
up is the upper
firca=.OB
low='l

Inferential

Statistics

and

7_:._:LI_:

up,=:LEBB

Distributions

13-5

Inferential

Displaying the
Inferential Stat
Editors

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
_:_
<_
Calculate

>_n
Orau

Note: When you select the ANOVA( instruction, it is pasted to the
home screen. ANOVA( does not have an editor screen.

Using an
Inferential Stat
Editor

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
The appropriate
editor is displayed.

is available.

3. Enter real numbers, list names, (Jr expressions
argument in the editor.

for each

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
available.
6. Select Calculate (Jr Draw (when Draw is available)
execute the instruction.
•

When you select Calculate, the results
on the honle screen.

•

When you select Draw, the t_sults
graph.

is

to

are displayed

are displayed

in a

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

Stats

Sete_ an alternative
hypothesis

Enter values for
arguments

Calculate
Selecting
Stats

Data or

Select Calculate
or Draw output

Omau

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

•

Select Stats to enter
and n, as input.

sunmm_

lists

_s input.

statistics,

To select Data or Stats, move the cursor
Stats, and then press [ggY_.
Entering
the
Values for
Arguments

such

as 2, Sx,

to either Data or

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.

Selecting
an
Alternative
Hypothesis

(_ < >)

Most of the inferential
prompt
you to select

stat editors
one of three

•

The first is a _ Mternative
the Z-Test.

•

The second
is a < alternative
for tile 2-SampTTest.

•

The third is a > alternative
the 2-PropZTest.

To select an alternative
appropriate
alternative,

Inferential

for the hypothesis
tests
alternative
hypotheses.

hypothesis,

such

hypothesis,
hypothesis,

as p¢p0 for

such
such

as pl<_t2

as pl>p2

hypothesis,
nlove the cursor
and then press [ggY_.

Statistics

and

Distributions

for

to the

13-7

Selecting
the
Pooled Option

Pooled (2-SampTTest
whether

the vmiances

or Draw

for a Hypothesis
Test

m'e to be pooled

only)

Select No if you do not want the vmiances
Population
vm'iances
can be unequal.

•

Select Yes if you want
wu'iances
m'e assumed

the wu'iances
to be equal.

option,

move

specifies

for the

•

To select the Pooled
then press [_T_].

Selecting
Calculate

and 2-SampTInt

calculation,
pooled.

pooled.

the cursor

Population

to Yes, and

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
inunediately
executed.
Selecting
Calculate
for a
Confidence
Interval

is

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.

Bypassing
Inferential
Editors

the
Stat

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 hypothesis
testorconfidenceinterval
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
Menu

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,..
Test for 1 p, known
2:T Test,.,
Test for i p, unknown
3:2 SampZTest...
Test compming 2 #'s, known _'s
4:2 SampTTest,..
Test compming 2 #'s, unknown
_'s
5:1 PropZTest...
Test for 1 proportion
6:2 PropZTest,..
Test compming 2 proportions
7:Zlnterval,.,
Confidence intmwal for 1 #, known
8:Tlnterval,.,
Confidence intmwal for 1 #, unknown
9:2

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
t test for regression slope and p
One-way analysis of variance

SampZlnt.,.

0:2 SampTlnt.,.
A:I PropZlnt.,.
B:2 PropZlnt.,.
C:X2 Test,,.
D:2 SampFTest...
E: LinRegTTest,..
F: ANOVA(

Note: When a new test or interval is computed, all previous output
variables are invalidated.

Inferential Stat
Editors for the
STAT TESTS
Instructions

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
that instruction
•

•

then shows the unique output
with the example results.

screen for

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

Z-Test (one-sample z test; 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:_
Input:

Calculated

results:

Stats

0.:3
List:L1
Fre_:l
_:#_
_
Calculate

>_o
Draw

Stats
Z-Test
InPt:Oata
v.n : 300
0:3
_: 299. 0333
n:6
v.:#v.n_
>_n
Calculate
Draw

Z-Test
v.<300. 0000
z= -. 7893
P=. 2150
_=299.
0333
mx= 1. 5029

Z-Test
u<300.0000
z=-.7893
e=.2150
R=299.0333

ir,=6.

I n=6.0000

0000
.@

.@

Drawn results:

:=-.7B9_ _=._I_
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

13-10

Inferential

Statistics

in the examples.

and

Distributions

T-Test

T-Test (one-sample

t test;

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_,:PPo (,u:>_.to)

In the example:
TEST={91.9 97.8 111.4 122.3 105.4 95}

Input:

Data
T-Test
InPt:_
_n:105
List:TEST
FPe_:l
_:_
<_n
Calculate

Stats

>_n
DPau

Stats
T-Test
InPt:Oata
p0:105
7,:103. 9667
Sx: 11.4669
n:6
Calculate

T-Test
_#105.0000
t=-.2207
P=.8340
R=103.9667
Sx=II.4669

T-Test

,,lo5.00oo
t=-.,_20_
Calculated

results:

P=. 8340

2= 100 • 9667
Sx= 1 I. 4669

in=6.

OPau

in=6.0000

0000

Drawn results:

t= -,i:_:07

_=,g3h

Inferential

Statistics

and

Distributions

13-11

2-SampZTest

2-SampZTest

(two-sample

z test;

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 (pl:>p2)

In the

example:

LISTA={154
LISTB={108

109 137 116 140}
115 126 92 146}
Data

Input:

2-SamPZTest
InPt =I_
¢I: 15.5
¢2:13.5
ListI:LISTR
List2:LISTB
FPe_l:l
_Fre_2:l
_I:#_2
Calculate

<_2

Stats

results:

2-SaMPZTest

P:. 695

z= I. 4795
P=. 0695

_1=131.0000

RI=131. 0000
Rz=117.4000
l.n i =5. 0000

2z=I17.4000

I
i

1_Sx,=18.6145

r,z=5.0000

S×z=20.1941
ni=5.0000

i

inz=5.0000

//
Drawn resutts:

z=l.h795

13-12

Inferential

=-LI:#p.2 _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}

Input:

Data
2-SamPTTest
InPt:liI_11_Stats
ListI:SRMPI
List2:SRMP2
Fre_l:l
Fre_2:l
SPooled:l_

9es

I Calc.ulate Draw

Calculated

results:

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

I

_LI:_
<_2 >_2
PooI_:[_
Yes
Calculate
Draw

2-SamPTTest

2-SamPTTest

t=2.2579
P=.0659
d_=5.8408
RI=15.9333
$_z=9.4998

t=2.2579
P=.0659
d€=5.8408
RI=15.9333
_2z=9.4998
Sxz=1.9501
ni=6.0000
I nz=6.0000
SXI=6"7014

m =6. 00e
I r,z=6. 0000

Drawn resutts:

Inferential

Statistics

and

Distributions

13-13

1-PropZTest (one-proportion
z test; item B) computes a test
for an unknown proportion
of successes (prop). It takes as
input the count of successes in the sample x and the count
of observations
in the sample n. 1-PropZTest tests the null
hypothesis H0:prop=p0 against one of the alternatives
below.

1-PropZTest

•
•
•

H_,:prop€p0 (prop:¢p0)
H_,:propp0 (prop:>po)
I

1-ProPZTest
pill

Input:

I

.5

x: 2848
I
n: 4848
I
eroI=Ei1"_,'1
Pal
Caloulate

Draw

l-ProeZTest
ProP#.

Calculated

results:

5000

z=. 8810
P=. o783
_=. 5069
in=4e4e.

0088

Drawn results:

13-14

Inferential

Statistics

and

Distributions

2-PropZTest (two-proportion
z test; 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.

2-PropZTest

•
•
•

Input:

Calculated

results:

H_,:pl;eP2 (pl:_p2)
H_,:plP2 (pl:>p2)

2-PPoeZTest
xi:45
hi:61
x2:38
n2:62
el:I
e2
Calculate
Draw
B2-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 (one-sample z confidence 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,

Zlnterval

In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data
ZInterval
In_t:l_ellI_Stats
Input:

Calculated

results:

List:L1
Fre_:l
C-Level:.9
Calculate

-BZInterval
(297.02,301.85)
R=299.0333
Sx=1.5029
|n=6.0000

13-16

Inferential

Statistics

and

Stats
ZInterval
Inet:Data
_:3
R: 299. 0333
n:6
C-Legel :. 9
Calculate

Zlnterval
(297.02,301.05)

I

Distributions

Tlnterval

Tlnterval

(one-sample

t confidence

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
L6={1.6

Input:

example:
1.7 1.8 1.9}

Data
Tlnterval
InPt:llL_u1_Stats
List:L_
Fre_:l
C-Level:.95
Calculate

Stats
T Interva I
InF.t:Data
_: 1.75
Sx:. 1291
n:4
C-Level: .95
Caloulate

-B-

Calculated

results:

TInterval
(1.5446,1.9554)
R=1.7500
Sx=.1291

TInterval
(1.5446, i.9554)
R=1.7500
Sx=.1291

|n=4.0000

|n=4.0000

Inferential

Statistics

and

Distributions

13-17

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 (or1 and a_) are known. The computed
confidence inte_'al depends on the user-specified
confidence level.

2-SampZlnt

In the

example:

LISTC={154
LISTD={108

Input:

109 137 116 140}
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
Calculated

results:

Sxi=18.6145
Sxz=20.1941
$ni=5.0000

n2=5.0000
|

Inferential

Statistics

and

C-Level:.99
Calculate

2-SamPZlnt
(-10.08,37.278)
21=131.0000
2_=117.4000
m=5.0000
inz=5.0000

|

13-18

Stats
2-SamPZ I nt
InPt:Data
_I: 15.5
¢2:13.5
21:131
ni:5
22:117.4
_n2:5

Distributions

2-SampTInt

2-SampTInt

(two-sample

t confidence

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 userspecified
confidence
level.
In the

example:

SAMP1={12.207
SAMP2={11.074

16.869 25.05 22,429 8.456 10.589}
9.686 12.064 9.351 8,182 6.642}

Stats
2-SaP/PT I r=t

Data

Input:

2-SamPTlnt
InPt:_
ListI:SRMPI
List2:SRMP2
Fne_l:1
Fne_2:l
C-Level:.95
$Pooled:l:_

Stats

Sxl :6. 7014
nl:6
R2:9.4998
Sx2:1.9581
_n2:6

Yes

C-Level :. 95
Pooled:l:_ Yes
Calculate

Calculate

Calculated

results:

2-SamPTlnt
(%5848,13.452)
d¢=5.8408
Ri=15.9333
Rz=9.4998
SxI=6.7014
$Sxz=1.9501
|

2-SamPT
Int
( -.5849, 13. 452)
df=5.8408
_i =15. 9333
R1=9.4998

SxI=6. 7014
_Sx1=1.9501

|
i
ni=6.0000
nz=6.0000

ni=6.8000
nz=6.0000

|

Inferential

Statistics

and

Distributions

13-19

1-PropZInt (one-proportion
z confidence 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 x and the count of obse_'ations
in the sample n.
The computed confidence intetnTal depends on the userspecified confidence level.

1-PropZlnt

input:

1-PPoeZlnt
x: 2848
n: 4848
C-Leve I :.99
Caicuiate

-Bl-ProeZlnt
(.4867,.5272)
A=.5069
Calculated

results:

|n=4040.0000

13-20

Inferential

Statistics

and

Distributions

2-PropZInt

2-PropZlnt

(two-proportion

z confidence

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_n input 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
-I

Calculated

results:

2-PPoeZInt
(.0334,.3474)
#I=.8033
#z=.6129
ni=61.0000
|nz=62.0000

Inferential

Statistics

and

Distributions

13-21

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.

z2-Test

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].

[ 5.0000

19.000

MATRIX[R]

J.3.000

3 x2

]

Note: Press _
select 1 :[A] from
EDIT menu.

[] [] 1 to
the MATRX

Matrix editor:

[ i0. o000
t,.000
Xi-Test
Observed:[R]
Exeected:[B]
Calculate
Draw
Input:

Note: Press_
display

[B]
[[8.0000

XZ-Test
XZ=3.3750
P=.1850
d€=2.0000
Calculated

results:

Inferential

Statistics

and

[B] _
[B].

16.000.

[ :888816.000...i

Drawn results:

13-22

matrix

Distributions

to

2-SampFTest

2-SampVTest

(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
H_,:(31>(32

•

In the

Calculated

results:

((51 :>(52)

example:

SAMP4={
SAMPS={

Input:

((51 :<(52)

7 -4 18
-1 12 -1

17
-3

-3
3

-5
-5

1 10 11-2}
5 2-11
-1-3}

Data
2-SamPFTest
InPt:_
SLats
ListI:SRMP4
List2:SRMP5
FPe_l:l
FPe_2:l
_i:_
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-SaMPFTest
zl #zz

2-SameFTest
zl#zz
F=2. 1956
P=. 2364
S× _=8. 7433
Sxz=5. 9007
_nl =10. 0000

F=2. 1955
P=. 2365
Sxl =8. 7433
Sx z =5. 9007

_i

=5. 0000

z= -.2727
n_=lO. 0000

nz=l I.0000

2

in _ = 1 I. 0000

Drawn results:

Inferential

Statistics

and

Distributions

13-23

LinRegTTest

LinRegTTest

(linear

regressk)n

t test;

item

E) computes

a

linear regression
on the given data and a t test 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
(MARS Statistics EQ secondary
menu).
If you enter
variable
name at the RegEO: prompt,
the eMeulated
regression
equation
is automatically
stored
to the
Y= equation.
In the example
below, the regression
is stored
to Y1, which is then selected
(turned on).
In the

specified
equation

example:

L3={38 56 59
L4={41 63 70

Input:

RegEQ
a Y=

64 74}
72 84}

LinRegTTest
Xlist:L_
91ist:L4
Fre_:l
B & P:_
<0
RegEQ:_
Calculate

>0

lJ-

Calculated

results:

LinRegTTest
_=a+bx
B_O and
p_O
t=15.9405
P=5.3684E-4

",371B-3. 6596+i.
69X
xYz=

d€=3.8888
4a=-3.6596

xY4=
PloLt
xVs=
xY_=

PloI:Z

PloL3

19

$b=i.1969
s_1.9820
P_=.9883
P=,9941
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(

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 4 6 6 5}
L2={6 5 5 8 7}
L3={4 7 6 7 6}

RNOVR(LI,Lz,L_)I

Input:

ll-

Calculated

results:

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

Inferential

and MS is mean square.

Statistics

and

Distributions

13-25

Inferential

Statistics

Input Descriptions

The tables in this section describe the inferential statistics inputs discussed
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.

in

Input

Description

_0

Hypothesized
testing.

G

The known population
number > 0.

List

The name of the list containing

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,
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,
Sx2, n2

Sununary

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

value of the population
standard

mean that you are

deviation;

must be a real

the data you are testing.

and sample

statistics (mean, standard deviation, and sample
size) for sample one and sample two in the two-salnple
tests and intervals.

Statistics

and

Distributions

Input

Description

P0

The
real
The
and

x

expected sample proportion for 1-PropZTest. Must be a
nmnber, such that 0 < I90 < 1.
count of successes in the sample for the 1-PropZTest
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.
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.

C-Level

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 'all integers _>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

variables

statistics

are calculated

as indicated

below.

variables
for use in expressions,
press [_,
5 (5:Statistics),
the VARS menu listed in the last column
below.

these
select

Variables

Tests

Intervals

To access
and then

LinRegTTest,
ANOVA

VARS
Menu

p-value

p

p

TEST

test

z, t, Z2_ F

t, F

TEST

df

TEST

statistics

degrees

of freedom

df

df

sample
sample

mean of x values
1 and sample 2

21,22

21, 22

TEST

sample
standard
deviation
of x
for sample
1 and sample
2

Sxl,
Sx2

Sxl,
Sx2

TEST

nulnber
of data points
1 and sample 2

nl, n2

nl, n2

TEST

SxP

SxP

/3

/3

TEST

pooled

standm'd

for

for sample

deviation

SxP

TEST

estimated

sample

proportion

estimated
population

sample
1

proportion

for

/31

/31

TEST

estimated
population

sample
2

proportion

for

/32

/32

TEST

lower,
upper

TEST

2

_

XY

Sx

Sx

XY

n

n

confidence
mean

interval

pair

of x values

sample

standm'd

nulnber

of data

standard

error

deviation

of x

points
about

the

line

XY
s

TEST

a, b

EQ

correlation

coefficient

r

EQ

coefficient

of determination

r2

EQ

regression

equation

RegEQ

EQ

regression/fit

13-28

coefficients

Inferential

Statistics

and

Distributions

Distribution

DISTR menu

Functions

To display
DISTR

the

DISTR menu,

press

[_

[DiSTR],

DRAW

Normal
Normal
Inverse

i: normalpdf(
2: normalcdf(
3:invNorm(

probability
distribution
cunmlative

densityprobability
normal
distribution

Student-t
probability
density
Student-t
distribution
probability
Chi-square
probability
densityChi-square
distribution
probability
F probability
densityF distribution
probability
Binomial
probability
Binomial
cunmlative
densityPoisson
probability
Poisson
cunmlative
density
Geometric
probability
Geometric
cunmlative
density-

4:tpdf(
5:tcdf(
6: z2pdf(
7: x2cdf
8: Fpdf(
9: Fcdf(
O: binompdf(
A: binomcdf(
B: poissonpdf(
C: poissoncdf(
D: geometpdf(
E: geometcdf(

Note: -1E99 and IE99 specify infinity. If you want to view the area left
of upp¢rbound,
for example, specify lowerbound_1E99.

normalpdf(

norwmalpdf( computes
the probability
density
function
(pdf) for the normal distribution
at a specified
x value, 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:
Xmin
Xmax
Ymin
Ymax

For this example,
= 28
= 42
=0
= .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(

normalcdf( computes
between
lowerbound
nlean u and standard
and 6= 1.

the normal distribution
probability
and upperbound
for the specified
deviation
or. The defaults
are u =0

normalcdf(_werbound,upperbound[,p,_])
noPmalod_(-iE99,
36,35,2)
.6914624678
invNorm(

invNorm( computes
the inverse
cumulative
normal
distribution
function
for a given area under the normal
distribution
cut_'e specified
by mean p and standard
de_iation
cr. It calculates
the x value associated
with an
area to the left of the x value. 0 _0. To plot the Student-t
distribution,
paste tpdf( to the Y= editor,
function
(pdf) is:
F [(df + 1)/2]
f(x)

probability

(1 + x2/df)

- (if + 1)/2
x/_f

dJ)

Pl_{:[ P1¢_: Plo{. _
",YI BtPd{'(X,
2)

I

Note: For this example,
Xmin = -4.5
Xmax = 4.5
Ymin = 0
Ymax = .4

13-30

Inferential

density-

=
F(df /2)

tpdf(x,

The

Statistics

and

Distributions

tcdf(

tcdf( computes the Student-t distribution probability
between lowo'bound
and uppe_"bound for the specified
(degrees of freedom), which nmst be > O.

df

tcdf(lowerbound,uppe'rbou.rwl,d]_
tc.d_" ( •9657465644
-2, 3, 18)
x2pdf(

z2pdf( computes
the probability
density
function
(pdf) ff)r
the X2 (chi-square)
distribution
at a specified
x value, df
(degrees
of freedoln)
nmst be an integer
> 0, To plot the X 2
distribution,
paste x2pdf( to the Y= editor, The probability
density function
(pdf) is:
f(x)

1

=
r(df

(1/2)df/2

x/f/:)

- 1e - x/:), x _>0

/2)

:2pdf(x,dj)
P1,;,tl PloLZ Plot_
\YI B:KZPdf'(X, 9)
",VZ I_I;_
Z Pdla (X _F)

Note:
Xmin
Xmax
Ymin
Ymax

xYs=
\Y_=
\Y_=
xY_=
\Y_=

x2cdf(

For this example,
=0
= 30
= -.02
= .132

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
x value, 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(X)

F[(n+d)/2]
= F(n/2)F(d/2)

where

(d)n/2xn/2
n = numerator
d = denominator

F pdf(x,numero

tor dr, denominator

Plot:l, plot:i: Plo_,3
_._1BFPdf

Fcdf(

l(l+,_a_./d)(n+d)/2,X>

(X,

24,

dJ_
Note: For this example,

19

Xmin
Xmax
Ymin
Ymax

== 05
=0
= 1

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.
F cdf(lowerbound,upperbound,numerator
denominator
dJ)
Fodf'(O, 2. 4523,24
,19)
-,
• 9_ 49989576

13-32

degrees
of freedom
degrees
of fi'eedom

Inferential

Statistics

and

Distributions

dr,

0

binompdf(

binompdf(

computes

a probability

at x ffw 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_ O. If you do not specify x, a list of probabilities
from 0 to numtrials
is returned.
The probability
density
function
(pdf) is:

f(

X

( _7/,

)=/xiP

x

n-x

(l-p)

where

,

X

=O,1,...,n

n = numtrials

binompdf(numtrials,p[,x

])

binomPd¢(5,. 6, {3
,4,5})
{. 3456 .2592 .0...
binomcdf(

binomcdf( computes a cunmlative probability at x ff)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_ 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(

poissonpdf(
computes
a probability
at x ff)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(

poissoncdf(

computes

a eunmlative

discrete
Poisson
distribution
which nmst be a real number

probability

at x for the

with the specified
mean _l,
> O. x can be a real number

or a list of real numbers.

poissoncdf(p,x)
eoissonod¢(.126,
{0,1,2,3})
{.8816148468
.9...
geometpdf(

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_0.
_Nom(effective

rate,compounding

_Nor_( 15.87,

,Eft(

14-12

Financial

periods)

4)15.00

)Elf( computes
compounding
compounding

the effective
periods
must
periods
must

_Eff(nominal

rate,compounding

_E€€(8,12)

Functions

rate

8.30

interest
be real
be >0.

rate. nominal
nulnbers.

periods)

rate and

Finding Days between Dates/Defining

dbd(

Use

the date

Payment Method

dbd( (menu

function

item

D) to calculate

the

number
of days between
two dates using the actual-daycount method,
datel and date2 can be numbers
or lists of
numbers
calendar.

within

the range

of the

dates

on the standard

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

Defining the
Payment Method

Pmt_End and Pmt_Bgn (menu items E and F) specify- a
transaction
_k_an ordinmy7 annuity
or an annuity
due. VC]mn
you execute
either conunand,
the TVM Solver is updated.

