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14411Index.pgs 8/14/08 4:38 PM Page 718 INDEX A Absolute value, 3 equations, 13 functions, 122, 136–138 inverse of, 164–165 inequalities, 14, 81–82 Addition of complex numbers, 210–211 distributive property of multiplication over, 99 of polynomials, 9–10 of radicals, 94–96 of rational expressions, 53–56 Addition property of equality, 5 of inequality, 7 Additive inverse, 2 of complex numbers, 210 Algebraic method in solving quadraticlinear systems, 231–233 Ambiguous case (SSA), 569–573 Amplitude, 447–449 of a periodic function, 448 Angle measures in degrees, 357–359, 383–384 in radians, 400–404, 407–409 Law of Cosines, finding triangle, 557–558 Angle(s) coterminal, 359–360 degree measures of, 357–359, 383–384 of depression, 575 of elevation, 575 fourth-quadrant, 389–391 function values of special, 378–380 initial side of, 358 quadrantal, 359 radian measures of, 400–404, 407–409 second-quadrant, 386–387 standard position of, 358 terminal side of, 358 third-quadrant, 387–389 Angular speed, 361 Antilogarithm, 333 Arccosine, 383. See also Inverse cosine function domain of, 420 graph of, 468–469 range of, 420 Arcsine, 383. See also Inverse sine function domain of, 420 graph of, 468 range of, 420 Arctangent, 383. See also Inverse tangent function domain of, 421 graph of, 469–470 range of, 421 Area under a normal curve, 702–703 of a triangle, 559–562 Arithmetic functions, transformations and, 152–153 Arithmetic of imaginary numbers, 205 Arithmetic mean(s), 255, 596–597 Arithmetic sequence(s), 252–254, 350 common difference for, 252 Asymptote, 465 horizontal, 300 vertical, 321 Axis of symmetry of the parabola, 140 B Base(s), 17 natural, 302 solving exponential equations with different, 306–307 solving exponential equations with same, 306 Base-ten number system, 39 Bernoulli experiment, 696–697. See also Binomial experiment Bimodal data, 599 Binomial, 10 Binomial distribution, 704 normal approximation to the, 703–706 Binomial expansion, 708–710 Binomial experiment, 696–697. See also Bernoulli experiment Binomial probability graphing calculator and, 698–699 normal curve and, 701–706 Binomial probability formula, 696 Binomial theorem, 708–710 Bivariate statistics, 634–638 Bombelli, Rafael, 203–204 Box-and-whisker plot, 600–604 Briggs, Henry, 319 Bürgi, Joost, 286 C Cause and effect, 644 Census, 588 Center of a circle, 167 Center-radius form of the equation of a circle, 167–171 Change of base formula, 339–340 Circle, 167–171 center of, 167 diameter of, 167 equation of center-radius form, 167–171 standard form, 169–171 radius of, 167 unit, 362–363 Coefficient correlation, 641–644 of a quadratic equation, 221–222 Cofunction, 425–427 Combination, 683–685, 688–690 Common binomial factor, 22 Common difference, for arithmetic sequences, 252 Common logarithms, 332–334 Common monomial factor, 22 Common ratio, 266 14411Index.pgs 8/15/08 3:15 PM Page 719 Index Commutative group, 3 Completely factored polynomial, 25 Completing the square, 187–191 Complex conjugate, 212 Complex fractions, 61 simplifying, 62–63 Complex number(s), 203–216 addition of, 210–211 additive inverse of, 210 division of, 214–215 graphing calculator and, 206, 207 multiplication of, 209, 211–214 multiplicative identity of, 212–213 operations with, 209 set of, 205–206 subtraction of, 211 Complex rational expressions, 61–63 Complex roots of a quadratic equation, 217–219 Composite functions, 155–156 Composition of functions, 155–159 Compounding periods, types of, 310–312 Conic sections, 183 Conjugates, 104 Consistent system, 229 Constant function, 122 Controlled experiment, 588 Convergence of sequences, 282 Coordinate plane positioning of triangles on, 549 triangles in the, 560–562 Correlation, 635–636 Correlation coefficient (r), 641–644 absolute value of, 641 properties of, 642 Cosecant function, 374–375, 416–417 domain of, 417 graph of, 463–464 range of, 417 Cosine function, 363, 415 