Pint_End

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
PMT to ordinmTy- annuity.

Pmt_Bgn

BEGIN line, select

Pmt_Bgn (payment
beginning)
specifies
where payments
occur at the beginning
period.
Most leases are in this catego_7.

END to set

an annuity
due,
of each payment

Pmt_Bgn
On the TVM Solver's PMT:END
set PMT to annuity
due.

BEGIN line, select

Financial

Functions

BEGIN to

14-13

Using the TVM Variables

FINANCE VARS
Menu

To display

the FINANCE VARS menu,

press _

[_. You can use TVM variables
in TVM functions
values to them on the home screen,
CALC VARS
1: N
Total number
of payment
2:1%
Annual interest
rate
3: PV
Present
value
4:
5:
6:
7:

PMT
FV
P/Y
C/Y

[FINANCE]
and store

periods

Payment
amount
Future value
Number
Number

of payment
periods
per year
of compounding
periods/year

N, [%, PV, PMT,
FV

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.

PlY and C/Y

PW is the number of payment
financial transaction.
C/Y is the number
salne transaction.

periods

of compounding

per year in a

periods

per year in the

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

5
Contents

CATALOG,Strings,
HyperbolicFunctions
Browsing tile TI-83 CATALOG ...........................
Entering and Using Strings ...............................
Storing Strings to String Variables
.......................
String Functions
and Instructions
in the CATALOG
Hyperbolic
Functions
in tile CATALOG ..................

......

15-2
15-3
15-4
15-6
15-10

T1=83

TEXAS INSTRUMENTS

m

CATALOG
_abs(
and

angle(

QNOUA(
Ans

augnenL(

AxesO_¢
J
STAT

PLOT

TBLSET

FORMAT

CATALOG,

Strings,

BALe

TABLE

Hyperbolic

Functions

15-1

Browsing

the TI-83 CATALOG

What Is 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 commandsyou can execute
from the home screen are GetCalc(, Get(, and Send(.
Selecting an Item
from the
CATALOG

To select a CATALOG item, follow these steps.
1. Press F_a] [CATALOG]

to display the CATALOG.

i*abs(
and
angle(
RNOVR(
Rn_
iCRTRLOG
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

Iabs(1

screen.

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

What

and Using Strings

Is a String?

A string

is a sequence

On the TI-83,

•

It defines

text

to be displayed

•

It accepts

input

Characters

Entering a String

of characters

quotation
marks,
applications.

from

Count

•

Count each instruction
cos(, as one character;
instruction
or function

number,

letter,

and space

to form

as one character,

a string
follow

on a blank line on the home
these steps.

1, Press

@

[,] to indicate

2, Enter

the characters

that

the beginning
comprise

Use any combination
names, or instruction

•

To enter

•

To enter several
alpha characters
[A-LOCK] to activate
alpha-lock.
@

space,

[-] to indicate

screen

or in a

of the string.

the string.

•

3, Press

a string.

or function
name, such as sin( or
the TI-83 interprets
each
name as one character.

To enter
program,

ablank

within

primaFy"

in a program,

that you combine

•

enclose

has two

in a p_x)gram.

the keyboard

are the units
each

that you

a string

of numbers,
letters,
function
names to create the string.
press

@

[_],
in a row,

press

[_

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

String Variables

to String Variables

The

TI-83

has

10 variables

You can use string
instructions.

to which

variables

with

you can

string

store

functions

strings.
and

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

a string

to a string

1. Press

@

[,], enter

2. Press

_.

To

store

3. Press _
4.

Select
which

variable,
the string,

7 to display

the string
you want

follow

these

and press

steps.

@

[-].

the VARS STRING menu.

variable
to store

(from $trl
the string.

to $tr9, or $tr0)

to

4:Str.4
5:StP5
6:_tr6
74Str-7
The string variable
is D_sted to the current
location,
next to the store symbol (-)).

cursor

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

Displaying
the
Contents
of a
String

Variable

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.

I

St.r2
HELLO

CATALOG,

Strings,

Hyperbolic

Functions

15-5

String Functions

Displaying String
Functions and
Instructions in
the CATALOG

and Instructions

String

functions

in the CATALOG

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

+ (Concatenation)

Equ)String(
expr(

Converts
Converts

inString(

Returns

a chm'acter's

length(

Returns

a string's

String)Equ(
sub(

Converts
Returns

a string to an equation,
a string subset
as a string,

To concatenate

two or more

1, Enter

stringl,

2, Press

[],

3, Enter

string2,

necessmT,
stringl
4, Press

15-6

CATALOG,

number.

chm'acter

length.

follow

name.

which

can be a string

or string

name,

press

[] and enter

to display-

Hyperbolic

steps,

or string

string3,

If

and so on,

, ,
the strings

as a single

string.

: 5tr

To select a string function
or instruction
current
screen, follow the steps on page

Strings,

these

can be a string

+string2+string3,
[_

strings,

place

which

1 +"LMHOP"
"HIJK
"+StPl
HIJK
LMNOP

Selecting a String
Function from
the CATALOG

an equation
to a string,
a string to an expression.

Functions

and paste
15-2.

it to the

Equ*String(

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)

expr(

"3X"÷Y1
E_u*String(gt,

Done
St

rl)

Done

expr( converts
an expression

the chm'acter
and executes

string contained
in string
to
it. string
can be a string or a

stringvariable.
expr(string)
,,l+2+XZ,,)

l_X:"5X"+Strl
x_r(Strl)÷R

inString(

10
I0

7

exPr(

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[
inStr

,start])

ing ( "PQRSTU

V", "STU" )
4
inStr ing ( "RBCRBC
,
Note:

RBC ,4)

4

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(

length(

returns

can be a string

the number
or string

of chara('ters

in st'ring,

string

variable.

Note: An instruction or function name, such as sin( or cos(, counts as
one character.

length(string)

WXYz"WXYZ"eStrl
length(Strl)

String*Equ(

4

String*Equ( converts
st'ring into an equation
and stores
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)

I

String*E_u(Str2,
'.?z)
Plot1

Done
Plot;"

Plot3

,,yl=
",YzB2X

15-8

CATALOG,

Strings,

Hyperbolic

I

I

Functions

tlle

sub( returns

sub(

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)

I

sub(StP5,4,2)
ABCDEFG"RBCDEFG"÷SLP5
DE

Entering
Function

a
to

Graph during
Program
Execution

Inapmgram,
youcanentera
programexecutionusin

Nnctiontographdunng
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

Hyperbolic
Functions

The

hyperbolic

in the CATALOG

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

sinh(, cosh(,
tanh(

c0 s h (
c 0 s h-1 (

Hyperbolic
Hyperbolic

cosine
arccosine

s i nh (
si nh-1 (

Hyperbolic
Hyperbolic

sine
arcsine

t a nh (
t a nh- 1(

Hyperbolic
Hyperbolic

tangent
arctangent

sinh(, cosh(, and tanh( are the hyperbolic
functions.
valid for real numbers,
expressions,
and lists.

Each

sinh(value)
cosh(value)
tanh(value)

sinh(.5)
.5210953055

cosh( {.25,. 5, I} )
{1.8314131

sinhd(, cosh-l(,
tanh-l(

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

is

6
Contents

Programming
Getting Started: Volume of a Cylinder ....................
Creating and Deleting Programs
.........................
Entering Colnmand
Lines and Executing
Programs
Editing Programs
........................................
Copying and Renaming
Programs
........................
PRGM CTL (Control)
Instructions
.......................
PRGM I/O (Input/Output)
Instructions
...................
('ailing Other Programs
as Subroutines
..................

'_

TEXAS

......

16-2
16-4
16-5
16-6
16-7
16-8
16-16
16-22

T1=83

INSTRUMENTS

PROGRRM: CYL INDER
:PromPt R, H
:_R zH÷V
:O ise "VOLUME
IS
.,.j
:I

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Programming

16-1

Getting

Getting

Started:

Started

Volume

is a fast-paced

of a Cylinder

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.

EXEC EDIT [{L_

BBCreate

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.

Flew

PIROGRRM: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_
[] 2 to 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.

16-2

Programming

PROGRRM: CYL INDER

Press J_
[] 3 to 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 VOLUME IS on one line and
the calculated value of V on the next.
6.

Press J_
screen.

PROGRAM:CYLINBER
l:ProMPt R,H
I
:=RZH+V
_DisP "VOLUME
IS

:i v

[QUIT]to display tile home

7. Press [gff_ to display- the PRGM EXEC
menu. The items on this menu are the
names of stored programs.

_EOIT

NEW

LINOER

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_. )

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.

PPgMCYLINDER
R=?1.5
H=?3
VOLUME
IS
21.20575041

I

Bone

Repeat steps 7 through 9 and enter
different values for R and H.

Programming

16-3

Creating

and Deleting

Programs

What Is a
Program.'?

A prograln

Creating a New
Program

To create a new program,

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.

1. Press _

k)llow these steps.

[] to display tile PRGM NEW menu.

EXEC EDIT IIL=I_
HBCreate
New
2. Press _
is displayed,

to select 1:Create New. The Name= proInpt
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 program name can be one to eight characterslong. The
first character must be a letter from A to Z or e. The second
through eighth characters can be letters, numbers, or e.
4. Enter zero to seven letters, numbers,
the new prograln nalne.
5, Press ITNYERI,
Tile prograin
6. Enter one or more prograln

editor is displayed.
commands

7. Press [_ [QUIT]to leave the progranl
to the holne screen.
Managing
Memory and
Deleting a
Program

or 0 to conlplete

(page 16-5).
editor and return

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

Entering a
Program
Command Line

Lines and Executing

Programs

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
CUrSOr

nloves

a eolnmand

tile next

to

line, press [NY_. The

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
and page 16-22).
Executing a
Program

prograln

as a subroutine

(page 16-15

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.
does not check for errors msyou enter a progranL
Breaking a
Program

To stop
nlenu

prograln

execution,

press

[_.

The

It

ERR:BREAK

is displayed.

•

To return

•

To go where

to the honle

screen,

the interruption

1:Quit.

select
occurred,

select

Programming

2:Goto.

16-5

Editing

Programs

Editing a
Program

To edit

a stored

1. Press

[V_

program,

ff)llow

[] to display-

these

the PRGM

steps.
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
then delete,
ove_wvrite, or insert.

•

Press @
to clear all program
eomnmnd
line (the lending colon
enter a new progrmn
eonmmnd.

location,
eominands
remains),

and
on the
and then

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 @
[_.

Inserting and
Deleting
Command
Lines

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

Copying and
Renaming a
Program

Programs

To copy

all conunand

program,
Program

follow steps 1 through
5 for Creating
a New
(page 16-4), and then follow these steps.

lines

fronl

one progranl

into

a new

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

3. Select a nalne fronl
the menu.
tile bottom
line of the program

EXEC menu.

prgmname
editor.

is pasted

to

4. Press [ENt_. All colnnland
lines fl'om the selected
program
are copied into the new program.
Copying programs
applications.

h_s

at least

•

You can create a template
that you use Kequently.

•

You can rename
a new program.

a program

two

convenient

for groups
by copying

of instl_ctions
its contents

into

Note: You also can copy all the command lines from one existing
program to another existing program using RCU

Scrolling the
PRGM EXEC and
PRGM EDIT
Menus

The

TI-S3 sorts PRGM EXEC and PRGM EDIT menu

automatically
into alphanumerical
order. Each
labels the first 10 itenls using 1 through
9, then

items

menu
0.

only

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)

PRGM CTL Menu

Instructions

To display the PRGM CTL (program control)
[_
from the prograln editor only.
CTL I/0
i: If
2: Then
3: Else

EXEC

4: For(
5: While
6:
7:
8:
9:
O:
A:
B:
C:

menu, press

Repeat
End
Pause
Lbl
Geto
IS>(
DS<(
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.
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
press @.
Controlling
Program Flow

OF

If N=I and M:l:Goto

Programming

selecting

an item,

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:
If A<7:A+I->A

16-8

editor without

Z

[ _se If for testing

and branching.

If condition

then the command
inunediately
following
condition
is true (nonzero),
then the next
executed.
If instructions
can be nested.

is false

(zero),

If is skipped.
If
command
is

:If condition
:command
:command

(if true)

Program
PROGRAM:
: O÷R _
:Lbl

COUNT

output
PrgmCOUNT
IR IS

::OisP
A+l÷A._ M T_-,,
i_ _,,,
: If' R_2

I: Stop
1:Goto

If-Then

R IS
Z

Then following
an If executes
condition
is true (nonzero).
group of commands.

a group of commands
if
End identifies
the end of the

:If condition
:Then
:command
:command
:End

(if true)
(if true)

:co_and

Program
PROGRRM:TEST
:I÷X:IO÷Y
:I_ X( is not a looping instruction.

Programming

16-13

DS<( (decrement

DS<(

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
:command (if answer

_>value)
< value)

Pro_lram
:DS\ (A, 6>
:DisP
"> DSKIP
6"
PROGRRM::
I+R
:DisP
'NOT > 6

I

Note: DS<( is not a looping instruction.

Menu( sets

Menu(

up branching

within

If Menu( is

a program.

encountered
during prograln
execution,
the menu screen
displayed
with the specified
menu items, the pause
indicator
is on, and execution
pauses
until you select a
menu item.

is

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
:Menu(
TOSS
DICE
","FRIR
OICE",R,
PROGRR_,!: TOSSDICE
;WEIGHTED
DICE
,
The progranl
above pauses
until you select
select 2, for example,
the menu disappears
program
continues
execution
at Lbl B.

16-14

Programming

DICE
i

1 or 2. If you
and the

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

DelVar deletes fronl nlenlory

the contents

of variable.

DelVar variable
PROGRRH:
DELMRTR
: DelUar.
[R]I
GraphStyle(

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 1 to 7
that corresponds
to the graph style, as shown below.
1
2
3
4

=
=
=
=

".
"i
![
[k

(line)
(thick)
(shade
(shade

above)
below)

5 = '_.)(path)
6 = .'.'.'(animate)
7 = ". (dot)

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)

PRGM I/0 Menu

To display
press

_

CTL

I10

i:

the
[]

Instructions

PRGM I/0 (progranl
fronl

within

menu,

editor

only.

EXEC

Enters

Input

a value

or uses

Prompts

3: Disp

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.

5: DispTable
6:Output(
7: getKey
8:C1 rHome
9: ClrTable
O: GetCalc(
A: Get(
B: Send(

for enhT

the cursor.

2: Prompt
4: DispGraph

These instructions
control
program
during execution.
and displayTo return
press

Displaying a
Graph with Input

input/output)

tile prograln

answers

input
They

during

to the program

values.

to and output fronl a
allow you to enter values

program

editor

of variable

execution.

without

selecting

an item,

@.

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

Output
Pr, gmG IHPUTI

X, V
I1=_:,6

[.
?=:!..5

PrgmG IHPUT
2.6
1.5
Done

16-16

Programming

Storing
Variable
with

a
Value

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

output
Pr.gFiH INPUT
?2

-'InPut

"YI=",YI

?{1,2,3}

-'InPut
DRTR
:OisP
:OisP

"DRTR=",

Vt ="2X+2"

VI(R)
YI(LI)

-"Oi_P

'_t (LORTR)

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

During

Prompt

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

output

:PromPt

V_ax=?3

XMin=?-le

X_ax=?lO
_Min=?-3
PrgMWINOOW

YMax

Done

Note: Y= functions are not valid with Prompt.

Displaying the
Home Screen

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

Disp [valueA,valueB,valueC,...,value
is a variable,

the value

of each.

n]

•

If value

•

If value is an expression,
it is evaluated
displayed
on tile right side of the next

•

If value is text within quotation
marks, it is displayed
the left side of the current
display- line. -) is not valid
text.

Program
:OisP "THE
PROGRRM:R
R IS
,x/2

RNSWE

If Pause is encountered
temporarily
so you can
execution,
press [_T_].

the current

value

is displayed.
and the result
line.

is
on
as

Output
PPgNA
THE ANSWER
IS
1.578796327
Done
after Disp, the program
halts
examine
the screen, To resume

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

DispGraph

(display-

graph)

displays

the current

graph.

Pause is encountered
after DispGraph,
the program
temporarily
so you can examine
the screen. Press
resume
execution,

If
halts

_

to

DispTable

DispTable (display
table) displays
program
halts temporarily
so you
Press _
to resume
execution,

Output(

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:

tile current table, The
can examine
the screen.

You may want to 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
row is 4.

value for

Programming

16-19

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

getKey

gaines.

Program
PROGRRM:GETKEV
:While 1
:getKeu+K
:While K=O
:getKe_eK
:End
:OisP K
:I¢ K=105

Output

PPg_GETKEV

Note: _,
[_,
[_,
and
were pressed during
program execution.

:Stop
:End
Note: You can press [_
program (page 16-5).

TI-83 Key Code
Diagram

at any time during execution to break the

C15D12_22!
IZD C_

IZ]

Ei_

--E521-

ClrHome (clear home screen)
during program execution.

ClrHome,
CIrTable

1
Done

clears the home screen

ClrTable (clear table) clears the values in the table during
program execution.

16-20

Programming

GetCalc(

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(

Get(, Send(

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
or picture,
variable
can be a list of elements.

database,

Send(variable)
PROGRRM:GETSOUND
:Send({3,.000_5,
99,1,0,0,0,0,1})
:Get(L1)
:Get(Lz)

Note: This program
and time in seconds
CBL 2/CBL.

gets sound data
from

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

Calling a
Program from
Another Program

as Subroutines

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
Subroutine

Output

H=5

62. 83185307
Done

I t

PROGRRM:RRERCIR:Return:n.RZ÷A:D/2÷R
I

Notes
Calling

about
Programs

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

7
Contents

Applications

Comparing
Test Results Using Box Plots ................
Graphing Pieeewise
Functions
...........................
Graphing Inequalities
....................................
Sohdng a System of Nonlinear
Equations
................
Using a Program to Create the Sierpinski
Triangle .......
Graphing Cobweb Attractors
............................
Using a Program to Guess the Coefficients
...............
Graphing the Unit Circle and Trigonometric
(;ma_es ......
Finding the Area between
Curves ........................
Using Parametric
Equations:
Ferris Wheel Problem ......
Demonstrating
the Fundamental
Theorem
of ('aleulus...
('omputing
Areas of Regular N-Sided Polygons
..........
Computing
and Graphing Mortgage
Payments
...........

TEXAS

17-2
17-4
17-5
17-6
17-7
17-8
17-9
17-10
17-11
17-12
17-14
17-16
17-18

TI-83

INSTRUMENTS

J
STATPLOT

TBLSET

FORMAT

CALC

TABLE

Applications

17-1

Comparing

Problem

Test Results

An experiment

Using Box Plots

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
Women
Le_

Women

8
9
12
11
10
8
12
7
9
11

Procedure

Guesses
Men

Men

Right

Left

Right

4
1
8
12
11
!1
13
!2
!1
12

7
8
7
5
7
8
11
4
!0
14
13
5

12
6
12
12
7
11
12
8
12
11
9
9

1, Press _
5 to 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
Right).

each

woman

made

using

her right hand

4. Likewise,
enter each lnan's correct
guesses
(Men Left) and MRGHT (Men Right).

(Women

in MLEFT

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
select
9:ZoomStat.
Thisadjusts
theviewing
windowand
displays
theboxplotsforthewomen's
results.
8. Press
_.

kd=9.5

Use

[]

and

[]

to

exalnine

minX, Ol, Med, O3,

right hand? With which hand
accurate
guessers,
according

maxX

and

for each plot. Notice the outlier to the women's
hand data. What is the median
ff)r the left hand?
were the women
to the box plots?

rightFor the
more

9. Examine
the men's results.
Redefine
plot 1 to use
MLEFT, redefine
plot 2 to use MRGHT. Press _.

_"

d=7.5

Men's right-hand data

" "

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

Problem

The

Functions

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

Procedure

fine (Y) as a function

of kilometers

per horn" (X) is:

Y=0

0Ymi
0->Xmi nn::l->Ymaxl->
Xmax

}

Set _qewing

window.

: rand->X: rand->Y
: Fo r ( K, 1,3 00 0 )
: rand->N

-1-- Beginning

of Fo

r

group.

:Then
:. 5X->X
::If.SY->Y
N<1/3
:End
:If
I/3X
:. 5( I+Y)->Y
:End

If/Then group.

:Then
:. 5 ( l+X )->X
::If. 5Y->Y
2/30

Dx

Ifx 1/t dt 1= 1/x

1.

Press

and that

1

1_.

Select

2. Press

_.
Xmin=.01
Xmax=10
Xscl=l

tile default

Set the viewing
Ymin=-l.5
Ymax=2.5
Yscl=l

settings.
window.
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

",Yt Bi'n InL(
1,X)
_¢2Bln(g)
4.

P1ot_

l/T,

T,

Press _.
Press [], [], [], and [] to eolnpare
values of Y1 and Y2,

the

5. 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
_,YuBI/X

, X,

Press _.
Again, use the cursor keys to compare
values of the two graphed functions, Y3 and Y4.

17-14

Applications

the

Problem 2

Explore

the functions
X

Y:f-2

Procedure 2

defined

by

X
t2dt'

f0

X
t2dt'

and

f2

t2dt

Press @, Turn off all functions
to define these three functions
the function
in Ys.

and stat plots.
sinmltaneously.

Use a list
Store

_'_=nDerib=(Yt"°Yz=lr_(x)l'x)Pl°t:L
Plol:Z
F'loL_. _ _
,,Y_B?nlnL(T

z,

'_Y_=I/X
i-::,o,2>,x)
2,

Press _

$ to select

3, Press _.
only shifted
Press

@,

T, (
$:ZStandard.

Notice that the functions
vertically
by a constant.
Enter

the numerical

\Y_=nDeriv(Y1,
X)
"*Y_=I/X
"..Y_B_nIn÷.(TZ,

appear

derivative

identical,

of Y5 in Y6,

X,
T, (

-2,0,2>,X)
\YeBnOer

iv(Y_,

X,

x)
Press _.

Notice that although the three graphs

defined by Y5 are different,
derivative,

they

share

tile

same

N="t.9£_Bi!_?i¢).6_,fiBt?9

Applications

17-15

Computing

Problem

Areas

Use

of Regular

the equation

N-Sided

solver

to store

regulm" N-sided polygon,
and then
given the other variables.
Explore
case is the area of a circle, _r 2.

Polygons

a fornmla

Consider
the fonnula
A = NB 2 sin(_/N)
m'ea of a regulm' polygon
with N sides
B distance
from the center to a vertex.

N = 4 sides

Procedure

ff)r the m'ea of a

solve for each vm'iable,
the fact that the limiting

cos(_/N)
for the
of equal length and

N = 8 sides

N = 12 sides

1, Press [_
0 to 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
then press [_.

as 0=A-NB2sin(_
The interactive

/ N)cos(_ / N), and
solver editor is

displayed.
R_NBZsin(_/N).,,=O

bound={
3, Enter

-1 E99,

1...

N=4 and B=6 to find the area

a distance

(B) from

center

to vertex

(A) of a square

with

of 6 centimeters,

4, Press [] [] to nlove the cursor
onto A, and then press
@
[SOLVE], The solution
for A is displayed
on the
interactive
solver editor.

:l-NBZsin(_/N)...=el

: 2.00o000000
I

B=6

bound={

-1 E99,

1...

le_t-rt=e
5. Now solve for B for 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 B for N=9, and
then for N=10.

17-16

Applications

FindtheareagivenB=6,
10000. Compare
with

radius

your

6), which

and N=10, 100, 150, 1000, and
results
with =62 (the area of a circle
is approximately

113.097.

7. Enter B=6. To find the area A, move
and then press @
[SOLVE]. Find
N=100, then N=160, then N=1000, and
Notice that as N gets large, the area

the cursor
onto A,
A for N=10, then
finally N=10000.
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 _.
Xmin=O
Xmax=200
Xscl=lO

Set the viewing window.
Ymin=O
Ymax=150
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 N Set 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 Y converges 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

8:tEE

_Y=lt3.0762B,

_Y:ti3.0973_

Applications

•

17-17

Computing

Problem

and Graphing

You at_ a loan

Mortgage

officer

Payments

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.

Procedure

1, Press [_
and set the fixed-decimal
lnode to 2 decimal
places. Set the other mode settings to the defaults.
2. Press [_ [FINANCE]
these values.

1 to display" the TVM Solver. Enter

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

Nowcompare
thegraphoftheamount
ofinterest
withthe
graphoftheamount
ofprincipal
foreachpayment.
4, Press
[NffffE].Set Par and Simul.
5, Press
these

@, Turn
equations

off all functions
and stat plots. Enter
and set the graph styles as shown.

Plot1 Plol:_ Plot_:
",XIT BT
Vi T BFPr'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
6, Press _.
Tmin=l
Tmax=360
Tstep=12

Set these window
Xmin:0
Xmax=360
Xscl=10

CALC menu,

variables.
Ymin=0
Ymax=1000
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
[] tomovethecursorontothefunction
for
interest
defined
byX2T
andY2T.
Enter240.

The graph shows that for the 240th payment (X=240),
441.97 of the 800 payment is interest (Y=441 .gT).
9. Press
home

_
[QUIT]
[_
screen.
Check

[FINANCE]

the figures

9 to paste 9:bal( to the
from the graph.

_ai(239)
-66295.33
_nsm(.08/12)
-441,97

At which monthly
payment
will the principal
surp_kss the interest
allocation?

17-20

Applications

allocation

18
Contents

Menrn2gq/ement

Checking A_ailable MemolTy .............................
Deleting Items from MemmTy ............................
Clearing Entries and List Elements
......................
Resetting the TI-83 ......................................

TEXAS INSTRUMENTS

I8-2
I8-3
18-4
18-5

TF83

RRM_
Delete...
3:Clear
Entries
4: CIRRI ILists
5: Reset...

J
STAT

PLOT

TBLSET

FORMAT

CALC

TABLE

Memory

Management

18-1

Checking

Available

MEMORY Menu

Memory

To display

the

MEMORY menu,

press

[_

[MEM].

MEMORY
i:

Check

RAM...

Reports
memory
availability/usage,
Displays
DELETE FROM menu,
Clem's ENTRY (l_kst-entry storage).

2: Delete...
3: Clear

Entries

4: ClrAllLists

Clears all lists in memo_T.
Displays RESET menu (all/defaults).

5: Reset..,

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
1. Press

RAM usage,

follow

[2_] [MEM] to display

these
the

steps.
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
String

Note:

The J_in the left column

of

the bottom row indicates that you
can scroll or page down to view
more variable types.

0
0

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 [_
@.
Both options
display- the home screen.

18-2

Memmw

Management

[QUIT] or

Deleting

Items from

Deleting an Item

Memory

To increase
any- variable
Y= variable,
follow these

available nlenlol_ by deleting the contents of
(real or colnplex nulnber, list, matrix,
prograln, picture, graph database, or string),
steps.

1. Press [2_] [MEN]to display the MEMORY lnenu.
2. Select 2:Delete to display- the DELETE FROM secondalTynleno.

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,
is displayed.

if you select 4:List, the DELETE:List screen

DELETE: Li_t
_LI
DATA

63
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 lastanswer variable Ans and the statistical variable RegEQ

Memory

Management

18-3

Clearing

Clear Entries

Entries

and List Elements

Clear Entries clears
storage
area
follow these
1, Press

[_

of the ENTRY (last entry)

the contents

(Chapter
steps.

1). To cleat" the

[MEM] to display

the

2, Select 3:Clear Entries to paste
home screen.
3. Press

[_

IcleaP

to clear

the

Entt'ie_one

area,

MEMORY menu.
the instruction

ENTRY storage

to the

area.

I

Clear Entries, press

To cancel

ENTRY storage

@,

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

CIrAIILists

sets to 0 tile

To clear

all elements

1, Press

[_

_

from

all lists,

[MEM] to display

2, Select 4:ClrAIIkists
screen.
3. Press

dimension

the

to paste

of each
follow

list in lllelllOl_yL
these

steps,

MEMORY menu,

the instruction

to set to 0 the dimension

to the home

of each

list in

nlenlory.

IC1rA11Lists
To cancel

CIrAIILists,

lionel
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

The

Resetting All
Memory

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.

seconda[7

RESET

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.

Tip: Before you reset all memory, consider restoring sufficient
available memory by deleting only selected data (page I8-3).
To reset

all nlenlory

1. Press

[2_] [MEM] to display

2. Select

5:Reset

_...

on the TI-83,

to display

the

follow

these

steps.

MEMORY menu.

the RESET

secondary

menu.

Mer_or-u...

2:: Defau
3, Select
tertimT

lts...

1 :All Memory to display

the

RESET MEMORY

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,
2:Reset. All factory defaults
are restored.
Mere cleared
is displayed
on the home screen.

I

Mem

select

cleared

Note:When you clearmemory, thecontrast
sometimeschanges.If
thescreenisfadedorblank,adjustthecontrast
(ChapterI).

Memory

Management

18-5

Resetting
Defaults

When

you reset

restored
are not

defaults

on the TI-83,

to the factory
changed.

settings.

Stored

These are some examples
of TI-83
restored
by resetting
the defaults.

defaults

are

and programs

that

are

Mode settings
such as Normal (notation);
Func
(graphing);
Real (numbers);
and Full (screen)

•

Y= functions

•

Window variable
values such
Xscl=l; YscI=I; and Xres=l

•

Stat plots

•

Format
settings
such as eoordOn
(graphing
on); AxesOn; and ExprOn (expression
on)

•

rand

seed

off

value

all TI-83

1. Press

[g_] [MEM] to display

factory

5:Reset

Consider

Xmax=lO;

coordinates

to 0

To reset

4.

as Xmin=-lO;

off

defaults,

to display

3. Select 2:Defaults
tertimT
menu.

to display

the

reset

follow

these

steps.

MEMORY menu.

the RESET

secondary

menu.

the RESET

DEFAULTS

of resetting

defaults.

the consequences

•

To cancel
1:No.

•

To restore
factory
default
settings,
select 2:Reset.
Default settings
are restored.
Defaults set is
displayed
on the home screen.

Defaults

Memmw

data

•

2. Select

18-6

all defaults

Management

and return

set

to the home

screen,

select

19
Contents

ci° municati°n
Getting Started: Sending Variables
.......................
TI-83 kINK ...............................................

19-2
19-3

Selecting Items to Send ..................................
Receiving Items ..........................................
Transmitting
Items .......................................
Transmitting
Lists to a TI-82 .............................
Transmitting
from a TI-82 to a TI-8:I .....................

19-4
19-5
19-6
19-8
19-9

Backing Up MemmTy".....................................

TEXAS INSTRUMENTS

19-10

1"1=83

RECEIVE

to TI82...

J
STAT

PLOT

TBLSET

FORMAT

CALC

T._,B L E

Communication

Link

19-1

Getting

Getting

Started:

Started

Sending

is a fast-paced

Variables

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 [] 5 Fgg6gl@
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 1 to
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_]
display the SENDmenu.

[LINK]

to

Z,_AI RECEIVE

6, Press 2 to select 2:All-. The All- SELECT
screen is displayed.

3:Prgm...
4:List...
5:List.s to TI82...
6:GOB...
7gPic...

Press [] until the selection cursor ( _ ) is
next to [A] MATRX.Press [ggTEg].

8. Press [] until the selection cursor is next
to Q REAL. Press [_.
A square dot next
to [A] and O indicates that each is selected
to send.

TRRNSMIT
k_
LIST
.L_
LIST
[R]
MRTRX
Window
WINOW
RclWindouZSTO
TblSet
TABLE
_Q
RERL

9.

SELECT

7,

On the sending unit, press [] to display the
TRANSMIT menu.

IdII._IIIiIIi

[llTransr_it
10. On the sending unit, press 1 to 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.
19-2

Conununication

Link

Receiving,..
[ R]
MRTRX
'Q

REDRLne

TI-83 LINK

TI-83 Link
Capabilities

The

TI-83

has a port to connect

and conlnlunicate

Linking Two
TI-83s

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
TI-83. To transmit
from one TI-83
steps on pages
19-6 and 19-7.

Linking a TI-82
and a TI-83

You can transfer
programs.
L1 through

fronl

a TI-82

that

enables

to another,

to a TI-83

Also, you cal_ tral_sfer
L6.

The softwaxe

from

Two
with

perform

follow

all variables
a TI-83

and
lisL_

is built int_) the

t_) a TI-83,

follow

•

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).

2. Insert

the other

calculator's

end of the cable

into

from

the

You cannot
TI-83,

either

backup

the

•

1. Insert

a memory

TM
TM

the

to a TI-82

this conunm_ication

TI-83. To tral_nlit
data from a TI-82
steps on pages 19-6 at_d 19-7.

Connecting
Calculators
the Cable

with

another TI-83, a TI-82, the Calculator-Based
Lal)oratory
(CBL 2 TM, CBL TM) System,
the Calculator-Ba_ed
Ranger
(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.

a TI-82

the port very

end of the cal>le into

to a

firmly.

the other

port.

Linking to a CBR
or the CBL 2/CBL
System

CBR and the CBL 2/CBL System are optional
that connect
to a TI-83 with the unit-to-unit
With a CBR or a CBL 2/CBL and a TI-83,
and analyze
real-world
data.

you can

Linking to a PC
or Macintosh

TI-GRAPH LINK TM is an optional
to enable conmmnication
with

that links
conlputer.

accessorya personal

Communication

accessories
link cal fie,
collect

Link

a TI-S3

19-3

Selecting

Items to Send

LINK SEND Menu

To display

LINK SEND menu,

the

press

[_

[LINK].

SEND RECEIVE
i : A11 +..,
2 : A11 -..,
3 : P rgm...
4:
5:
6:
7:
8:
9:
0:
A:
B:

Displays
Displays
Displays

Li st...
Lists
to T182...
GDB...
Pi c...
Matrix...
Real ...
Compl ex..,
Y Vars...
String.,.

C: Back Up.,,

M1 items
'all items

selected.
deseleeted.

all progranls
names.
'all list names,
Displays
Displays
list names L1 through
Displays
'all graph databases.
Displays
M1 picture
data types,
Displays
'all matrix
data types.
M1 real vmiables,
Displays
Displays
'all complex
variables.
M1 Y= variables.
Displays
Displays
all string variables.
Selects
all for backup
to TI-83.

Ls.

When you select an item on the LINK SEND menu, the
corresponding
SELECT screen is displayed.
Note: Each SELECT screen, except All+ SELECT, is displayed
initially with no data selected.

Selecting Items
to Send

To select items to send on the sending
steps.

unit, follow these

1. Press [2_] [LINK]to display" the LINK SEND 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
item you want to select or deselect.
4. Press _
nalnes

are

to select or deselect
with a ..

cursor

(_) to an

the iteln. Selected

nlarked

_

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

19-4

Conununication

Link

items.

Receiving

LINK RECEIVE
Menu

Receiving Unit

Items

To display

LINK RECEIVE menu,

the

SEND RECEIVE
1 : Re e e i v e
Sets

unit to receive

press

data

_

[LINK] C_.

transmission.

VClmnyou select 1:Receive from 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.

DuplicateName
Menu

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

Prompts to rename
Ove_wvrites data in
Skips transmission
Stops transmission

3: Omit
4: Quit

receiving variable.
receiving variable.
of sending variable.
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
data in the duplicated
variable
name. Transmission
resumes
with the next item.
When

you select

receiving

Insufficient
Memory in
Receiving Unit

unit

4:Quit, transmission

exits

receive

stops,

send

the

and the

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
select 2:Quit.

and exit receive mode,

Communication

Link

19-5

Transmitting

Items

Transmitting
Items

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.
unit to display- the TRANSMIT

1. Press [] on tile sending
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.

*'79
9t

EQoUoneEQU
I

*V_
VIRotei_,,i
ng...
EQ_oneEQU
I

After all selected items have been transmitted,
the lnessage
Done is displayed on both calculators. Press [] and [] to
scroll through the names.
Stopping a
Transmission

To stop a link transmission,
press []_]. The Error in Xmit
menu is displayed on both units. To leave the error menu,
select 1 :Quit.

Error Conditions

A transnlission

error

occurs

after

one or two seconds

•

A cable

is not

attached

to the sending

•

A cable

is not

attached

to the receiving

if:

unit.
unit.

Note: If the cane is attached, push it in firmly and try again.
•

The receiving

•

You

•

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.

attempt

unit is not
a backup

Although a transmission
conditions nlay prevent

19-6

Conununication

set to receive

between

transmission.

a TI-82

and a TI-Sa.

error does not occur, these two
successful transmission.