domain of, 415 evaluating, 411 graph of, 442–445 unit circle and, 445 writing the equation of, 455–457 inverse, 420–421, 468–469 period of, 443 range of, 415 Cosine (A+B), 493–495 Cosine (AB), 488–494 Cotangent function, 375 domain of, 418 graph of, 465 range of, 418 Coterminal angles, 359–360 Counting numbers, 2 Counting Principle, 673–675 probability form of, 689 Cube root, 84–85 principal, 85 Cubic curve, 648 Cumulative frequency, 606 Cycle, 436 of the sine function, 436 D Data, 588 bimodal, 599 collection of, 588–589 frequency distribution tables, for grouped data, 607–611 for individual data values, 605–607 grouped, measures of central tendency for, 605–611 linearized, 669 organization of, 590–593 Decimals, converting infinitely repeating, to common fractions, 41 Degree measures of angles, 383–384 Degrees changing radians to, 402–404 changing to radians, 401 relationship between radians and, 400–401 Denominator least common, 54 rationalizing, 104–107 Dependent events, 674 Depression, angle of, 575 Descartes, René, 204, 286 Diagrams box-and-whisker plots, 600–604 scatter plots, 634 stem-and-leaf, 590–593 tree, 673–674 Diameter of a circle, 167 Difference of two perfect squares, 25 Differences of angle measures cosine, 488–491 sine, 497 tangent, 500 Directly proportional, 119, 133 Direct variation, 132–133 Discriminant, 198–201 Distributive property of multiplication over addition or subtraction, 99 Divergence of sequences, 282 Division of complex numbers, 214–215 of exponents, 287, 290, 291, 295 of radicals, 102–103 of rational expressions, 50–51 Division property of equality, 5 of inequality, 17–19 719 Domain, 5, 120 of cosecant function, 417 of cosine function, 415 of cotangent function, 418 of secant function, 416 of sine function, 415 of tangent function, 417 Double-angle formulas, 504 cosine, 504–505 sine, 504 tangent, 505 Double root, 143, 199 E e, 277 Element (), 121 Elements (Euclid), 79 Elevation, angle of, 575 Empirical probability, 688. See also Experimental probability Equality addition property of, 5 division property of, 5 multiplication property of, 5 subtraction property of, 5 Equation(s), 5–6 absolute value, 13 of a circle center-radius form, 167–171 standard form, 169–171 equivalent, 5 exponential, 340–343 logarithmic, 344–346 quadratic, 27 radical, 108 rational, 64–69 solving linear, 10 Equilateral triangle, function values, 378 Equivalent equations, 5 Eratosthenes, 353 Euclid, 79 Euclidean perfect numbers, 38 Evaluating powers, 288 Even function, 446 Events, 674 dependent, 674 independent, 674 Experimental probability, 688. See also Empirical probability Experiment(s) Bernoulli, 696 binomial, 696 controlled, 588 Exponent(s), 17 fractional, 293–296 laws of, 287–288 negative, 290–291 14411Index.pgs 8/14/08 720 4:38 PM Page 720 Index Exponent(s) (continued) solving equations involving, 304–305 zero, 289–290 Exponential curve, 647 Exponential decay, 298 Exponential equations, 306, 340–343 solving with different bases, 306–307 with the same base, 306 Exponential function(s), 299 applications of, 308–310 compound periods and, 310–312 graphs of, 298–302 inverse of an, 320–322. See also Logarithm natural, 302 Exponential growth, 298 Extraneous root, 66 Extrapolation, 656–658 Extremes, 59 F Factored, completely, polynomial 25 Factorials, series containing, 275–276 Factoring, polynomials, 22–25 binomial factors, 23 common binomial factor, 22 common monomial factor, 22 special products and factors, 25 difference of squares, 25 and solving trigonometric equations, 526–529 Factors of monomial, 22 of polynomial, 22–25 common binomial, 22 common monomial, 22 opposite, 46–47 Fibonacci, 39 Finite sequence, 248 Finite series, 258 graphing calculator and, 259–260 First-degree trigonometric equations, 519–523 First-quadrant angle, 386 FOIL, 18 Formula(s) binomial probability, 696 logarithmic change of base, 339 quadratic, 193–195 trigonometric area of triangle, 560 differences