•

You ttT to use Get( with a calculator
CBL 2/CBL or CBR.

•

You tit to use GetCalc( with a TI-82 instead

Link

instead

of a
of a TI-83,

Transmitting
Items to an
Additional TI-83

After sending
transmission
sending
reselect

or receiving
to additional

data, you can repeat
the same
TI-83 units--from
either the

unit or the receiving
unit--without
data to send. The current
items

having to
remain
selected.

Note: You cannot repeat transmission if you selected All+ or All-.
To transmit

to an additional

1, Set the TI-83

TI-83,

to receive

(page

follow

these

steps.

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
to the additional
TI-83,
4.

Set the additional

TI-83

from

one TI-S3

to receive

5, Press [7_ [LINK] on the sending
LINK SEND menu.

(page

TI-83

and connect

19-5),

to display

the

6, Select the menu item that you used for the l_kst
transmission.
The data from your last transmission
still selected.
7, Press
8,

[] to display

Confirm
(page

9, Press

that

the

LINK TRANSMIT

the receiving

unit

it

is

menu,

is set to receive

19-5).
[EfiY_ to select

1 :Transmit

and begin

Communication

translnitting.

Link

19-7

Transmitting

Lists to a TI-82

Transmitting
Lists to a TI-82

The

only data

is list data
To transmit
lists

type

stored

you can transmit
in L1 through

to a TI-82

the list data

L1, L2, L3, L4, LS, or L6, follow

1, Set the TI-82

to receive

fronl

a TI-83

to a TI-82

L6.

(page

that

is stored

these

steps.

to TI-83

19-5).

2, Press [_
[LINK] 5 on the sending
TI-83 to select
5:Lists to TI82. The SELECT screen is displayed.
3, Select
4. Press

each

[] to display

5, Confirm that
(page 19-5).
6, Press

list to transmit.

[_

the

LINK TRANSMIT

the receiving

to select

unit

menu,

is set to receive

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

but differences
between
tile two products
may affect some
transmitted
data, This table shows differences
for which

GenerMly,

you can transmit

items

to a TI-83

fronl

the software
built into the TI-83 automatically
when a TI-83 receives
TI-82 data,
TI-82

TI-83

nMin

PlotStart

nStart
Un
Vn

nMin
u
v

UnStart
VnStart
TblMin

u(nMin)
v(nMin)
TblStart

a TI-82,

adjusts

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
conlnland
line,

Unresolved
Differences
between the TI-82
and TI-83

The

s(dtware

differences
described

built

into

replaced

nStart

the TI-S3 cannot

on the

resolve

some

between
the TI-82 and TI-83, which are
below. You nmst edit the data on the TI-83

you transmit
to account
for these
will misinterpret
the data.

differences,

The TI-83 reinterprets
TI-82 prefix functions
()pen parentheses,
which may add extraneous
to transmitted
expressions.

after

or the TI-83

to include
parentheses

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 5 and 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

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:
receiving
receiving

C:Back Up ove_wvrites
the lnelnol_y- in the
unit; all information
in the lnelnory
of the
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_
2: Quit

Receiving Unit

i t

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,
The backup transmission
begins.
To prevent the backup, select 2:Quit.

Note:If a transmissionerroris returnedduring
unit is reset.
Memory Backup
Complete

(domnmnication

a backup,

the receiving

When the backup is complete, both the sending calculator
and receiving calculator display a confirlnation
screen.
IMEMOR'? BACKUDPonel

19-10

select 1:Continue.

Link

A
Contents

Tablesand Reference
Information
Table

of Functions

and Instructions

.....................

TI-83 Menu Map .........................................
Variables
................................................
Statistics
Formulas
......................................
Financial Formulas
......................................

Tables

and

Reference

A-2
A-39
A-49
A-50
A-54

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/
Arguments
abs(value)

abs(complex

'value)

Returns the nmgnitude of a
complex nmnber or list.

ANOVA(listl,list2
[,list3,...,list20])

Ans

and

CPX
5:abs(
[_ [TEST]
LOGIC
1 :and

Returns 1 if both valueA and
valueB are € 0. valueA and
valueB ean be real numbers,
expressions, or lists.
Returns the polar angle of a
[_
complex number or list of
CPX
complex numbers.
4:angle(
Performs a one-way analysis of [gg_]
variance for comparing the
TESTS
means of two to 20
F:ANOVA(
populations.
Returns the last answer.
[_
[ANS]

angle{value)

Tables

Key or Keys/
Menu or Screen/Item

Returns the absolute value of a [_
real number, expression, list,
NUM
or matrix.
1 :abs(

valueA and valueB

A-2

Result

Reference

Information

2-13
10-10

2-19

2-26

2-19

13-25
1-18

Function or Instruction/
Arguments

Result

Key or Keys/
Menu or Screen/Item

Retm'ns a mahlx, width is
matrixB
appended to matrixA
as new colunms.

MATH
7:augment(

10-14

augment(listA,listB)

Returns a list, which is listB
concatenated
to tile end of
listA.

_
[LIST]
OPS
9:augment(

11-15

AxesOff

Turns off the graph axes.

; [2_

AxesOn

Turns on tile graph axes.

; [2_ [FORMAT]
AxesOn
3-14

a+bl

Sets tile mode to reetangular
complex number mode (a+bi).

i I_
a+bi

bal(npmt[,roundvalue])

Computes
the balance at npmt
for an amortization
schedule
using stored values for PV, I%,
and PMT and rounds the
computation
to roundvalue.

[_
[FINANCE]
CALC
9:bal(

binomcdf(numtrials,p[,x])

Computes
a cumulative
probability
at x for the discrete
binomial distribution
,slth tile
specified numtrials
and
probabilityp
of success
on
each trial.

[_
[D}STR]
DISTR
A:binomcdf(

binompdf(numtriols,p[,x])

Computes
a probability
tile discrete binomial

at x for

[_
[DtSTR]
DISTR

distribution
_ith tile specified
nuratrials
and probabilityp
of
success on each trial.

0:binompdf(

Computes
tile g 2 distribution
probability
between
lower'bound
and upped)ound
for the specified
degrees of
freedom dJ2

_
[DISTR]
DISTR
7:x2cdf(

augment(matrixA,matrixB)

[FORMAT]

AxesOff

x2cdf(low6_pbound,
upperbound,dy')

Tables

and

Reference

3-14

1-12

14-9

13-33

13-33

13-31

Information

A-3

Function or Instruction/
Arguments
z2pdf(x,dj ")

Key or Keys/
Menu or Screen/Item

Result
Computes the probabi]ity
density function (pdf) for tile
X2 distribution
at a specified
x
value for the specified
degrees
of freedom
df

[_

z2-Test(observedmatrix,
expeetedmatrix
[,drawflag])

Performs
a ehi-square
test.
drmqflag=l
draws results;
drmqflag=O
calculates
results.

i [_
TESTS
C:x2-Test(

Circle(X,Y, radius)

Draws a circle with
(X,Y) and radius.

[_

Clear Entries

center

Clears the contents of the Last
EntKy storage area.

ClrAIILists

Sets to 0 the dimension
lists in memoKy'.

ClrDraw

Clears all drawn elements
a graph or dra_lng.

from

ClrHome

Clears

Clrkist listnamel
[,listuame2,
...,
listname
n]

Sets to 0 the dimension
or more listnames.

ClrTable

Clears
table.

conj(value)

Returns tile complex
of a complex number
complex numbers.

Connected

Sets connected
plotting mode;
resets all Y= editor graph-style
settings to "...

A-4

Tables

and

Reference

the home

of all

all values

Information

screen,

of one

from the

conjugate
or list of

[DISTR]

DISTR
6:z2pdf(
13-31

13-22

[DRAW]

DRAW
9:Circle(

8-11

[_dl [MEM]
MEMORY
3:Clear Entries

18-4

[_
[MEM]
MEMORY
4:ClrAIIkists

18-4

[_
[DRAW]
DRAW
1 :ClrDraw

8-4

i [0ggM]
IIO
8:Clrl-tome

16-20

[gg_]
EDIT
4:ClrList

12-20

i [gggM]
I/O
9:ClrTable

16-20

[_TH]
CPX
1 :conj(

2-18

i
Connected
1-11

Function or Instruction/
Arguments
CoordOff

Key or Keys/
Menu or Screen/Item

Result
TLims oft" cursor coordinate
value display.

i- _

CoordOn

Turns on cursor
value display.

1 [2_

cos(value)

Returns cosine of a
real nunlber,
expression,
list.

[FORMAT]

CoordOff

coordinate

CoordOn
or

arccosine
of areal
expression,
or list.

2-3

Returns
number,

cosh(value)

Returns hyperbolic
cosine of a
real number,
expression,
or
list.

Kffd] [CATALOG]
cosh(

cosh-l(value)

Returns hyperbolic
arccosine
of a real number,
expression,
or list.

Kffd] [CATALOG]
cosh-l(

CubicReg [Xlistname,
Ylistname_fr_qlist,
regequ]

Fits a cubic regression
model
to Xlistname
and Ylistname
with frequencyfrvqlist,
and
stores tile regression
equation
to vegequ.

NTAf]
CALC
6:CubicReg

cumSum(list)

Returns a list of the cumulative
stuns of tile elements
in list,
starting _lth the first element.

[_
[LIST]
OPS
6:cumSum(

cumSum(matrix)

Returns a matrix
cunmlative
sums

MATH

of tile
of matrix

Kffd] [cos -1]
2-3

15-10

15-10

12-26

elements.
returned

Each element inthe
nmtrlx is a cunmlative
SUnl
of a matrix
cohlnln fi'om
to[) to bottom.

0:cumSum(

dbd(datel,date2)

Calculates
the number of days
between date1 ram date2 using
the actual-day-count
method.

Kffa] [F,NANCE]
CALC
D:dbd(

value_Dec

Displays a real or complex
number, expression,
list, or
matrix in decimal format.

MATH
2:_Dec

and

3-14

[g6N]

cos-l(volue)

Tables

3-14

[FORMAT]

Reference

11-12

10-15

Information

14-13

2-5

A-5

Function or Instruction/
Arguments

Result

Key or Keys/
Menu or Screen/Item

Degree

Sets degree angle mode.

i

DelVar variable

Deletes from nlemolTy" the
contents
of .variable.

i

DependAsk

Sets table to ask for
dependent-variable
values.

-1-[_

DependAuto

Sets table to generate
dependentwariable
values
automatically.

-;- [_

Degree

det(matrix)

Returns
matrix.

determinant

DiagnosticOn

Sets

dim(listname)

Returns tile dilnenslon
listname.

of

dim(matri:vname)

Returns tile dimension
matri:_'name
as a list.

of

Depend: Auto
7-3

Assigns anew dimension
(length) to a new or existing
listname.
Assigns new dimensions
to a
new or existing matri:vname.

Disp

Displays

and Reference

10-12

_
[CATALOG]
DiagnosticOff
12-23

mode; r, r2, [_
[CATALOG]
and R2 m'e displayed as
DiagnosticOn
regression model results.

Disp [valueA,valueB,
valueC,...,value
n]

7-3

[TBLSET]

diagnostics-on

{rows,columns}->
dim(matri:vname)

Tables

Depend: Ask

MATH
l:det(

Sets dia_lostlcs-offmode;
r, r2,
and R 2 are not displayed as
regression model results.

length->dim(listname)

16-15

[TBLSET]

of

DiagnosticOff

A-6

CTL
G:DelVar

1-11

Displays

the home

each value,

Information

screen.

12-23

[_
[LIST]
OPS
3:dim(

11-11

MATH
3:dim(

10-12

_

[LIST]

OPS
3:dim(

11-11

MATH
3:dim(

10-13

i
IIO
3:Disp

16-18

I/O
3:Disp

16-18

i

Function or Instruction/
Arguments

Result

DispGraph

Displays tile graph.

DispTable

Displays

value_DMS

Displays

Key or Keys/
Menu or Screen/Item
; I_
I/O

tile table.

value

4:DispGraph

16-19

IIO
5:DispTable

16-19

-;-

il1 [)MS fornlat.

[_

[ANGLE]

ANGLE
4:_DMS
Dot

Sets (lot plotting

mode; resets

all.Y= editor graph-style
to ...
DrawF expression

Draws expression
X) on the graph.

i [_

settings

(in terms

of

Dot
[DRAW]
DRAW
6:OrawF

Draws the immerse of
expression
by plotting X values
on the y-axis and Y values on
the x-axis.

[_
[DRAW]
DRAW
8:Drawlnv

:DS<(variable,value)
:commandA
:commands

Decrements
variable by 1;
skips cornmandA
if variable
value.

i

e^(power)

Returns

e^(list)

Returns a list of e raised
list of powers.

Exponent:
valueEexponez_t

Returns value
exponez_t.

Exponent:
listEe_onent

Retm'ns list elements
to the exponent.

Exponent:
rnatrixEexponecnt

Returns matrix
elements
10 to the exponea_t.

_Eff(nominal
rate,
compounding
periods)

Computes
rate.

8-9

8-9

<

to power.

1-11

[_

Drawlnv expression

e raised

2-24

CTL
B:DS<(
_

[ex]

_

[ex]

[_

[EE]

[_

tEE]

[_

tEE]

16-14
2-4

times

to a

2-4

10 to the

1-7

the effective

times 10

1-7
times

1-7
interest

[_
[FINANCE]
CALC
C:_Eff(

14-12

Else
See If:Then:Else

Tables

and

Reference

Information

A-7

Function or Instruction/
Arguments
End

Key or Keys/
Menu or Screen/Item

Result
Identifies
end of For(,
If-Then-Else,
Repeat, or While
loop.

Eng

Sets engineering

display

-;CTL
7:End

mode.

Eng
Equ)String(Y=

va_;Stru)

1-10

Converts
tile contents
of a Y=
vat to a string and stores it in
Stru.

[_
[CATALOG]
Equ)String(

expr(string)

Com_erts
expression

[_

ExpReg [Xlistname,
}qistuame,flreqlist,regequ]

Fits an exponential
regression
model to Xlistuame
and
lqistuame
with frequency
freqlist, and stores the
regression
equation to regequ.

ExprOff

Turns off the expression
display during TRACE.

-;- [_

ExprOn

Turns on the expression
display during TRACE.

-;- [_

Fcdf(lowerbound,
upperbound,
numerator
df,
denominator
dr)

Computes
the F distribution
probability
between
lowerbound
and upperbound
for the specified
numerator
(degrees of freedom) and
denominator
djr

_M]

Fill(value,raatri:_name)

Stores value
mat.ri:vname.

to each

Fill(volue,listuame)

Stores value
listuame.

to each

Fix #

Sets fixed-decimal
of decimal places.

Float

A-8

SD'_ng

and

Reference

Information

decimal

15-7

all

and executes

Sets floating

Tables

to

[CATALOG]

expr(

it.

15-7

CALC
0:ExpReg
12-26
[FORMAT]

ExprOff

3-14

[FORMAT]

ExprOn

3-14

[DISTR]

DISTR
9:Fcdf(
df

element

element

mode for #

mode.

16-12

i

13-32
in
MATH
4:Fill(

10-13

in _
[LIST]
OPS
4:Fill(

11-11

i
0123456789
(select
one)

1-10

Float

1-10

i

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

fMax(expression,variable,
lower',upper'[,tolerance])

Retm'ns the value of variable
where the local maximum
of
expression
occm's, between
lower" and upper', with
specified
toleronee.

fMin(expression,variable,
lower',upper'[,toleranee])

Returns tile value of variable
where the local mininmn] of
expression
occm's, between
lower" trod upper', with
specified
toleronee.

fnlnt(expression,variable,
lower',upper'[,tolerance

Returns the function
integral of [_
expression
with respect to
MATH
variable, between/ower,
and
9:fntnt(
upper', with specified
toleronce.

FnOff [function#,
function#,...,function
FnOn [function#,
.function#,..._function

D

n]

Deselects
specified

all Y= functions
Y= functions.

n]

Selects all Y= fimctions
specified Y= functions.

MATH
7:fMax(
2-6
MATH
6:fMin(
2-6

Y-VANS On/Off
2:FnOff

3-8

Y-VANS On/Off
1 :FnOn

3-8

or

:For(variable,begin,er_d
[,incremer_t])
:commands
:End
:commands

Executes
commands
through
End, incrementing
variable
fi'om begin by increment
until
variable>end.

i [gggM]
CTL
4:For(

fPart(value)

Returns the fractional
part or
pm'ts of a real or complex
number, expression,
list, or
matrix.

[_
NUM
4:fPart(

Computes
tile g distribution
probability
between
lower'bound
and upperbound
for tile specified
numerator
(degrees of freedom)
and
dermminator
df

[_

Fpdf(x,numerotardf,
denominator
dy)

2-7

or

16-10

Tables

and

2-14
10-11

[DtSTR]

DISTR
8:Fpdf(
df

Reference

13-32

Information

A-9

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

value_Frac

Displays a real o1"eon]plex
nmnber, expression,
list, or
matrix as a fraction simplified
to its simplest terms.

[_
MATH
1 :_Frac

Full

Sets full screen

i [_
Full

Func

Sets function

mode.
graphing

mode.

2-5

Func
gcd(valueA,

valueB)

geometcdf_,x)

geometpdf(p,x)

Get(variable)

GetCalc(variable)

Returns the greatest
common
divisor of volueA and valueB,
which can be realnmnbers
or
lists.

[_
NUM
9:gcd(

(;omputes
a emnulative
probability
at x, the number of
the trial on which the first
suceess oeeurs, for tile diserete
geometric distribution
with tile
specified
probability
of success
p.

[_

Computes a probability at x, the
number of the trial on which the

[_
[DISTR]
DISTR

first success occurs, for the
discrete geometric distribution
wlth the specified probability of
success p.

D:geometpdf(

Gets data from the CBL 2/CBL
System or CBR and stores it in
variable.

-;-

Gets contents of variable
on
another TI-83 and stores it to

i

variable

1-12

i
1-11

2-15
[DISTR]

DISTR
E:geometcdf(

13-34

13-34
I/O
A:Get(

16-21

I/O

on the receix_ N TI-83.

0:GetCalc(

16-21

getKey

Returns tile key code for the
current keystroke,
or 0, if no
key is pressed.

i [0_
IIO
7:getKey

16-20

Goto label

Transfers

i

control

to label.

CTL
O:Goto

A-IO

Tables

and

Reference

Information

16-13

Function or Instruction/
Arguments

Result

Key or Keys/
Menu or Screen/Item

GraphStyle(function#,
grophstyle#)

Sets a grophstyle
function#.

GridOff

Turns

off grid format,

i- _

GridOn

Turns on grid format.

-;- _

G-T

Sets graph-table vertical
split-screen
mode.

i

Horiz

Sets horizontal
split-sereen
mode.

for

-;CTL
H:GraphStyle(
16-15
[FORMAT]

6ridOff

Horizontal

y

identity(dimension)

Draws

a horizontal

line at y.

Returns the identity matrix of
dimension
rows x dimension
eolumns.
= O (false),

skips

3-14

[FORMAT]

GridOn

3-14

G-T

1-12

i I_bg]
Horiz

1-12

[_
[DRAW]
DRAW
3:Horizontal
MATH
S:identity(

:If condition
:commandA
:commands

If condition
commandA.

i [g_
CTL
1:If

:If condition
:Then
:commands
:End
:commands

Executes
commands
from
Then to End if condition
= 1
(true).

i [0ggM]
CTL
2:Then

:If condition
:Then
:commands
:Else
:commands
:End
:commands

Executes
commands
from
Then to Else if condition
= 1
(true); from Else to End if
condition
= O (false).

i [0ggM]
CTL
3:Else

imag(value)

Returns the imaginmTy
(nonreal)
part of a complex
number or list of complex
numbers.

8-6

10-13

16-9

16-9

16-10

Tables

and

Reference

CPX
3:imag(
2-18

hfformation

A-11

Function or Instruction/
Arguments
IndpntAsk

Key or Keys/
Menu or Screen/Item

Result
Sets table to ask for
independent-variable

-;-[_
[TBLSET]
Indpnt: Ask

values.

IndpntAuto

Sets table to generate
independent-variable
values
automatically.

-1-[2_
[TBLSET]
Indpnt: Auto

Input

Displays

graph.

-1IIO
1:Input

Input [.variable]

Prompts

for value

Input

variable.

["text",variable]

Input [Strn,variable]

to store

7-3

to

I/0
1:Input

16-17

I/O
1:Input

16-17

-;-

inString(s#qng,subs#qng
[,start])

Returns tile (-haraeter position
in string of tile first eharaeter
of substring
beginning
at start.

[_
[CATALOG]
inString(

int(value)

Returns the lm'gest integer
real or complex ntmlber,
expression, list, or matrkx.

[_TH]
NUM
5:int(

_(variable,value)
:commandA
:commands

Increments
variable
by 1; skips commandA
variable>volue.

i

Llistname

Identifies
characters
list name.

LabelOff

Turns off axes

14-8

LabelOn

if

the next one to five
as a user-created
labels.

CTL
A:IS>(

16-13

[_
[UST]
OPS
B:L

11-16

-1-[_
[FORMAT]
LabelOff

Turns ol1 axes labels,

i- [_

[FORMAT]

LabelOn
Lbl label

3-14
3-14

Creates a label of one or two
characters.

i

Icm(valueA,valueB)

Returns the least conunon
inultiple of volueA and valueB,
which can be real nulnbers
or
lists.

[_
NUM
8:lcm(

length(string)

Returns the number
chm'aeters
in st_ng,

[_
[CATALOG]
length(

Line(X1,Y1Jd2,Y2)

[)raws a line from
(X2,Y2).

(X1,Y1)

to

[_
[DRAW]
D RAW
2:Line(

S-5

Line(X1,Y1,X2,Y2,0)

Erases a line from
(X2,Y2).

(X1,Y1)

to

[_
[DRAW]
D RAW
2:Line(

8-5

Tables

and

of

Reference

CTL
9:Lbl

16-13

2-15

Information

15-8

A-13

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

LinReg(a+bx) [Xlistname,
Iqistname,freqlist,
regequ]

Fits a linear regression inodel
to Xlistname
and Iqistname
with frequencyfrvqlist,
and
stores the regression
equation
to regequ.

kinReg(ax+b)
[Xlistname,
Iqistname_freqlist,
regequ]

Fits a linear regression
model
to Xlistname
and Iqistname
with frequency.fr_qlist,
and
stores the regression
equation
to regequ.

[g_g]
CALC
4:kinReg(ax+b)

LinRegTTest [Xlistname,
Iqistname,freqlist,
olternative,regequ]

Performs
a linear regression
and a t-test, alternative=-1
is
<; alternative=O
is €;
alternative=l
is >.

i [g_g]
TESTS
E:LinRegTTest

AList(list)

Returns a list containing
the
differences between
consecutive
elements in list.

_

Fills matrixname
colunm by
cohmm with the elements from
each specified listuame.

[_

In(value)

Returns the natural logarithm
of a real or complex number,
expression,
or list.

@

knReg [Xlistname,
Ylistname,fr_qlist,
regequ]

Fits a logarithmic
regression
model to Xlistuame
and
}qistuame
with frequency
freqlist, and stores the
regression
equation to regequ.

[g_T]
CALC
9:LnReg

log(value)

Returns

[[OG]

List_ matr(listnamel,...,
listname n,matri:_'name)

complex

logarithm
nilnlber,

or list.

A-14

Tables

and

Reference

Information

of a real or
expression,

CALC
8:LinReg(a+bx)
12-26

12-25

13-24
[LIST]

OPS
7:AList(

11-12

[LIST]

OPS
0:List _ matr(

10-14
11-15

2-4

12-26

2-4

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

Logistic [Xlistname,
YTist.name,fr_ql.ist,
regequ]

Fits a logistie regression mode]
to Xlistname
and YTistname
with frequeneyfr_qlist,
and
stores the regression
equation
to regequ.

[gTAT]
CALC
B:kogistic

Matr_ list(matrix,
listnameA,...,listname

Fills each listname
with
elements
from eaeh column
matrix.

[_
[LIST]
OPS
A:MatO list(

n)

MatrMist(mat.rix,
column#,listname)

Fills a listuame
from a specified
matrix.

rnax(valueA,valueB)

Returns the larger
and valueB.

in

_lth elements
eoluran#
in

12-27

[_

10-14
11-16

[LIST]

OPS
A:MatO list(

10-14
11-16

of valueA
NUM
7:rnax(

2-15

max(list)

Returns largest real or
complex element in list.

[2_] [LIST]
MATH
2:max(

rnax(listA,listB)

Retm'ns a real or eomplex list of
the larger of each pair of
elements in listA and listB.

[2_] [LIST]
MATH
2:max(

max(value,

Retm'ns a real or complex list of
the larger of value or each list
element.

[_
[LIST]
MATH
2:max(

11-16

rnean(list[,frvqlist])

Returns the mean
frequeney frvqlist.

[_
[LIST]
MATH
3:mean(

11-16

median(list[,fr_qlist])

Returns the median
frequeney frvqlist.

[_
[LIST]
MATH
4:median(

11-16

Med-Med [Xlistname,
Ylistname_fr_qlist,
regequ]

Fits a median-median
model to
Xlistname
and Ia'ist'name _lth
frequeneyfrvqlist,
and stores
the regression
equation to
regequ.

Menu("title","textl"',labell
[,...,"textT',labelT])

Generates
a menu of up to
seven items during program
exeeution.

11-16

11-16
list)

Tables

and

of list with

of list with

Reference

CALC
3:Ned-Ned
12-25
i [_
CTL
C:Menu(

16-14

hfformation

A-15

Function or Instruction/
Arguments
min(valueA,valueB)

Key or Keys/
Menu or Screen/Item

Result
Returns
valueB.

smaller

of valueA

and
NUM
6:min(

min(list)

Returns smallest
complex element

real or
in list.

_

2-15

[LIST]

MATH
l:min(

11-16

min(listA,listB)

Returns real or complex
list of
tile smaller of each pair of
elements
in listA and listB.

[_
[LIST]
MATH
1 :min(

11-16

min(value,list)

Returns a real or complex list
of the smaller of value or each
list element.

_
[LIST]
MATH
1 :min(

11-16

Returns the number of
combinations
of valueA
valueB at a time.

[_
PRB
3:nOr

2-21

Returns a list of the
combinations
of value taken
each element in list at a time.

PRB
3:nCr

2-21

Returns a list of the
combinations
of each element
in list taken value at a time.

PRB
3:nCr

2-21

nCr valueB

valueA

value

nCr list

list nCr value

listA

nCr listB

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

*Nom(ef_t_ct'ive
compounding

rate,
pe/riods)

Normal

taken

Returns a list of the
combinations
of each element
in listA taken each element in
listB at a time.

[_TH]
PRB
3:nOr

Returns approximate
numerical
derivative
of
expression
with respect
variable at value, with
specified
e.

[_
MATH
8:nDeriv(

Computes
rate.
Sets normal

the nominal

display

to

2-21

2-7
interest

mode.

[2_] [FINANCE]
CALC
B:*Nom(
Normal

A-16

Tables

and

Reference

Information

14-12

i
1-1O

Function or Instruction/
Arguments
normalcdf(low_rbound,
upperbound
[, _,(_])

Key or Keys/
Menu or Screen/Item

Result
(;omputes
tile normal
distribution
probability
between low_rbound
and
upperbound
for the specified
and _.

[_
[DISTR]
D IST R
2:normalcdf(
p
13-27

normalpdf(x[,p,(_])

(;omputes
tile probability
[_
[DtSTR]
density function for the nornlal
DISTR
distribution
at a specified x
1 :normalpdf(
value for tile specified/_ and c_.

not(value)

Returns 0 if value is :/: 0. value
can be a real number,
expression,
or list.

[_
[TEST]
LOG IC
4:not(

2-26

Returns tile number of
permutations
of volueA
valueB at a time.

taken

[_TH]
PRB
2:nPr

2-21

nPr list

Returns a list of tile
permutations
of value taken
each element in list at a time.

[_TH]
PRB
2:nPr

2-21

list nPr value

Returns a list of tile
permutations
of each element
in list taken value at a time.

[_TH]
PRB
2:nPr

2-21

Returns a list of tile
permutations
of each element
in listA taken each element in
listB at a time.

[_TH]
PRB
2:nPr

npv(interest
rate,CFO,
CFList[,CFFreq])

Computes
the sum of the
present values for cash inflows
and outflows.

[2_] [FINANCE]
CALC
7:npv(

valueA

Returns 1 if valueA or volueB
is € 0. volueA and valueB can
be realnumbers,
expressions,
or lists.

[2_] [TEST]
LOGIC
2:or

valueA

value

listA

nPr valueB

nPr listB

or volueB

Tables

and

Reference

13-29

2-21

14-8

2-26

hfformation

A-17

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

Output(vow,coluran,"text")

Displays
specified

text beginning
at
row and column.

i [P_M]
I/O
6:Output(

16-19

Output(row,column,value)

Displays
specified

value begiJming at
row and column.

i [gggN]
I/O
6:Output(

16-19

Param

Sets parametric
mode.

Pause

Suspends
program
until you press _.

Pause ['value]

Displays value; suspends
program execution
until you
press [_.

i

Plot#(type,Xlistuame,
YTistname,mark}

Defines Plot# (1, 2, or 3) of
type Scatter
05"xyLine for
Xlistuame
and Iqistuame
using mark.

1 [2_]

Plot#(type,Xlistuame,
,frvqlist)

Defines Plot# (1, 2, 05"3) of
type Histogram 05"Boxplot for
Xlistuame
_lth frequency
fr_qlist.

; [2_] [STAT PLOT]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
12-37

Plot#(type,_istuame,
.fr_qlist,mark)

Defines Plot# (1, 2, or 3) of
type ModBoxplot for
Xlistname
_lth frequency
frvqlist using mark.

-;-[_
[STAT
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(

Plot#(type,datalistname,
data axis,mark)

Defines Plot# (1, 2, 05"3) of
-;-[_
[STAT PLOT]
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
or more specified stat [)lots (1,
2, 05"3).

_
[STAT
PLOT]
STAT PLOTS
4:PlotsOff
12-35

PlotsOn [1,2,3]

Selects all stat plots o1" one or
more specified
stat plots (1, 2,
or 3).

[_
[STAT PLOT]
STAT PLOTS
5:PlotsOn
12-35

A-18

Tables

and

Reference

Information

graphing

i
Par

execution

1-11

i [gggN]
CTL
8:Pause
CTL
8:Pause
[STAT

PLOTS
1:Plot1(
2:Plot2(
3:Plot3(

16-12

16-12
PLOT]

12-37

PLOT]

12-37

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

Pmt_Bgn

Specifies an mmuity due,
where payments
occur at the
beginning
of each payment
period.

F2Ta] [FINANCE]

Pmt_End

Specifies an ordinary annuity,
where payments
occur at the
end of each payment period.

F2na][FINANCE]
CALC
E:Pmt_End

poissoncdf(,u,x)

(;omputes
a cumulative
probability
at x for the discrete
Poisson distribution
with
specified
mean ,u.

[_

Computes a probabilii7 at x for
the discrete Poisson distribution

F2na][DtSTR]
DISTR

with the specified

B:poissonpdf(

poissonpdf(_,x)

Polar
eomplex

Sets polar
'value i.Polar

CALC
F:Pmt_Bgn
14-13

nlean _.

graphing

Displays eomplex
polar format.

PolarGC

Sets polar graphing
coordinates
fornmt.

prgmname

Executes

DISTR
C:poissoncdf(
13-34

Pol

1-11

CPX
7:_Polar

2-19

'value in

; r2_ [FORMAT]
PolarGC
3-13

the program

name.

EPrn(pmtl,pmt2
[,roundvolue])

Computes
the sum, rounded
roundvalue,
of the prineipal
amount between pmtl
and
pint2 for an amortization
schedule.

prod(list[,sta,r¢,e/nd])

Returns product
of list
elements
between start
end.
n]

Prompts for value for
variableA,
then variableB,
so on.

Tables

13-33

i

mode.

i
CTRL
D:prgm

Prompt variableA
[,variableB,...,vaviable

14-13

[DtSTR]

and

to

16-15

[_
[FINANCE]
CALC
0:EPrn(
14-9

and

and

Reference

[_
[LIST]
MATH
6:prod(

11-18

i [0ggM]
I/O
2:Prompt

16-18

hfformation

A-19

Function or Instruction/
Arguments

Result

1-PropZlnt(x,n
[,confidence
level])

Computes
a one-proportion
z eonfidence
interval.

i

2-PropZlnt(xl,nl
[,confidence

Computes
a two-proportion
z eonfidence
interval.

i

1-PropZTest(pO,x,n
[,alternative,drawflag])

Computes
a one-proportion
z test. olternative=-I
is <;
alternative=O
is _;
alternative=l
is >. d'rmqflog=l
draws results; drawflog=O
calculates
results.

i

2-PropZTest(xl
,nl ,x2,n2
[,alternative,drawflog])

Computes
a two-proportion
z test. olternative=-I
is <;
alternative=O
is €;
alternative=l
is >. drmqflog=l
draws results; drawflog=O
calculates
results.

i [g_g]
TESTS
6:2-PropZTest(

Pt-Change(x,y)

Reverses

[_
[DRAW]
POINTS

Pt-Off(x,y[,mark])

Erases
mark.

a point

at (x,y) using

Pt-On(x,y[,mark])

Draws
mark.

a point

at (x,y) using

PwrReg [Xlistname,
Ylistname,freqlist,
regequ]

Fits a power regression
model
to Xlistname
and Ylistname
with frequencyfr_qlist,
and
stores the regression
equation
to regequ.

,x2,n2
level])

Key or Keys/
Menu or Screen/Item

a point

at (x,y).

TESTS
A:l-PropZlnt(

13-20

TESTS
B:2-PropZlnt(

13-21

TESTS
5:1 -PropZTest(

13-14

13-15

3:Pt-Change(

2:Pt-Off(

Tables

and

Reference

Information

8-15

[_
[DRAW]
POINTS
l:Pt-On(

A-20

8-15

[_
[DRAW]
POINTS

8-14

[g_
CALC
A:PwrReg
12-27

Function or Instruction/
Arguments

Result

Key or Keys/
Menu or Screen/Item

Pxl-Change(row,column)

Reverses pixel at
(_w,column);
0 <_row <_62
and 0 _. drawflag= l
draws results; drawflag=O
calculates
results.

i

2-8ampFTest
Sxl,nl,
Sx2,n2[,alternative,
drowflag]
(Summary stats input)

Performs
a two-sample
F test.
alternative=-1
is <;
alternative=O
is _;
alternative=l
is >. drawflag=l
draws results; drawflog=O
calculates
results.

i

2-SampTInt [listnamel,
listname2,
frvqlistl
_frvqlist2,
canfidezwe
level,pooled]
(Data list input)

Computes
a two-sample
t
confidence
intm_'al, pooled=l
pools variances;
pooled=O does
not pool variances.

i

2-SampTInt 21,Sx1,n1,
22,Sx2,n2
[,confidence
level,pooled]
(Sununary
stats input)

Computes
a two-sample
t
confidence
intm_,al, pooled=l
pools variances;
pooled=O does
not pool variances.

i

2-SampTTest
[listnamel,
listname2_frvqlistl
,
frvqlist2,alternative,
pooled,draw
flag]
(Data list input)

Computes
a two-sample
t test.
alternative=-1
is <;
alternative=O
is _;
alternative=
l is >. pooled= l
pools variances;
pooled=O does
not pool vm'iances,
drawflog=l
draws results; drawflog=O
calculates
results.

i

A-24

Tables

and

Reference

TESTS
D:2-SampFTest

13-23
TESTS
D:2-SampFTest

13-23
TESTS
0:2-SampTInt
13-19

Information

TESTS
0:2-SampTInt
13-19
TESTS
4:2-SampTTest

13-13

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

_r_tq

2-Sam pTTest 5l,Sxl,nl,
22 ,Sx2 ,n2[ ,o lternative
pooled,draw.flag]
(Smmnary stats input)

Computes
a two-sample
t test.
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.

2-SampZInt(_l,a,
[,listnamel
,listname2
frvqlistl
_frvqlist2,
canfidence
level])
(Data list input)

Computes
confidence

2-SampZlnt(_l,_,
_1,nl ,_2,n2
[,confidence
level])
(Smmnary stats input)

Computes a two-sample z
confidence intm_al.

2-SampZTest(_l,_
[,listnamel
,listname2
.frvqlistl ,frvqlist2,
alternative,drowflag])
(Data list input)

Computes
a two-sample
z test.
alternative=-1
is <;
alternative=O
is _ ;
alternative=l
is >. drawflag=l
draws results; drawflag=O
calculates
results.

2-SampZTest(61
,_,
_1 ,nl ,_2,n2
[,alternative,drawflog])
(Summary stats input)

Computes
a two-sample
z test.
alternative=-1
is <;
alternative=O
is ;_;
alternative=
l is >. draw.flag= l
draws results; drawflog=O
calculates
results.

i [gt_]
TESTS
3:2-SampZTest(

Sci

Sets scientific
mode.

i [MODEl
Sci

Select(Xlistname,
Iqistname)

a two-sample
intm_al.

TESTS
4:2-SampTTest

13-13

z
TESTS
9:2-SampZlnt(
13-18
TESTS
9:2-SampZlnt(
13-18

notation

display

Seleets one o1" more speeific
data points from a scatter plot
or xyLine plot (only), and then
stores the selected data points
to two new lists, Xlistname
and Ylistname.

Tables

and

Reference

TESTS
3:2-SampZTest(

13-12

13-12

_

1-10

[LIST]

OPS
8:Select(

11-12

hfformation

A-25

Function or Instruction/
Arguments
Send(variable}

Key or Keys/
Menu or Screen/Item

Result
Sends contents
of variable
to
the CBL 2/CBL System or CBR.

-;-

seq(expression,variable,
begin,end[,increment])

Returns list ereated by
evaluating
expression
_lth
regard to 'variable, from begin
to end by incremez_t.

_

Seq

Sets sequence

i

Sequential

Sets mode to graph ftmetions
sequentially.

SetUpEditor

Removes all list names from
the stat list editor, all(] then
restores list names L1 through
L6 to eolumns 1 through 6.

graphing

mode.

I/O
B:Send(
OPS
5:seq(

11-11
Seq

1-11

Sequential

1-12

i

EDIT
5:SetUpEditor
12-21

SetUpEditor
listnamel
[,listname2,...,
listname20]

Removes all list names from
the stat list editor, then sets it
up to display one or more
listnames
in the specified
order, starting _lth eohmm 1.

Shade(lowe:rfune,
upperfunc[,Xleft_rqght,
pattern,patres])

Draws lowerfune
and
upperfune
in terms of X on the
current graph and uses
pattern
and pat'r_s to shade the
area bounded
by lowerfunc,
upperfunc,
Xleft, and X'rqght.

[_

Shadez2(lowerbound,
upperbound,dy')

Draws the density function
the Z2 distribution
specified
degrees of freedom
dfand
shades tile area between

[_
[DISTR]
DRAW
3:Shade)_2(

lowerbound

A-26

Tables

and

Reference

and upper_ound.