of angle measures, 488–491, 497, 500 double-angle, 504–505, half-angle, 508–511 Law of Cosines, 553, 557 Law of Sines, 565 triple-angle, 515 sums of angle measures, 493–494, 497, 501 Fourth-quadrant angle, 389–391 Fraction(s) complex, 61 converting infinitely repeating decimal to, 41 reducing to lowest, 46 unit, 76 Fractional exponents, 293–296 Fractional radicands, 89–91 Frequency, 459 cumulative, 606 Frequency distribution table, 591 for grouped data, 607–611 for individual data values, 605–607 Function(s), 120 absolute value, 122, 136–138 composite, 155–156 composition of, 155 constant, 122 domain of, 120 even, 446 identity, 160–161 inverse, 161–164 linear, 122 odd, 440 polynomial, 140–141 quadratic, 122, 140–141 range of, 120 sequential, 247 square root, 122 Function arithmetic, 149–151 transformations and, 152–153 Function composition, transformations and, 158–159 Function from set A to set B, 120–121 Function notation, 127–128 Function values from the calculator, 381–383 in the right triangle, 376 of special angles, 378 equilateral triangle, 378–380 isosceles right triangle, 378 of cotangent function, 465 of exponential functions, 298–302 of logarithmic functions, 321–322 of quadratic functions, 190–191 of secant function, 464 of sine function, 435–438 unit circle and, 438–440 of tangent function, 460–462 of y = ex, 302 Graphic method in solving quadratic-linear systems, 230 of tangent function, 460–462 Graphing calculator complex numbers, 206 function values from the, 381–383 probability binomial, 698 combinations, 684 factorial, 680–681 permutations, 680–681 reference angles, 386–391 trigonometric equations 523–524 two variable inequalities, 235 sequences, 250 recursive, 282 series, finite, 259–260 statistics binomial probabilities, 698–699 box-and-whisker plot, 601–602 with outliers, 616 correlation coefficient, 641 histogram, 593 mean, 610 median, 610 normal distribution, 630–631 normal approximation, 704–705 regression linear 635, 641 non-linear, 648–649 standard deviation population, 622 sample, 624–625 Grouped data, measures of central tendency for, 605–611 H G General triangle, solving, 576–579 Geometric means, 267–269 Geometric probability, 690–691 Geometric sequence, 266–269, 350 Geometric series, 270–272 Graph(s) of complex numbers, 207 of cosecant function, 463–464 of cosine function, 442–445 unit circle and, 445 Half-angle formulas, 508 cosine, 508 sine, 509 tangent, 509 Harmonic motion, simple, 459 Hérigone, Pierre, 286 Higher degree polynomial equations, 224–226 Higher degree polynomial functions, 143–144 Histogram, 592–593 14411Index.pgs 8/14/08 4:38 PM Page 721 Index Horizontal asymptote, 300 Horizontal line test, 130–131 Hume, James, 286 Hyperbola, 175 Hypotenuse, 354 I i, powers of, 204–205 Identities, 411 proving, 485–487 Pythagorean, 411–412, 413, 483 quotient, 413, 486 reciprocal, 413, 483 Identity function (I), 160–161 Imaginary numbers arithmetic of, 205 pure, 203 set of, 203–204 Independent events, 674 Index, 85 Inequalities, 7 absolute value, 14, 81–82 graphing, on the number line, 80–81 property of, addition, 7 division, 7 multiplication, 7 subtraction, 7 quadratic, 30–34 solving, 32, 233–235 Infinite sequence, 248 Infinite series, 258, 273–275 Infinity (`), 258 Initial side of an angle, 358 Integers, 2 Interest, compounded annually, 310 compounded continuously, 310–311 Interpolation, 655–656 Interquartile range, 615–617 Interval notation, 81 Inverse additive, 2 of functions, absolute value, 164–165 cosine, 468–469 exponential, 320–322 quadratic, 165 sine, 468 tangent, 469–471 multiplicative, 40 Inverse cosine function, 420–421. See also Arccosine domain of, 421 graph of, 468–469 range of, 421 Inverse of an exponential function, 320–322 Inverse functions, 161–165 Inverse sine function, 419–420. See also Arcsine domain of, 420 graph of, 468 range of, 420 Inverse tangent function, 421–423. See also Arctangent domain of, 421 graph of, 469–470 range of, 421 Inverse trigonometric functions, 419–423 graphs of, 468–471 Inverse variation, 174–176 Inversely proportional, 119. See also Vary inversely, two numbers Irrational numbers, 79–80 Isosceles right triangle, function values, 378 K al-Khwarizmi, Mohammed ibn Musa, 186 L Law of Cosines, 552–554 using to find angle measure, 557–558 Law of Sines, 564–567 Laws of exponents, 287–288 Leaf, 590 Least common denominator (LCD), 54 Least common multiple (LCM), 54 Legs, 354 Leonardo of Pisa, 39 Like radicals, 95 Like terms, 10 Linear function(s), 122, 130–131 non-constant, 130 transformations of, 131–132 Linear regression, 635–637, 641–642 Linearized data, 669 Line of best fit, 635 Line segments commensurable, 79 incommensurable, 79 Logarithm(s). See also Inverse of an exponential function basic properties of, 327–328 change of base formula, 339–340 common, 332–334 natural, 336–338 of powers, 329–331 of products, 328 of quotients, 328–329 Logarithmic curve, 647 721 Logarithmic equations, 344–346 Logarithmic form of an exponential equation, 324–325 Logarithmic function(s), 319–351 common logarithms, 332–334 exponential equations, 340–343 graphs of, 321–322 inverse of an exponential function, 320–322 logarithmic equations, 344–346 logarithmic form of an exponential equation, 324–325 logarithmic relationships basic properties of logarithms, 327–328 logarithms of powers, 329–331 logarithms of products, 328 logarithms of quotients, 328–329 natural, 336–338 Logarithmic growth, 322 Logarithmic relationships basic properties of logarithms, 327–328 logarithms of powers, 329–331 logarithms of products, 328 logarithms of quotients, 328–329 Lowest terms, 45 reducing fraction to, 46 M Many-to-one correspondence, 136 Mean, 59, 596–597 arithmetic, 255 geometric, 267–269 Measures of central tendency, 596–606 box-and-whisker plot, 600–604 mean, 596–597 median, 597–598 mode, 599 Measures of dispersion, 614–617 interquartile range, 615–617 range, 614–615 Median, 597–598 Mode, 599 Monomial, 9 multiplication of monomial by, 17–18 multiplication of polynomial by, 18 Multiplication of complex numbers, 209, 211–214 distributive property of, over addition or subtraction, 99 of exponents, 287, 290, 291, 294 of polynomials, 17–19 of radicals, 98–100 of rational expressions, 48–50 special products and factors in, 25 of sums that contain radicals, 99–100 14411Index.pgs 7/1/09 722 3:44 PM Page 722 Index Multiplication property of equality, 5 of inequality, 17–19 Multiplicative inverse, 40 of complex numbers, 212–213 Number sentences, writing and solving, 5–6 Number system, base-ten, 39 O N Napier, John, 39, 319, 350 Napier’s bones, 350 Natural base, 302 Natural exponential function, 302 Natural logarithm, 336–338 Natural numbers, 2 Negative exponents, 290–291 Non-linear regression, 647–651 exponential, 647–650 logarithmic, 647–648, 650–651 power, 647–650 cubic, 648 quadratic, 648 sinusoidal, 654–655 Normal approximation to the binomial distribution, 703–706 Normal curve, 628 area under a, 702–703 binomial probability and, 701–706 standard deviation and the, 628–629 Normal distribution, 628–632 normal curve in, 628 standard deviation and the normal curve in, 628–629 z-scores in, 629–632 Notation function, 127–128 interval, 81 set-builder, 120 sigma, 257–260 n factorial, 275 nth partial sum (Sn), 262–263 nth root of a number, 85–87 Number(s) complex, 203–216 counting, 2 imaginary, 203–204 irrational, 79, 80 natural, 2 nth root of, 85–87 perfect, 38 Euclidean, 38 prime, 89 rational, 40, 41 real, 80 whole, 2 Number e, 277 Number line, 2 graphing inequalities on the, 80–81 Observational study, 588 Odd function, 440 One-to-one correspondence, 130 Onto, 121–122 Opposites, 2 Oscillation of sequences, 282 Outcome(s), 673 probability with two, 695–699 Outlier, 615 P Parabola, 140 axis of symmetry of the, 140 turning point or vertex of, 140 Pascal’s Triangle, 709 Percentile, 607 Perfect numbers, 38 Euclidean, 38 Perfect square