Information

16-21

[LIST]

for
by

EDIT
5:SetUpEditor
12-21
[DRAW]

DRAW
7:Shade(

8-10

13-36

Function or Instruction/
Arguments
ShadeF(lowerbound,
upperbound,
numerator
df,
denominator
d,f)

Key or Keys/
Menu or Screen/Item

Result
Draws the density function
for
the F distribution
specified by
numerator
(lf and
denorainator
df and shades the
area between
lower'bound
and

_
[DISTR]
DRAW
4:ShadeF(

upperSound.

13-36

$hadeNorm(lower'bound,
upper'bound[,p,G])

Draws the normal density
function specified
by p and (_
and shades the area between
lower'bound
and upper'bound.

_
[DISTR]
DRAW
1 :ShadeNorm(

Shade_t(lower'bound,
upperbound,dJ')

Draws the density function
for
the Student-t distribution
specified
by degrees of
freedom df, and shades the
area between
lower'bound
and
upperSound.

[_
[DISTR]
DRAW
2:Shade_t(

Simul

Sets mode to graph
simultaneously.

i [_Dg]
S imul

sin(volue)

Returns
number,

tile sine of a real
expression,
or list.

Ig]N]

sin-l(volue)

Returns
number,

tile m-csine
expression,

[_

sinh(volue)

Returns tile hypet%olic
sine of
a real number,
expression,
or
list.

_
[CATALOG]
sinh(

Returns the hyperbolic
arcsine
of a real number,
expression,
or list.

_
[CATALOG]
sinh -1(

sinh-l(value)

Tables

and

functions

of a real
or list.

Reference

13-35

13-36
1-12
2-3
[SIN-1]
2-3

15-10

15-10

hfformation

A-27

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

SinReg [iterations,
Xlistname,I_istname,
period,regequ]

Attempts iterations
times to fit
a sJnusoJdal regression
model to
Xlistname
and Iqistname
using
aperiod
guess, and stores the
regression
equation to regequ.

solve(expression,variable,
guess,{lower',upper_)

Solves expression
for variable,
given an initial guess and lower"
and upper" bounds within
which the solution is sought.

i

SortA(listuame)

Sorts elements
of listname
ascending
order.

_
[LIST]
OPS
1 :SortA(

SortA(keylistuame,
dependlistl
[,dependlist2,
...,dependlist
n])

Sorts

SortD(listuame)

Sorts elements of listname
descending order.

elements

of

in

keylistuame

in ascending
order, then sorts
each dependlist
as a dependent
list.
in

SortD(keylistuarae,

Sorts

de_er_dlistl
dependlist

in descending
order, then sorts
each dependlist
as a dependent
list.

[,deper_dlist2,...,
n])

elements

of

keylistuarae

CALC
C:SinReg
12-27
MATH
0:solve(
2-12

[2_] [LIST]
OPS
l:Sorth(
[_
[LIST]
OPS
2:SortD(
[_
[LIST]
OPS
2:SortD(

stdDev(list[,frvqlist])

Returns the standard deviation
of the elements in list with
frequencyfrvqlist.

[_
[LIST]
MATH
7:stdDev(

Stop

Ends program execution;
returns to home screen.

i [gggM]
CTL

Store: value_variable

Stores value

_

StoreGDB

Stores current graph
datahase GDBn.

F:Stop

A-28

n

Tables

and

Reference

in variable.

Information

in

[_

11-10
12-20

11-10
12-20
11-10
12-20

11-10
12-20

ll-lS

16-15
1-14

[DRAW]

STO
3:StoreGDB

8-19

Function or Instruction/
Arguments
StorePic

n

String_*Equ(string,Y=

Key or Keys/
Menu or Screen/Item

Result
Stores eun'ent pleture
picture Picn.
vat')

in

[_

[DRAW]

STO
l:StorePic

Converts stt'ing iJlto an
equation and stores it in Y:
vat_

_
[CATALOG[
String_Equ(

sub(string,begin,h_.ngth)

Returns a string that is a subset
of another string, from begin
to length.

[gffd][CATALOG]
sub(

sum(list[,stat't,end])

Returns the sum of elements
list from start to end.

[gffd][LIST]
MATH
5:sum(

tan(value)

Returns
nunlber,
or list.

the ttmgent
expression,

8-17

15-8

of

15-9

11-18

of a real
2-3

tan-l(value)

Returns the aretangent
of a
real nunlber,
expression,
or
list.

[gffd][TAN-1]

Tangent(ea_ression,value)

Draws a line tangent to
expression
at X=value.

[gffd][DRAW]
D RAW
5:Tangent(

tanh(value)

Returns hyperbolic
tangent of a
real number, expression,
or list.

[_
[CATALOG]
tanh(
15-10

tanh-l(value)

Returns the hyperbolic
aretangent
of a real number,
expression,
or list.

_
[CATALOG]
tanh-l(

tcdf(lowerbound,
upp_rbound,dJ_

Computes
the Student-t
distribution
probability
between lower_ound
and
upperSound
for the specified
degrees of freedom
4/:

[2_

Text(row,column,textl,
text2,...,text
n)

Writes text on graph
at pixel (row,column),
0 <_row <_57 and
0 <_column <_94.

beginning
where

[_
[DRAW]
DRAW
0:Text(

Tables

Reference

2-3

8-8

15-10
[DISTR]

DISTR
5:tcdf(
13-31

8-12

Then
See If:Then

and

hfformation

A-29

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

Time

Sets sequenee graphs
with respect to time.

Tlnterval [listname,
.fr_qlist,eonfidence
(Data list input)

Computes
inte_ral.

a t confidence

Tlnterval ;7,Sx,n
[,confidence
level]
(Summary stats input)

Computes
inte_ral.

a t confidence

tpdf(x,df)

Computes
the probability"
density" function
(pdf) for the
Student-t distribution
at a
specified x value _ith specified
degrees of freedom
ddq

Trace

Displays the graph
TRACE mode.

level]

T-Test pO[,listname,
frvqlist,alternative,
d'r'o_ag]
(Data list input)

Tables

and

Performs
a t test with
frequeneyfrvqlist.
alternative=-1
is < ;
alternative=O
is €: ;
alternative=l
is >. drawflag=l
draws results; drawf!og=O
ealeulates
results.

Reference

Information

-;-[_
[FORMAT]
Time

6-8

i
TESTS
8:Tlnterval

13-17

TESTS
8:Tlnterval

13-17

i

[_
[DISTR]
DISTR
4:tpdf(
13-30

and enters

Performs
a t test with
frequeneyfrvqlist.
alternative=-1
is <;
alternative=O
is €;
alternative=
l is >. drawflag=
draws results; drawfiag=O
calculates
results.

T-Test pO, _,Sx,n
[,olternative,drawflag]
(Summary stats input)

A-30

to plot

3-18
i
TESTS
2:T-Test
l
13-11
i
TESTS
2:T-Test

13-11

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

tvm_FV[(N,I%,PV,PMT,
P/Y,C/Y) ]

Conlptltes

tile ftlture va]ue.

[_
[FINANCE]
CALC
6:tvm_FV

14-7

tvm_I%[(N, PV,PMT,FV,
PlY, C/Y)]

(;omputes
rate.

tile annual

[_
[FINANCE]
CALC
3:tvm_I%

14-7

tvm_N[(I%,PV, PMT,FV,
P/Y,C/Y)]

(;omputes tile number
payment periods.

of

tvm_Pmt[(N,I%,PV,FV,
P/If, C/Y)]

(;omputes
payment.

the amount

tvm_PV[(N,I%,PMT,FV,
P/Y,C/Y) ]

(;omputes

tile present

uvAxes

Sets sequence graphs to [)lot
u(n)on the x-axis and v(n)on
the y-axis.

; [2_]

Sets sequence graphs to [)lot
u(n) on the x-axis and w(n) on
the y-axis.

; [2_]

[Xlistname,

Performs
one-variable
analysis
on tile data in XTistname
_ith
frequeneyfrvqlist,

[gT_]
CALC
l:l-Var

2-Mar Stats [Xlistname,
Ylistnarae,fr_qlist]

Performs two-variable
analysis
on the data in Xlistnarae
and
Iaistname
with frequeney
fr_qlist.

[gT_]
CALC
2:2-Mar Stats

variance(list[,fr_qlist])

Returns the variance
of the
elements
in list wlth frequeney
frvqlist.

[g_] [LIST]
MATH
8:variance(

Vertical

Draws
at x.

[_
[DRAW]
D RAW
4:Vertical

uwAxes

1-Mar Stats
.frwqlist]

vwAxes

Web

x

a vertical

interest

_

[FINANCE]

CALC
5:tvm_N

14-7

of eaeh

[_
[FINANCE]
CALC
2:tvm_Pmt

14-6

value.

[_
[FINANCE]
CALC
4:tvm_PV

14-7

line

[FORMAT]

uv
6-8
[FORMAT]

uw
6-8

Stats

12-25

Sets sequenee graphs to [)lot
v(n) on the x-axis and w(n) on
the y-axis.

i- [2_]

Sets sequence
as webs.

; [2_] [FORMAT]
Web

Tables

graphs to trace

and

Reference

12-25

11-18

S-6

[FORMAT]

vw
6-8

hfformation

6-8

A-31

Function or Instruction/
Arguments

Key or Keys/
Menu or Screen/Item

Result

:While condition
:commands
:End
:command

Executes
condition

valueA

Returns 1 if only valueA or
valueB = O. valueA and valueB
can be real numbers,
expressions,
or lists.

_
[TEST]
LOGIC
3:xor

Displays a graph, lets you draw
a box that defines a new-

-;-

xor valueB

ZBox

commands
is true.

_ewing window,
the window.
ZDecimal

while

i
CTL
5:While

2-26
ZOOM

and updates

1:ZBox
3-20

Adjusts tile _dewing window so
that aX=0.1 and AY=0.1, and
displays tile graph screen with
tile origin centered on the
screen.

i

Redefines
tile viewing window
using these dimensions:
AX=I
XscI=10
AY=I
YscI=I 0

i

Zlnterval c_[,listname,
.fr_qlist,confidence
level]
(Data list input)

Computes
intel_al.

a z confidenee

i

Zlnterval c_,;7,n
[,confidence
level]
(Summary stats input)

Computes
intel_al.

a z confidenee

Zoom In

Magnifies tile part of the graph
that surrounds
the eursor
location.

i

Displays a greater portion of
the graph, centered on the
cursor location.

i

Zlnteger

Zoom Out

A-32

Tables

and

Reference

Inforination

16-11

ZOOM
4:ZDecimal
3-21
ZOOM
8:Zlnteger
3-22
TESTS
7:Zlnterval

13-16

i [_
TESTS
7:Zlnterval

13-16

ZOOM
2:Zoom

In

ZOOM
3:Zoom Out

3-21

3-21

Function or Instruction/
Arguments
ZoomFit

ZoomRcl

ZoomStat

Recalculates Ymin and Ymax
to hmlude tile nlininluni
and
nlaxinmm
Y values, between
Xmin and Xmax, of the
selected functions
and replots
tile functions.

i

Graphs tile selected functions
in a user-defined
_dewing
window.

i

Redefines
tile viewing window
so that all statistical
data

i

points
ZoomSto

ZPrevious

ZSquare

ZStandard

Key or Keys/
Menu or Screen/Item

Result

ZOOM
O:ZoomFit

3-22
MEMORY
3:ZoomRcl
ZOOM

are displayed.

Immediately
stores
viewing window.

tile current

i

Adjusts tile X or Y window
settings so that each pixel
represents
m] equal width and
height in the coordinate
system, and updates
the
viewing window.

i

Replots the functions
immediately,
updating
the
window variables
to the
default values.

i

and

Reference

9:ZoomStat

3-22

MEMORY
2:ZoomSto

3-23

i

Replots tile graph using the
window variables
of the graph
that was displayed
before you
executed
the last ZOOM
instruction.

Tables

3-23

MEMORY
1:ZPrevious
3-23
ZOOM
5:ZSquare

3-21
ZOOM
6:ZStandard
3-22

Information

A-33

Function
or Instruction/

Key or Keys/
Menu or Screen/Item

Arguments

Result

Z-Test(pO,_[,listname,
f_qlist,elternative,
drawflag])
(Data list input)

Performs
a z test with
frequencyfreqlist.
alterr_ative=-I
is <;
alterr_ative=O is €;
alterr_ative= l is >. drawflag=
draws results; drawflag=O
calculates
results.

i [_
TESTS
1:Z-Test(
l
13-10

Z-Test(pO,_,_,n
[,olterr_ative,drawflag])
(Smmnary stats input)

Performs a z test.
alterr_ative=-I
is <;
alterr_ative=O is €;
alterr_ative=l
is >. draw.flag=l
draws results; drawflog=O
calculates
results.

i

ZTrig

Replots the functions
immediately,
updating

i

Factorial:

value!

Factorial:

Degrees

Radian:

the

ZOOM
7:ZTrig

faetodal

Returns factorial
elements.

notation:

value °

angle r

13-10

window variables
to preset
values for plotting trig
functions.
Returns

list!

TESTS
1:Z-Test(

3-22

of value.
PRB
4:!

2-21

PRB
4:!

2-21

of list

Interprets
designates
fornlat.

value as degrees;
degrees in [)MS

[_

Interprets

angle as radim]s.

[_

[ANGLE]

ANGLE
1 :°
ANGLE
3: r

Transpose:

A-34

matrix

Tables

T

and

Retrains a matrix in wltich each
element (row, column) is
swapped with tile
corresponding
element
(cohmm, row) of matrix.

Reference

Information

g-23

[ANGLE]

g-24

MATH
2: T
10-12

Function or Instruction/
Arguments

Result

xt_ZrootX_value

Retm'ns

xtlZrootX_list

Returns

listAX_listB

Cube

Returns

value 3

root: 3_(value)

Equal: valueA=valueB

Not equal: valueAcvalueB

Less than:

x_root

Returns xthroot
elements.

listX_value

Cube:

Key or Keys/
Menu or Screen/Item

valueA_valueB.
can be real

2-6
10-10

2-6

2-25
1O- 11

2-25
10-11

nunlbers,

or lists.

and

2-25

Reference

hfformation

A-35

Function or Instruction/
Arguments
Greater than:
valueA>valueB

Key or Keys/
Menu or Screen/Item

Result
Returns 1 if valueA
Returns 0 if valueA
valueA and valueB
O1" eonlplex

[_
[TEST]
TEST
3:>

llUIslbers_

expressions,
Less than or equal:
volueA<_volueB

> valueB.
<_valueB.
can be real

or lists.

Returns 1 if valueA
Returns 0 if valueA
valueA and volueB
O1"eoIslplex
expressions,

2-25

<_valueB.
> volueB.
can be real

_
[TEST]
TEST
6:_<

nunlbers,
or lists.

2-25

Greater than or equal:
valueA>valueB

Returns 1 if volueA 2 valueB.
Retunls 0 if volueA < valueB.
valueA and volueB can be real
O1"eonlplex nunlbers,
expressions,
or lists.

_
[TEST]
TEST
4:>

Inverse:

Returns

[]

value -1

1 dix_ded by a real or

eonsplex

nunsber

2-25

or

expression.
Inverse:

list -1

Inverse:

matrix

2-3

Returns 1 divided
elements.
-1

Returns

Squm'e: value 2

matrix

by list

[]

inverted.

[]

2-3

Returns value multiplied
by
itsel£ value can be a real or
eonlplex nunlber
expression.

10-10

[]

or
2-3

Square:

list 2

Returns

list elements

squared.

[]

Square:

mat'ri:_ _

Returns
itsel£

matrix

by

[]

Powers:

value^power

Returns value raised to power.
value can be a real 05"eoinplex
number or expression.

[]

Powers:

list^power

Returns
power'.

[]

Powers:

value^list

Returns value
elements.

2-3

A-36

Tables

and

Reference

multiplied

10-10

list elements

Information

raised

to

2-3
2-3

raised

to list

[]
2-3

Function or Instruction/
Arguments
Powers:

mat'rix^pow_"

Negation:

-volue

Key or Keys/
Menu or Screen/Item

Result
Returns matrix
raised to power.

elements

[]
1O- 10

Returns the negative of a real
o1"complex number,
expression,
list, o1"matrix.

[]
2-4
10-9

Power

of ten: lo^(volue)

Returns 10 raised to tile value
power, volue can be a real or
conlplex ntlnlber or
expression.

_

[10x]

Power

of ten: lo^(list)

Returns a list of 10 raised
the list power.

_

[10x]

Square

root: ,[(value)

Returns square root of a real or
complex number, expression,
or list.

_

[_]

Multiplication:
volueA*valueB

Returns

[]

Multiplication:
volue*list

Returns
element.

Multiplication:
list*value

Returns each
times volue.

Multiplication:
listA*listB

Returns listA elements
listB elements.

Multiplieation:
value*matrix

Returns value times
elements.

Multiplication:
matrixA*matrixB

Returns matrixA
matrixB.

Division:

valueA/valueB

Returns
valueB.

Division:

list/value

Division:
Division:

volueA

times

to

2-4
2-4

volueB.

2-3
2-3

volue

times

each list

[]
2-3

valueA

list element

[]
2-3

times

[]
2-3

matrix

[]
10-9

times

[]
10-9

dMded

by

[]

Returns list elements
by value.

dMded

[]

value/list

Returns value
elements.

by list

[]

listA/listB

Returns
by listB

2-3
2-3

dMded

2-3

listA elements
elements.

Tables

and

dMded

Reference

[]
2-3

hfformation

A-37

Function or Instruction/
Arguments

Result

Key or Keys/
Menu or Screen/Item

Addition:

valueA+valueB

Returns

Addition:

list+value

Returns list in which value
added to each list element.

Addition:

listA+listB

Returns listA elements
listB elements.

valueA

plus valueB.

[]
is

plus

2-3
[]
2-3

Addition:
matrixA+matrixB

Returns matrixA
elements
plus matrixB
elements.

[]

Concatenation:
string l +string2

Concatenates
strings.

[]

Subtraction:
valueA -valueB

Subtracts

valueB

Subtraction:
value-list

Subtracts
value.

list elements

Subtraction:
list- value

Subtracts
elements.

value

Subtraction:
listA-listB

Subtracts
listB
listA elements.

Subtraction:
matrixA-matrixB

Subtracts
matrixB
elements
from matrixA
elements.

[]

Minutes notation:
degrees°minutes
seeonds"

[_

'

Interprets
minutes
angle
nleasurement
as minutes.

Seconds notation:
degrees°minutes
seeonds"

'

A-38

Tables

2-3

[]

10-9

two or more

15-6
from val'ueA.

[]
2-3

from

[]
2-3

from list

[]
2-3

elements

Interprets
seconds angle
nleasurenlent
as seconds.

from

[]
2-3
10-9
[ANGLE]

ANGLE
2:'
@

2-23
[.]
2-23

and

Reference

Information

TI-83 Menu Map

The TI-83

Menu

tile keyboard

Map

layout

I

begins
from

at the top-left

left to right.