trinomial, 197–198 Period, 436, 449–451 of the cosine function, 443 of the sine function, 436 of the tangent function, 460 Periodic function, 439 Permutations, 678–683, 688–690 with repetition, 681–683 Phase shift, 451–453 Pi (p), 80 Plane, finding sine and cosine using any point on the, 367 Plot box-and-whisker, 600–604 scatter, 634–636 Polynomial(s), 9 addition of, 9–10 completely factored, 25 factoring, 22–25 binomial factors, 23 common binomial factor, 22 common monomial factor, 22 special products and factors, 25 difference of squares, 25 multiplication of, 17–19 by binomial, 18 by monomial, 18 by polynomials, 19 prime, 25 Polynomial equation(s) of degree two, 27 solving higher degree, 224–226 Polynomial function(s), 140–147 degree three or greater, 143–144 roots of, 142–144 and graph of, 144–147 solving higher degree, 224–226 Population, 588 standard deviation based on the, 622 Power(s), 17 evaluating, 288 of i, 204–205 of a product, 287, 290, 291 of a quotient, 287, 290, 291 logarithms of, 329–331 Power curve, 647 Prime number, 89 Prime polynomial, 25 Principal cube root, 85 Principal nth root, 85 Principal square root, 84 Probability binomial graphing calculator and, 698–699 normal curve and, 701–706 binomial theorem and, 708–710 combinations in, 683–685, 688–690 counting principle and, 673–675 empirical, 688 experimental, 688 geometric, 690–691 permutations in, 678–681, 688–690 permutations with repetition in, 681–685 theoretical, 687 with two outcomes, 695–699 Product, logarithm of, 328 Properties of equality, 5 Properties of inequality, 7 Proportion, 59–60 Pure imaginary number, 203 Pythagorean identities, 411–413, 483 Q Quadrantal angle, 359 Quadratic curve, 648 Quadratic equation, 27 coefficients of, and its roots, 221–222 complex roots of, 217 discriminant and, 198–199 real roots of a, 187–190 solving, 27 standard form, 27 writing, given the roots of the equation, 219–221 Quadratic formula, 193–195 alternate derivation of the, 197–198 14411Index.pgs 7/1/09 3:44 PM Page 723 Index using, to solve trigonometric equations, 530–533 Quadratic function, 122, 140–141 graph of, 190–191 inverse of, 165 roots of, 142–143 transformations of, 141–142 Quadratic inequalities, 30–34 solving, 32, 233–235 two variable, 234–235 Quadratic-linear system, 229–235 of equations, 229–233 solving, 229–233 algebraic method, 231–233 graphic method, 230 of inequalities, 233–235 solving, 233–235 using the graphing calculator, 235 Quartile, 599–600 first or lower, 600 second, 600 third or upper, 600 Quotient identities, 413, 483 Quotient, logarithm of, 328–329 R Radian(s), 399, 400 changing degree to, 401 changing to degrees, 402–404 finding angle measures in, 407–409 in finding trigonometric function values, 406–407 relationship between degrees and, 400–401 unit circle and, 410–411 Radical(s), 85 addition of, 94–95 division of, 102–103 like, 95 multiplication of, 98–100 simplifying, 88–89 simplifying unlike, 95–96 subtraction of, 94–95 unlike, 95 Radical equation, 108 solving, 108–112 Radicand, 85 fractional, 89–91 Radius of a circle, 167 Raising an exponent to a power, 287, 290, 291, 295 Range, 614–615 of cosecant function, 417 of cosine function, 415 of cotangent function, 418 of the function, 120 interquartile, 615–617 of secant function, 416 of sine function, 415 of tangent function, 417 Ratio, 57 common, 266 simplest form of, 266 Rational equations, solving, 64–69 Rational expressions, 44 addition of, 53–56 complex, 61–63 division of, 50–51 multiplication of, 48–50 simplifying, 44–46 subtraction of, 53–56 Rational inequalities, solving, 70–73 Rationalizing a denominator, 104–107 Rational numbers, 40, 41 Real numbers, 80 Real roots of a quadratic equation, 187–190 Reciprocal, 40 Reciprocal functions, 374 Reciprocal identities, 413, 483 Reciprocal trigonometric functions, 374 cosecant function, 374–375 cotangent function, 375 function values in the right triangle, 376 graphs of, 463–466 secant function, 374 Recursive definition, 248–249 Reference angles, 387–391, 519 of fourth-quadrant angles, 389–391 of second-quadrant angles, 386–387, 391 of third-quadrant angles, 387–389, 391 Regression linear, 635–637, 641–642 non-linear, 647–651 Regression line, 635 Relations, 120–124 Repetition, permutations with, 681–685 Restricted domain, 420 Right triangle(s) function values in the, 376 hypotenuse of, 354 isosceles, 378 legs of, 354 solving, 575–576 trigonometry of, 354–356 Roomen, Adriaan van, 286 Roots, 5 of a polynomial function, 142–143. See also Zeros double, 143 723 of a quadratic equation, 187–190 complex, 217–219 double, 199 sum and product of, 219–222 writing quadratic equation given, 219–221 and radicals, 84–85 cube, 84–85 principal, 85 nth, 85–87 principal, 85 square, 84 principal, 84 with index n, 91–93 Rotations, angles and arcs as, 357–360 S Sample, 588 standard deviation based on a, 623–625 Sample space, 673 Scatter plot, 634–636 Secant function, 374, 415–416 domain of, 416 graph of, 464 range of, 416 Second-quadrant angle, 386–387 Sequence(s), 248–250 arithmetic, 252–254 convergence of, 282 divergence of, 282 finite, 248 geometric, 266–269 graphing calculator and, 250 infinite, 248 oscillation of, 282 Series, 257 containing factorials, 275–276 finite, 258 graphing calculator and, 259–260 geometric, 270–272 infinite, 258, 273–275 Set of complex numbers, 205–206 of imaginary numbers, 203–204 Set-builder notation, 120 Sigma, Greek letter capital (S), 257 lowercase (s, sx), 622 Sigma notation, 257–260 Similar terms, 10 Similar triangles, 354, 548–551 Simple harmonic motion, 459 Simplest form, of rational expression, 45 of radical, 89 of ratio, 57–58, 14411Index.pgs 7/1/09 724 3:45 PM Page 724 Index Simplifying radicals, 88–93 Simplifying unlike radicals, 95–96 Sine (A + B), 497 Sine (A – B), 497 Sine function, 363, 415 cycle of, 436 domain of, 415 evaluating, 411 graph of, 435–438 unit circle and, 438–440 writing the equation of, 455–457 inverse, 419–420 inverse of, 468 period of, 436 range of, 415 and the unit circle, 363 Sine regression, 654–655 Sinusoidal regression equation, 654–655 SohCahToa, 355 Solution, 5 Solutions of a triangle determining the number of, 569–573 finding, 575–579 Space, sample, 673 Special products and factors, 25 Speed, angular, 361 Square root function, 122 Square root, 84 principal, 84 Standard deviation, 622 based on a sample, 623–625 based on the population, 622 normal curve and, 628–629 symbols (s, sx), 622 Standard form of the equation of a circle, 169–171 Standard form of a quadratic equation, 27 Standard position, angle in, 358 Statistical summary, 600 Statistics, 587–669 bivariate, 634–638 cause and effect and, 644 collection of data in, 588–589 correlation coefficient in, 641–644 extrapolation in, 656–658 interpolation in, 655–656 measures of central tendency in, 596–606 measures of dispersion, 614–617 non-linear regression in, 647–651 normal distribution in, 628–632 organization of data in, 590–593 pitfalls of surveys in, 589–590 standard deviation in, 622–625 univariate, 588 variance in, 619–621 Stem, 590 Stem-and-leaf diagram, 590–592 Stevin, Simon, 39 Substitution in solving trigonometric equations involving different angle measures, 538–540 when more than one function is involved, 534–537 synthetic, 228 Subtraction, 3 of complex numbers, 211 distributive property of multiplication over, 99 of radicals, 94–95 of rational expressions, 53–56 Subtraction property of equality, 5 of inequality, 7 Sums of angle measures, cosine, 493–494 sine, 497 tangent, 501 Survey(s), 588 pitfalls of, 589–590 Synthetic substitution, 228–229 Systems of equations, 229–233 T Table, frequency distribution, 591 Tangent function, 368–372, 417 domain of, 417 graph of, 460–462 inverse, 421–423, 469–471 range of, 417 and the unit circle, 369 Tangent (A + B), 500 Tangent (A – B), 501–502 Term(s), 9 like, 10 lowest, 45 similar, 10 Terminal side of an angle, 358 