I

(Func
Plotl
Plot3
",,YI=
",,Y2=
",Y3=
",,Y4=
......
",,Y9=
",,YO=

mode)
Plot2

and follows

and settings

are shown,

I

(Pol mode)
Plotl
Plot2
Plot3
",rl=
",r2=
",r3=
",r4=
",rS=
",r6=

",X6T=
Y6T=

(Seq mode)
Plotl
Plot2
Plot3
nMin=l
",u(n)=
u(nMin)=
",v(n)=
v(nMin)=
",w(n)=
w(nMin)=

[_][STATPLOT]

__1
I

I

I

STAT PLOTS
l:Plotl...Off
_:L LI L2 m
2:Plot2...Off
_:L LI L2 _
3:Plot3...Off
_:L LI L2 m
4:PlotsOff
5:PlotsOn

I

(PRGM editor)
PLOTS
l:Plotl(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn

I

I

(PRGM editor)
TYPE
l:Scatter
2:xyLine
3:Histogram
4:ModBoxplot
5:Boxplot
6:NormProbPlot

I

I

(Par mode)
WINDOW
Tmin=O
Tmax=_2

(Pol mode)
WINDOW
Omin=O
Omax=_2

Xscl=1
Ymin= 10
Ymax=10
Yscl=1
Xres=1

Tstep=_/24
Xmin= 10
Xmax=iO
Xscl=1
Ymin= 10
Ymax=iO
Yscl=1

Ostep=_/24
Xmin= 10
Xmax=iO
Xscl=1
Ymin= 10
Ymax=iO
Yscl=1

[TBLSET]
iI
TABLE SETUP
TblStart=O

(PRGM editor)
MARK
Z:D

2:+
3:,

I

(Func mode)
WINDOW
Xmin= i0
Xmax=lO

ATbI=I
Indpnt:Auto
Depend:Auto

of the keyboard

values

I

(Par mode)
Plotl
Plot2
Plot3
",XIT=
YIT=
",X2T=
Y2T=

[STATPLOT]

corner

Default

(Seq mode)
WINDOW
nMin=1
nMax=10
PlotStart=1
PlotStep=1
Xmin= i0
Xmax=lO
Xscl=l
Ymin= i0
Ymax=lO
Yscl=l

_

[TBLSET]
FI
(PRGM editor)
TABLE SETUP
Ask
Ask

Indpnt:Auto
Depend:Auto

Tables

Ask
Ask

and

Reference

Information

A-39

i 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

MEMORY
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors_

MEMORY
(Set Factors,.,)
ZOOM FACTORS
XFact=4
YFact=4

[FORMAT]
I

I

I

(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]
I

I

(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

I

(Pol mode)
CALCULATE
1:value
2:dy/dx
3:dr/dO

H
Normal Sci Eng
Float
0123456789
Radian Degree
Func Par Pol Seq
Connected
Dot
Sequential
Simul
Real a+bt re^Bt
Full
Horiz
G T

A-40

Tables

and

Reference

Information

I

(Seq mode)
CALCULATE
1:value

I

SEND
1:A11+...
2:All-...
3:Prgm...
4:List._
5:Lists
to
6:GDL
7:Pic._
8:Matrix...
9:Real._

I

RECEIVE
1:Receive

T182...

O:Complex._
A:Y Vars...
B:String._
C:Back Up...

i I

EDIT
1:Edit._
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor

I

I

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]

I
1

I

NAMES
l:listname
2:listname
3:listname

1

OPS
l: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

I I

1

MATH
l:_Frac
2:_Dec
3:3

4:3_r(
5: x_
6:fMin(
7:fMax(
8:nDeriv(
9:fnlnt(
O:Solver._

MATH
1:min(
2:max(
3:mean(
4:median(
5:sum(
6:prod(
7:stdDev(
8:variance(

1

NUM
l:abs(
2:round(
3:iPart(
4:fPart(
5:int(
6:min(
7:max(
8:Icm(
9:gcd(

CPX
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:_Rect
7:_Polar

[2nd][TEST]
I

I

TEST
i:=
2:_
3:>
4:>
5:<

LOGIC
l:and
2:or
3:xor
4:not(

6:<

A-42

Tables

and

Reference

Information

1

PRB
1:rand
2:nPr
3:nCr
4:!
5:randlnt(
6:randNorm(
7:randBin(

I I

NAMES
I:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
O:[J]

I

I

r_q [AN_LE]

I

MATH
1:det(
2: I
3:dim(
4:Fill(
5:identity(
6:randM(
7:augment(
8:Matr_list(
9:List_matr(
O:cumSum(
A:ref(
B:rref(
C:rewSwap(
D:row+(
E:*row(
F:*row+(

EDIT
l:name

2:na_

2:na_e

I

6:Repeat
7:End
8:Pause
9:Lbl
O:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm

EDIT
I:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
O:[J]

I

EXEC
l:nan_

(PRGM editor)
CTL
1:If
2:Then
3:Else
4:For(
5:While

F--

I

1: °
2:'

3: r
4:_DMS
5:R_Pr(
6:R_PO(
7:P_Rx(
8:P_Ry(

I

NEW
1:Create

I

(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(

ANGLE

New

I

(PRGM editor)
EXEC
m:name
2:name

E:Return
F:Stop
G:DelVar
H:GraphStyle(

Tables

and

Reference

Information

A-43

I

I

DRAW
l:C]rDraw
2:Line(
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:Drawlnv
9:Circle(
O:Text(
A:Pen

I

POINTS
1:Pt
On(
2:Pt
Off(
3:Pt
Change(
4:Pxl
On(
5:Pxl
Off(
6:Pxl
Change(
7:pxl
Test(

1

STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecalIGDB

I

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

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

A-44

Tables

I

(Window...)
T/e
1:Tmin
2:Tmax
3:Tstep
4:emin
5:6max

(Window...)
U/V/W
1:u(nMin)
2:v(nMin)
3:w(nMin)
4:nMin
5:nMax

6:6step

6:PlotStart
7:PlotStep

and

Reference

Information

VARS
I

I

I

(Zoom...)
ZX/ZY

(Zoom...)
ZT/Ze

(Zoom...)
ZU

l:ZXmin
2:ZXmax

l:ZTmin
2:ZTmax

l:Zu(nMin)
2:Zv(nMin)

3:ZXscl
4:ZYmin
5:ZYmax

3:ZTstep
4:ZOmin
5:Z@max

3:Zw(nMin)
4:ZnMin
5:ZnMax

6:ZYscl
7:ZXres

6:Z@step

6:ZPlotStart
7:ZPlotStep

VARS
I

I

(GDB...)
GRAPH DATABASE
I:GDB1
2:GDB2

(Picture...)
PICTURE
1:Picl
2:Pic2

9:GDB9
O:GDBO

9:Pic9
O:PicO

VARS
I

(Statistics...)
XY
l:n
2:_
3:Sx
4:_x

I

(Statistics...)
Z
I:Zx
2:Zx 2
3:Zy
4:Zy
5:Zxy

6:Sy
7:_y
8:minX
9:maxX
O:minY

2

I

I

I

(Statistics...)
EQ

(Statistics...)
TEST

(Statistics...)
PTS

I:RegEQ
2:a
3:b

1:p
2:z
3:t

i:xl
2:yi
3:x2

4:c
5:d

4:Z 2
5:F

4:y2
5:x3

6:e
7:r
8:r 2
9:R 2

6:df
7:#
8:#1
9:#2
O:s

6:y3
7:Q1
8:Med
9:Q3

A:maxY

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...)
TABLE
1:TblStart

(String...)
STRING
1:Strl

2:ATbl

2:Str2

3:TbIInput

3:Str3
4:Str4
9:Str9
O:StrO

Y VARS
I
I

I

(Function...)
FUNCTION
I:YI
2:Y2
3:Y3
4:Y4

(Parametric...)
PARAMETRIC
I:XIT
2:YIT
3:X2T
4:Y2T

I

(Polar...)
POLAR
i:ri
2:r2
3:r3
4:r4
5:r5

O:Yo

A-46

B:Y6T

Tables

and

Reference

Information

I

(On/Off._)
ON/OFF
1:FnOn
2:FnOff

[_

[DISTR]

I
I

I

DISTR
1:normalpdf(
2:normalcdf(
3:invNorm(
4:tpdf(
5:tcdf(
6:z2pdf(
7:z2cdf(
8:Fpdf(
9:Fcdf(
O:binompdf(
A:binomcdf(

DRAW
1:ShadeNorm(
2:Shade t(
3:Shadez2(
4:ShadeF(

B:poissonpdf(
C:poissoncdf(
D:geometpdf(
E:geometcdf(
I_

[FINANCE]
I
I

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

I

VARS
I:N
2:1%
3:PV
4:PMT
5:FV
6:P/Y
7:C/Y

Tables

and

Reference

Information

A-47

MEMORY

[MEM]
i--J

I

I

MEMORY
l:Check
RAM_
2:Delete._
3:Clear
Entries
4:ClrAllLists
5:Reset...

MEMORY
I

I

(Check
RAM...)
MEM FREE 27225
Real
15

(Delete...)
DELETE FROM...
1:All...

Complex
List
Matrix
Y Vars

2:Real._
3:Complex._
4:List...
5:Matrix...

0
0
0
240

Prgm
Pic
GDB

14
0
0

String

0

6:Y
Vars...
7:Prgm...
8:Pic...
9:GDB...
O:String...

(Reset...)
I

Resetting
erases
all

12_]_ALOG]

I

(All
Memory...)
RESET MEMORY
1:No
2:Reset

(Defaults...)
RESET DEFAULTS
1:No
2:Reset

memory
data

CATALOG
cosh(
cosh-l(
Equ_String(
expr(

and
inString(

programs•

length(
sinh(
sinh-1(
String_Equ(
sub(
tanh(
tanh-1(

A-48

Tables

and

Reference

Information

I

(Reset...)
RESET
1:All
Memory...
2:Defaults._

Variables

User Variables

The

TI-83

Some

uses

variables

the variables

listed

are restricted

below

to specific

in various
data

ways,

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
lists; you cannot store another
type of data to them.
The wu'iables
(matrix
names)
to matrices;
you cannot store
The vm'iables
Pie1 through
pictures;
you cannot store

to

[A] through
[J] are restricted
another
type of data to them,

Pie9 and Pic0 are restricted
to
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
string is determined
when the function
is evaluated.

System

Variables

of the

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,
other ZOOM variables.

The variables
cannot store

below are resetwed
to them.

Zu(nMin),

for use by the TI-83.

and
You

n, _, Sx, _x, minX, maxX, Ey, Ey 2, Exy, a, b, e, RegEQ, xl, x2,
yl, z, t, F, Z2, p, xl, Sxl, nl, lower, upper, r2, R 2 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:
N

j

:z(-i÷o>,
4
c

which is the sunl of the squares
where:

of the residual

errors,

x = the independent
variable list
y = the dependent variable list
N = the dimension of the lists

This technique attempts to estimate the constants
e t_cursively to make J as small as possible.
SinReg

a, b, and

The sine regression algorithm applies nonlinear recut_ive
least-squares
techniques to optimize the following cost
function:
N
J=

E[a
i=1

siyt(bxi

+ e)+

d-

yi]2

which is the sunl of the squares
where:

of the residual

errors,

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 d to make J as small as possible.

A-50

Tables

and

Reference

Inforination

ANOVA(

The ANOVA

F

F statistic
is:

Factor

MS'

Error MS

The

mean

Factor

Error

squares

MS'

MS' =

The sum
are:

(MS) that

Factor

SS

Factor

df

Error

SS

Error

df

of squares

make

(SS) that

up F are:

make

up the mean

squares

I
Factor

SS

= E

ni(xi

- 2) 2

i=1

I
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

I
Ermrdf

where:

= E
i=l

(hi

- 1) = denolninator

I = number
_:i
Sxi

if)r

= the length

_:

= the mean

and

F

of populations

= the mean of each list
= the standard
deviation

ni

Tables

df

of each

of each

list

list

of all lists

Reference

Information

A-51

Below

2-SampFTest

for the 2-SampFTest.

is the definition
Sxl,

Sx2

= Sample
nl-1

standard

and n2-1

deviations
degrees

having

of freedom

df,

respectively.

F = F-statistic
dr(x,

nl-1 , n2-1 )

[ Sx2 )

= Fpdf(

) with

fl'eedom
p = reportedp

2-SampFTest

p = i f(x,

for the alternative

degrees

of

df, hi-1 , and

n2-1

wdue

hypothesis

(s 1 > (s 2.

hypothesis

(_1< (_2-

hypothesis

(_1 :_ (_2.Limits

nl - 1,n 2 - 1)dx

2-SampFTest for the alternative
F
p = ff(x,n
0

1-1,n

2-1)dx

2-SampFTest for the alternative
nmst satisfy the following:
Lb nd

/92=

f f(x'nl0

where:

l'n2-1)dx=

[Lbnd, Ubnd]

ff(x,n
U_,_

1-1,n

2-1)dx

= 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
t statistic
with degrees
of freedom
dfis:
t=

Xl--X2

s
where tile computation
whether the variances
pooled:
S = ]_/$2b'12q
V nl

d f-

l

nl-lk

of S and df are dependent
are pooled. If the variances

on
are not

SX22
n2

S:t;12

+ ,gXd2 )2

nl }

nz-lk

l (s.s/,,
nz )

otherwise:
(n I -

1)SXl

_:t;p =

2 + (n 2 - 1)SX2 2

df

S = J1 + 1 Sxp
V)'_I n2
df = nl+n2-2
and Sxp is the pooled

Tables

variance.

and

Reference

Information

A-53

Financial

This

Formulas

section

contains

amortization,
Time Value
Money

cash
of

financial
flow,

fommlan

interest-rate

for computing
conve_\sions,

time

and days

value

of money,

between

dates.

i=[e(y×ln(x+l))]_l
where:

PMT

€ 0
y = C/Y + P/Y

x = (.01 ×1%)
= compounding

P/Y

= payment

I% = interest
i = (-FV

+ PV)( 1+ N)

_

PMT

= 0

The

used

to compute

0 = PV + PMT

1% = 100 × C/Y
where:

periods

periods
rate

per

per

year

per year
yem"

1

where:
iteration

+ C/Y

C/Y

x G i [1-(1+i)

i:

NI+FV×(I+i)

N

× [e(Y × ln(x + 1)) _ 1]
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

N-

where:

[PMTxGi+PVxi)
ln(1 + i)
i € 0

N = -(PV + FV) + PMT
where:

A-54

Tables

and

Reference

i = 0

Information

payments

PMT=-ix[PV_
Gi

PV+FV
(I+i)N-

[

where:
PMT

i € 0
= -(PV

+ FV)

where:

+ N

i = 0

J
where:
+ PMT

where:

PMT x Gi
i

× N)
i = 0

PMT i x G i

where:
FV = -(PV
where:

(l+i)

i € 0

PV = -(FV

FV

]
lJ

(l+i)N×

( PV-_

PMT×Gi.)

i € 0
+ PMT

x N)
i = 0

Tables

and

Reference

Information

A-55

Amortization

If computing
Let hal(O)
Iterate

bal(),

pint2

= npmt

= RND(PV)

fronl

m = 1 to pint2

Lm = RND[RND12(-i
x bal(m - 1))]
hal(m)
= bal(m - 1) -[m+ RND(PMT)
then:
hal()
E Prn(
Z Int(
where:

= hal(pint2)
) = bal(pmt2)
) = (pint2
RND

- bal(pmtl)

- pmtl
= round

+ 1) x RND(PMT)
the display-

decimal
RND12

= round

places

A-56

Tables

and

Reference

Information

to the number

selected

to 12 decimal

Balance,
principal,
and interest
values of PMT, PV, I°/o,and pmtl

- Z Prn(

places

are dependent
and pint2.

on the

)
of

Cash Flow

N

npv() = CF0 + _CFj(1
j=l

where:Sj=

ni

+/)

& _(1 - (1 _/)

rq)

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

i satisfies

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
NOM = nominal rote

Tables

and

Reference

periods

Information

A-57

Daysbetween Withthedbd(function,
youcanenterorcompute
adate
Dates

within

the range

Jan.

1, 1950, through

Actual/actual
day-count
number
of days per month

Dec. 31, 2049.

method
(assunles
and actual number

actual
of day-s per

year):
dbd(

(days

Number

between
Number
of Days

dates)
of Days

=
II - Number

I = (Y1-YB)

of Days

I

× 365

+ (number
+ DT1

of days

MB to M1)

(Y1 - YB)
+

4
Number

of Day-s II = (Y2-YB)

x 365

+ (number
+ DT2

of days

MB to 11//2)

(Y2 - YB)
+

4
where:

M1
DT1

= month

of first

= day of first

date

date

Y1 = year of first date
M2 = month of second
DT2

= day of second

Y2 = year
= base

month

DB

= base

day (1)

YB = base

A-58

Tables

and

Reference

Information

date

of second

MB

year

date

date

(January)
(first

year

_ter

leap year)

B
Contents

GeneralInformation
Batte_" Infommtion ......................................
In Case of Difficulty .....................................
Error Conditions .........................................
Accuracy Infomlation ....................................
Support and Sep_iee Information .........................
Warranty Infornlation ....................................

General

Information

B-2
B-4
B-5
B-10
B-12
B-13

B-1

Battery

Information

When to Replace
the Batteries

The

TI-83

uses

five batteries:

and one lithium
auxilimTF power
AAA batteries.
When the battery
the TI-83 displays
_Jour

four

AAA alkaline

batteries

battery-. The lithium battery
pro_qdes
to retain menlot T while you replace

voltage level
this message

the

drops below a usable level,
when you turn on the unit.

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
time
you
the
you

low-battery
message
continues
to be displayed
each
you turn on the unit until you replace
the batteries.
If
do not replace
the batteries
within about two weeks,
calculator
may turn off by itself or fail to turn on until
install new batteries.

Replace

Effects

of

Replacing
Batteries

the

Battery
Precautions

Take these precautions
•

•
•
•
•
General

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.

•

B-2

the lithimn

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.

hfformation

Replacing
Batteries

the

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

memory,
you nmst
turn off the
remove
the AAA batteries
and
simultaneously.
3. Replace
all four
time. Or, replace

stored
calculator.
the lithium

AAA alkaline
batteries
the lithium batte_Ty-.

in
Do not
battery

at the same

•

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
nlay need to be adjusted.

on the screen,

the contrast

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
ARCHIVED VAR

ARGUMENT
BAD GUESS

Possible Causes and Suggested Remedies
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.
A function or instruction does not have the co_Tect number
of arguments. See Appendix A and the appropriate
chapter.
• 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
entered lower >_upper.

solver, you

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
a nmtrix, to a list.

data type, such as

DIMMISMATCH

You attempted to perform an operation that references
more than one list or lnatrix, but the dimensions do not
lnateh.

DIVIDE BY 0

• 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

General

Infornmtion

line.

B-5

Error Type

Possible

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
-X or an exponential
or power
regression
with a -Y.

•

You attempted
pint2
< pint1.

Duplicate

Name

Error in Xmit

Causes

and Suggested

to compute

A variable
you attempted
because
a variable
with
receiving
unit.

Remedies

a

XPrn( or Xlnt( with

to transmit
cannot be translnitted
that name already
exists in the

•

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

•

You attempted
TI-83.

•

You attempted
to transfer
data
1.6) from a TI-83 to a TI-82.

•

You attempted
a TI-82 without

[_

to break
to perform

during

transmission.

a backup
(()tiler

from
than

a TI-82

to a

kl through

to transfer
kl through
L6 from a TI-83 to
using 5:Lists to TI82 on the LINK SEND

nlenu,

ILLEGAL NEST

You attempted
to use an invalid function
a function,
such as seq( within e_ression

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

•

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
was transferred

INVALID

in a For( loop

in an argument
for seq(.

is 0,

to reference
a variable
or function
that
from the TI-82 and is not valid for the

TI-S3. For example,
you may have transfen'ed
U n-1 to
the TI-83 from the TI-82 and then tried to reference
it.
•

B-6

General

In Seq mode, you attempted
to graph a phase
without
defining
both equations
of the phase

hfformation

plot
plot.

to

Error Type

Possible Causes and Suggested Remedies

INVALID (cont.)

• In Seq nlode, you attempted to graph a recursive
sequence without having input the correct number
initial conditions.
• In Seq mode, you attempted
than (n-l) or (n-2).

to reference

of

terms other

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
appropriate
for the operation.
You specified a list dimension as something
an integer between 1 and 999.

that are not
other than

You specified a matrix dimension as something
than an integer between 1 and 99.
You attempted
ITERATIONS

to invert a matrix

other

that is not square.