Theoretical probability, 687 Theta (u), 358 Third-quadrant angle, 387–389 Tower of Hanoi, 252 Transformations function arithmetic and, 152–153 function composition and, 158–159 of linear function, 131–132 of quadratic functions, 141–142 Tree diagram, 673–674 Triangle(s), 353, 518 area of, 559–562 in the coordinate plane, 560–562 determining the number of solutions of, 569–573 equilateral, 378 general, 576–579 Pascal’s, 709 positioning of, on coordinate plane, 549 right, 575–576 function values in the, 376 hypotenuse of, 354 isosceles, 378 legs of, 354 trigonometry of, 354–356 similar, 548–551 solving, 575–579 Trigonometric equation(s), 519 factoring in solving, 526–529 first-degree, 519–523 graphing calculator and, 523–524 quadratic formula in solving, 530–533 solving linear, 520 substitution in solving involving different angle measures, 538–540 when more than one function is involved, 534–537 Trigonometric functions, 353–481 angles and arcs as rotations, 357–360 cofunctions, 425–427 degree measures of angles, 383–384 domain and range of, 414–419 cosecant function, 416–417 cosine function. 415 cotangent function, 418 secant function, 415–416 sine function, 415 tangent function, 417 factoring equations with two, 528–529 function values approximations, 399, 411 from the calculator, 381–383 of special angles equilateral triangle, 378–380 isosceles right triangle, 378 graphs of, 434–479 amplitude, 447–449 cosine function, 442–445 inverse of the cosine function, 468–469 inverse of the sine function, 468 inverse of the tangent function, 469–471 period, 449–451 phase shift, 451–453 reciprocal functions, 463–467 sine function, 435–440 sketching, 472–473 tangent function, 460–462 writing the equation of a sine or cosine, 455–457 inverse cosine function, 420–421 inverse sine function, 419–420 14411Index.pgs 8/14/08 4:38 PM Page 725 Index inverse tangent function, 421–423 Pythagorean identities, 411–413 radian measure, 400 changing degrees to radians, 401 changing radians to degrees, 401–404 relationship between degrees and radians, 400–401 radians in finding values, 406–407 reciprocal, 374 cosecant function, 374–375 cotangent function, 375 function values in the right triangle, 376 secant function, 374 reference angles and the calculator fourth-quadrant angles, 389–391 second-quadrant angles, 386–387 third-quadrant angles, 387–389 tangent function, 368–372 trigonometric function values and radian measure finding angle measures in radians, 407–409 units radians to find trigonometric function values, 406–407 using radians to find trigonometric function values, 406–407 trigonometry of the right triangle, 354–356 unit circle, sine, and cosine, 362–365 Trigonometric graphs, sketching, 472–473 Trigonometric identities, 482–515 basic identities, 483–484 cosine (A 1 B), 493–495 cosine (A 2 B), 488–494 cosine 12 A, 508 cosine of 2A, 504–505 graphical support for, 512–513 proving an identity, 485–487 sin (A 1 B), 497 sin (A 2 B), 497 sine 12 A, 509 sine of 2A, 504 tangent (A 1 B), 500 tangent (A 2 B), 501–502 tangent 12 A, 509–511 tangent 2A, 505–506 Trigonometry, 353 of the right triangle, 354–356 Trinomial, 10 Triple-angle formulas, 515 Turning point, 140. See also Vertex unwrapping, 439 Unit fractions, 76 Univariate statistics, 588 Unlike radicals, 95 simplifying, 95–96 V Value, absolute, 3, 641 Variance, 619–621 Variation, inverse, 174–176 Vary directly, variables, 133 Vary inversely, two numbers, 174. See also Inversely proportional Vertex, 140. See also Turning point Vertical asymptote, 321 Vertical line test, 123 W U Unit circle, 362–363, 411 cosine function and the, 363 graph of the cosine function and, 445 graph of the sine function and, 438–440 radians and, 410–411 sine function and the, 363 tangent function and the, 369 725 Whole numbers, 2 Z Zero exponent, 289–290 Zeros of a polynomial function, 142–143. See also Roots Z-score, 629–632
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