• 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
was exceeded.

1%,the nl_Lxinlunl number
is not defined

of iterations

LABEL

The label in the Goto instruction
instruction in the program.

with a Lbl

MEMORY

Memory is insufficient to perform the instruction or
function. You nmst delete items from memory (Chapter
before executing the instruction or function.

18)

Reeursive problems return this error; for example,
graphing the equation YI=Y1.
Branching out of an If/Then, For(, While, or Repeat loop with
a Goto 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
a sign change.

_;i the equation

......

• You atteinpted to compute I%when FV, (N*PMT), and PV
are all _>O, or when FV, (N*PMT), and PV are all _ 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
See Appendix A.

SINGULAR MAT

• A singular matrix (determinant
argument for %

variable

inappropriately.

= 0) is not valid as the

• The 8inReg instruction or a polynomial regression
generated a singular matrix (determinant
= 0) because
could not find a solution, or a solution does not exist.
This error is not returned during graphing.
allows for undefined values on a graph.

B-8

General

hfformation

Tile TI-83

it

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
appropriate.
• Statistical
• Ned-Ned
partition.

a stat calculation
analyses

with lists that are not

must have at least two data points.

must have at least three points in each

• 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
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 _ 0 (or xqce versa).
to define Tstep=0.
Tmax _ 0 (or vice versa).

• Window variables are too SLUM1
or 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
• A ZOOM operation

of a box, is defined

returned

in ZBox.

a math error.

General

Information

B-9

Accuracy

Computational
Accuracy

Information

To maximize

accuracy-,

internally
than it displays.
using up to 14 digits with

the TI-83

carries

more

digits

Values m_ stored
in nlemo_a two-digit
exponent.

•

You can store a value in the window
to 10 digits (12 for Xscl, Yscl, Tstep,

vm'iables
using
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.

Graphing

Xmin is the center

Accuracy

of the next-to-the-rightmost
pixel. (The rightmost
reserved
for the busy indicator,)
AX is the distance
between
the centers
of two adjacent
pixels.
•

•

of the leffmost

pixel,

up

Xmax is the center

In Full screen
mode, AX is calculated
zks
(Xmax - Xmin) / 94. In G-T split-screen
mode,
calculated
as (Xmax - Xmin) / 46.

pixel

is

AX is

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.
•

•

B-IO

General

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,

Information

Cursor
coordinates
aredisplayed
aseight-character
numbers
(whichmayinclude
anegative
sign,decimal
point,andexponent)
whenFloatmode
isselected.
XandY
areupdated
withanlaxinmln
accuracy
ofeightdigits.
minimum and maximum

on the CALCULATE

are

menu

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

sn

Range of Input Values

cos. "

....................
0

sin -1 2a', COS-1 X

...........
-1 < x <_1

.......
...............................

ex

-10100< x -<230.25850929940

1_

-10 i00 < x < 100

sinh x, cosh w
tanh x

Ixl _<230.25850929940
Ixl < 10 i°°

sinh :_ x

Ixl < 5 x 109!_
..............................

cosh-1 .%,
l_
>

(factorial),
2-21, A-34
(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

-1
<
<
{}
[]

•
.
(mx.erse),
2-3,o 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
2
_(
-->
....

(seconds
(square),

notation),
2-23, A-38
2-3, A-36

(square root),
2-3, A-37
Store, 1-1]-_, A-28
(string indicator),
15-3
(subtraction),
2-3, A-38

-Aa+bl (rectangular
complex
1-12, 2-16, A-3
above graph style(N), 3-9
abs( (absolute value),
10-10,A-2

mode),

2-13, 2-19,

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,
amortization
hal( (amortization
A-3

13-7
balanee),

14-9,

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__),
applications.
,fee examples,
applications
areeosine
(cos < 0, 2-3
aresine (sin<0,
2-3
aretangent
(tan "10, 2-3

1-2

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,
AxesOn,

3-14t, A-3
3-14t, A-3

Index-1

-Bbacking

- C (continued)

up calculator
19-10

memmTy, 19-4,

bal( (amortization
balance),
batteries,
1-2, B-2
below- graph style (6), 3-9

14-9, A-3

C

calculating,
14-8
fornmla, A-57
irr( (internal rate of return),
A-13

1-12,

2-16, A-3,

1-12, 2-16, 2-18, A-22
variable

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
13-8

14-8,

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

Index-2

re^01),

(c/Y), 14-4, 14-14

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

colon separator
(:), 6, 16-5
combinations
(nCr), 2-21, A-16

modes (a+bl,
A-22
numbers,

-

CALCULATE metal, 3-25
Calculate output option, 13-6,
cash flow"

complex

compounding-periods-per-year

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
-

-

)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
A-19

eonversion),

2-19,

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,
to 12-27

12-25

cos((cosine),
2-3, A-5
cos'l((areeosine),
2-3, A-5
cosh(

(hyperbolic

cosine),

15-10, A-5

- D (continued)cosh'l(

(hyperbolic
A-5

- D (continued)

arceosine),

cosine (cos(), 2-3, A-5
cross pixel mark (+), 8-15,
cube (3), 2-6, A-35
cube root (3_(), 2-6, A-35

15-10,

12-34

CubicReg (cubic
A-5

regression),

12-26,

cubic regression
A-5

(CubicReg),

12-26,

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
A-58

dates),

14-13, A-5,

_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,

dimensioning

-

a list or matrix,

10-13, 11-11, A-6
dim((dimension),
10-12,
->dim( (assign dimension),
11-11, A-6

10-12,

11-11, A-6
10-13,

Disp (display), 16-18, A-6
DispGraph
(display graph),
display contrast,
1-3
display cursors, 1-5

16-19,

A-7

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
notation), 2-23, A-38
_DMS (to degreegminutes/seconds),
2-224, A- 7

entity"

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

2-8, 3-28, 4-8, 5-6

Index-3

- D (continued)drawing

- E (continued)

on a graph

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
A-7
Else, 16-10
End, 16-12,

rate),

14-12,

A-8

Eng (engineering
A-8
entry cm'sor,

interest

notation

mode),

1-10,

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
Index-4

roots,

2-12

-

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
17-16

n-sided

polygons,

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

- E (continued)
exalnp]es_--Getting
Started
quadratic formula

(continued)

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,
l J-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
lllxprOn (expression

off), 3-1].t, A-8
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
A-8

mode

(Float),

1-10,

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
t test, 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
A-IO

function,

graphing

definition

function graphing,
accuracy,
3-17

mode),

1-11,

of, 1-7
3-1 to 3-28

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

-

- G (continued)

(continued)

graph

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-l J-t
present value, 14-5, 14-7, 1J-t-l}-t
FV (future-value
vm'iable), 1J4-J4, 1J4-1J4
-G

gcd( (greatest
A-IO

common

-

divisor),

2-15,

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, 1 to 18. See also
examples,
Getting Started
Goto, 16-13, A-IO

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
1-12, 9-5, A-11

(G-T),

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
A-12

(intO, 2-14,

GridOff, 3-14, A-11
GridOn, 3-14, A-11
G-T (graph-table
split-screen
1-12, 9-5, A-11
-

H

10-11,

mode),

-

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,
imaginary
part (imagO, 2-18,
implied nmltiplieation,
1-23

A-11
A-11

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

Index-6

-

stat editors,

13-6

- I (continued)

-K-

-

inferential
statistics. See also stat tests;
confidence
intervals
alternative

hypotheses,

bypassing
calculating
13-8

editors, 13-8
test results (Calculate),

13- 7

keyboard
layout, 2, 3
ninth operations,
key-code

2-3

diagrmn,

16-20
-

L-

confidence
interval calculations,
13-8, 13-16 - 13-21
data input or stats input, 13-7

L (user-created
list nmne
11-16, A-13
LabelOff, 3-14, A-13

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

LabelOn,
labels

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
rate), 14-12,
formula, A-57
_Nom( (compute
rate), 1#-12,

interest

A-7
nondnal
A-16

interest

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

symbol),

3-14, A-13

graph, 3-14, A-13
program,
16-13, A-13
Last Entry, 1-16
Lbl (label), 16-13, A-13
Icm( (least common
multiple),
A-13
least

common
A-13

nmltiple

(Icm(),

2-15,
2-15,

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
12-26, A-14
LinReg(ax+b)
(linear
12-25, A-14

regression),
regression),

LinRegTTest
(linear regression
13-2#, A-14
AList(, 11-12, A-14
LIST MATH menu, 11-17

t test),

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)

-

- M (continued)

lists, 11-1 to 11-18

matriees,

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
-

MATH CPX (eomplex
MATH menu, 2-5

M

-

menu),

2-18

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

Index-8

-

(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,
elem'tng entries from, 18-4
deleting items from, 18-3
insufficient
during transmission,
19-5

18-4

resetting
defaults, 18-6
resetting
memory, 18-5
MEMORY menu, 18-2
Menu( (define menu),
menus, 4, 1-19

16-14,

A-15

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,
minutes notation
('), 2-23, A-38
ModBoxplot
plot type (4>.), 12-32

A-9

- M (continued)
modified

-

box [)lot type (o..),

- N (continued)
12-32

mode settings, 1-9
a+bl (complex
rectangular),
2-16, A-3
re^Of (complex
A-22

polar),

1-12,

1-12, 2-16,

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),
A-26

1-12,

Simul (graphing
order), 1-12, A-27
modified box [)lot type (o..), 12-32
multiple entries on a line, 1-6
multiplication
multiplieative

N

-

N (number
of payment periods
variable),
14-4, 14-14
nCr (number of combinations),
A-16
nDeriv(

(numerical
A-16

negation
(-), 1-23,
_Nom( (to nominal
A-16

derivative),

(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
z confidence
inte_ral
(1-PropZInt),
13-20, A-20
one-proportion
z test (1-PropZTest),
13-14, A-20
one-sample
t confidence
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

(*), 2-3, A-37
inverse, 2-3
-

normalcdf(

-

2-21,
2-7,

2-4, A-37
interest rate),

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

14-12,

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)

-

- P (continued)

-

Pause, 16-12, A-18

pooled

pausing a graph,
Pen, 8-13

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

pernmtations
phase plots,

3-15

(nPr), 2-21, A-17
6-13

Pi (_), 2-4
Pic (pictures),
8-17,
pictures
(Pic), 8-17,
pixel, 8-16

9-6

14-4,

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

5-3

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
Index-lO

13-8

PRGM EDIT menu, 16-7
PRGM EXEC menu, 16-7

pixels in Horiz/G-T modes, 8-16,
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),
14-14

free-moxqngcursor,

13-6,

prexqous entlT (Last Entry), 1-16
PRGM CTL (program
control menu),
16-8

8-18
8-18

graph), 5-6
defining and displaying,
equations,
5-4

option,

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

(prgm), 16-15,
renaming, 16- 7
name

A-19

stopping, 16-5
subroutines,
16-22
Prompt, 16-18, A-19
1-PropZlnt
(one-proportion
z confidence
interval),
A-20

13-20,

1-PropZTest
(one-proportion
13-1].t, A-20
2-PropZlnt
(two-proportion
z confidence
interval),
A-20

z test),

2-PropZTest
(two-proportion
13-15, A-20

z test),

13-21,

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

- P (continued)
PV (present value
114-114
p-value, 13-28
PwrReg

(power
A-20

-

- R (continued)

variable),

lJ4-J4,

regression),

12-27,

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-peryear variable),
l J4-J4, l J4-1J4

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, R 2 (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

RegEQ (regression
equation
12-22, 12-29
regression
model
automatic
regression
12-22
automatic
12-22

vm'iable),

equation,

residual

list feature,

diagnostics
display
models, 12-25

mode,

12-23

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
13-23,

-

(two-sample
A-2J4

g-Test),

RecallPic, 8-18, A-22
_Rect (to rectangulm'),
2-19, A-22
rectangular
form, complex numbers,
2-17

2-SampTInt
(two-sample
t confidence
illtel_ral), 13-19, A-24
2-SampTTest
(two-sample
t test),
13-13, A-2J4, A-25
2-SampZlnt
(two-sample
z confidence
inte_5,al), 13-18, A-25
2-SampZTest (two-sample
z test),
13-12, A-25
Scatter plot type (L_), 12-31
Sci (scientific
notation mode), 1-10,
A-25

RectGC (rectangular
graphing
coordinates),
3-13, A-22
recursive
sequences,
6-6
ref( (row-echelon
form), 10-15, A-22

scientific notation,
1 -7,1-10
screen modes, 1-12
second cursor (2nd), 1-5
second key (2nd), 3

RCL (recall), 1-15, 11-9
re^Oi (polm" complex
mode),
2-16, A-22
Real mode, 1-12, A-22

1-12,

real( (real part), 2-18, A-22
RecalIGDB, 8-20, A-22

Index-

11

- S (continued)
seconds

DMS notation

-

('),

- S (continued)

program,
3-8
functions
in tile Y= editor,
items

from

stat plots

nlenus,

SetUpEditor, 12-21, A-26
shade above (7) graph style, 3-9
shade below- (6) graph style, 3-10

2-23

Select(, 11-12, A-25
selecting
data points from a plot, 11-13
functions from the home screen

or a

3-7

J4

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,
TI-83 versus TI-82 table,
tracing, 6-9
web plots, 6-11
window variables,
6- 7
Y= editor, 6-J4

6-4
6-15

Index-12

from a program,

7-3

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
A-28

3-10

regression),

12-27,

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
A-28

descending),

11-10,

12-20,

mode, 9-5
mode, 9-#

setting, 9-3, 9-6
split-screen
values, 8-12, 8-16,
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
12-1J.t

modes from a program,
1-9
split-screen
modes, 9-3
split-screen
modes from a program,
9-6
tables

Shade(, 8-9, A-26
Shadexi(,
13-36, A-26

split-screen
modes
G-T (graph-table)
Horiz (horizontal)

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,
modes, 1-9

-

9-6

to list names,

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

- S (continued)
star list editor

-

- S (continued)

(eonthmed)

statistieal

editing elements of fornmlagenerated
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
t test), 13-24
1-PropZlnt
(one-proportion
z confidence
interval),
13-20
1-PropZTest (one-proportion
z test),
13-14
2-PropZlnt (two-proportion
z eonfidence
interval),
13-21
2-PropZTest
(two-proportion
z test),
13-15
2-SampFTest
13-23

(two-sample

2-SampTInt (two-sample
t eonfidenee
interval),
2-SampTTest
13-13

F-Test),

13-19

(two-sample

t test),

2-SampZlnt (two-sample
z eonfidenee
interval),
2-SampZTest (two-sample
13-12

13-18
z test),

Tlnterval (one-sample
t eonfidenee
inte_x_al), 13-17
T-Test (one-sample
t test), 13-11
Zlnterval (one-sample
z eonfidenee
inte_x_al), 13-16
Z-Test (one-sample
z test), 13-10
Stats input option, 13-6, 13-7
STAT TESTS menu, 13-9
statistieal
distribution
functions.
See
distribution
functions

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,
functions

15-3
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-

- T (continued)

TABLE SETUP screen, 7-3
tables, 7-1 to 7-6
description,
7-5
variables, 7-3 to 7-5

time value

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

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
12`1-12`1
formulas, A-54
FV vm'iable (furore
I% variable (annual
12.t-12.t

Index-14

value),
interest

(eontinued)

N vm'iable (number of payment
periods),
14-12-t
PMT vm'iable (payment
amount),
14-14

tan((tangent),
2-3, A-29
tan'l((aretangent),
2-3, A-29

features, 17, 18
keyboard, 2, 3
key code diagram,

of money

-

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
A-31

amount),

14-6,

tvm_PV (present Vahle), 12`1
- 7, A-31
TVM Solver, 12-1-2-1
vm'iables,
12-1-14
Tlnterval (one-sample
t eonfidenee
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,
5-6, 6-9
expression
display, 3-12`1,3-18
Trace instruction
in a program,
A-30

4-8,

3-19,

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,

per year),

12`1-12`1
rate),

A-30

- T (continued)

-

complex,

tvm_PV (present value), 114-7, A-31
two-proportion
z confidence
inte_a_al
(2-PropZlnt),
13-21, A-20
two-proportion
z test (2-PropZTest),
13-15, A-20
two-sample
F-Test formula, A-52
two-sample
t test formula, A-53
two-vm'iable
statistics
(2-Var Stats),
12-25, A-31

uv/uvAxes
uw/uwAxes

-

6-3

(axes format),
(axes format),

6-8, A-31
6-8, A-31

-V-

function,

7-5

vm'ianee

of a list (variance(),
A-31
VARS menu

11-18,

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
(axes

format),

6-3

6-8

W

1-Var Stats (one-variable
12-25, A-31

statistics),

2-Var Stats (two-variable
12-25, A-31

statistics),

value operation

1-11t

real, 1-13
recalling values, 1-15
solver editor, 2-9
statistical,
12-29
string, 15-].L 15-5
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

vw/uvAxes
v sequence

values,

graph databases,
1-13
graph pictures,
1-13
independent/dependent,
list, 1-13, 11-3
matrix, 1-13, 10-3

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

u sequence function,
user variables, A-49

1-13

displaying
and storing
equation solver, 2-10

functions,
3- 7
grid, 3-1J4
labels, 3-1J4
pixels, 8-16

U

-

vmialAes

turlling Ol1and off
axes, 3-1J4
calculator,
1-2
coordinates,
3-14
expressions,
3-1J4

-

- V (continued)

on a graph,

3-25

w sequence
function,
warranty
inforlnation,

6-3
B-13

Web (axes format),
web plots, sequence
While, 16-11,A-32
window variables

6-8, A-31
graphing,

6-11

function graphing, 3-11
parametric
graphing, ]4-5
polar graphNg,
5-]4
sequence graphing,
6- 7

Index-15

-X-

- Z (continued)

-

XFact zoom factor, 3-2J4
x-intercept
of a root, 3-26

ZoomSto (store zoom _lndow),
A-33

xor (Boolean)
exclusive
2-26, A-32
x m root (_), 2-6

ZPrevious (use previous
3-23, A-33

or operator,

Z-Test (one-sample
ZTrig (trigonometric
A-3J4

-y-

3-2J4

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
z confidence
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),
A-33

3-22,

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

Index-16

(statistics

zoom),

window),

ZSquare (set square pixels), 3-21, A-33
ZStandard (use standard
window),
3-22, A-33

xyLine ([__) plot type, 12-31
AX window variable, 3-12

YFact zoom factor,
Y= editor

3-23,

3-22, A-33

z test), 13-10, A-3]-_
window), 3-22,

_

T1=83

TEXAS INSTRUMENTS

J
STAT

PLOT

TBLSET

A-LOCK

FORMAT

QUiT

INS

LiNK

LiST

CALC

TEST

A

ANGLE

E{

DRAW

FINANCE

D

SIN

E

COS

I

EE

J

{

K

-1

-1

C

DISTR

F

TAN

-1

TABLE

G

1T

N

}

L

e

IvI

e x

S

L4

T

L5

U

L6

V

_

W

RCL

X

L1

Y

L2

Z

L3

®

ME[V]

f_

i

:

ANS

?

OFF

CATALOG _

ENTRY

SOLVE



Source Exif Data:
File Type                       : PDF
File Type Extension             : pdf
MIME Type                       : application/pdf
PDF Version                     : 1.2
Linearized                      : No
Page Count                      : 446
Page Layout                     : SinglePage
Page Mode                       : UseNone
Producer                        : Goby Monitor Application version 4, 0, 0, 13
Create Date                     : Mon Jul 21 04:13:34 2008
Author                          : 
Title                           : 
Subject                         : 
EXIF Metadata provided by
EXIF.tools

Navigation menu