I-2 INDEX Composite function definition of, 302 derivative of, 305 Composition of functions, 302 Compound amount, 455 Compound events, 1102–1103 Compounding continuously, 456 Compound interest definition of, 454 general formula for, 454 Concours d’elegance, 430 Conditional equation, 108, 109 Conditional statement converse of, 204 definition of, 204 Conditional trigonometric equations with half-angles, 744 linear methods for solving, 740 with multiple angles, 745–746 satisfying, 740 solving with the quadratic formula, 742 steps to solve algebraically, 743 using trigonometric identities to solve, 742 – 743 zero-factor property method for solving, 741 Congruence axioms, 772 Congruent triangles, 772 Conic definition of, 1007 eccentricity of, 1007 Conic sections definition of, 992 equations of, 1025, 1127 geometric definition of, 1029 geometric interpretation of, 992 identifying from equations, 1027 polar form of, 1121–1123 summary of, 1026–1027 Conjugate(s) of a binomial, 90 complex, 127, 352 properties of, 352 Conjugate zeros theorem, 352 Consistent systems, 874 Constant function, 230, 239 Constant of variation, 411 Constant velocity problems, 113–114 Constraints, 943 Continuity of a function, 267–268 Continuous compounding, 456 Continuous function, 267–268, 1040 Contradiction equations, 108, 109 Convergent sequence, 1041 Converse of a conditional statement, 204 Coordinate(s), photographic, 786 Coordinate plane, 202 Coordinates of a point on a line, 19, 202 Coordinate system definition of, 19 polar, 620, 839 rectangular, 839 Corner point of a region of feasible solutions, 944 Cofunctions of trigonometric functions, 550 Collinear points, 205 Column matrix, 951 Column of a matrix, 892 Combinations definition of, 1091 distinguishing from permutations, 1093 – 1094 formula for, 1092 Combined variation, 413 Common denominators, 5–6 Common difference of an arithmetic sequence, 1051 Common factors in fractions, 2 of a rational expression, 72–73 Common logarithms applications of, 478 definition of, 477 modeling with, 478 Common ratio of a geometric sequence, 1061 Commutative properties, 32–33, 957 Complement of an event, 1100 of a set, 17, 18, 19 Complementary angles, 527 Completing the square, 133, 326 Complex conjugates definition of, 127 property of, 127, 352 Complex fractions definition of, 28, 77 simplifying, 77 – 78 Complex numbers absolute value of, 822 addition of, 126 argument of, 822 conjugates of, 127 definition of, 123 De Moivre’s theorem for, 832 division of, 128 graph of, 821 imaginary part of, 123 modulus of, 822 multiplication of, 126–127 nonreal, 124 nth root of, 833 nth root theorem for, 834 operations on, 125–129 polar form of, 822 powers of, 832 product theorem for, 826 pure imaginary, 124 quotient theorem for, 827 real part of, 123 rectangular form of, 821 roots of, 833–836 standard form of, 123–124, 821 subtraction of, 126 trigonometric form of, 822 Complex plane imaginary axis of, 821 real axis of, 821 Components of a vector horizontal, 811 vertical, 811 C Calculators. See Graphing calculator(s) Carbon dating, 504 Cardano, Girolamo, 358 Cardioid, 843 Cartesian coordinate system, 202 Cartesian equations, 842 Celsius-Fahrenheit relationship, 112, 265 Center of a circle, 213 of an ellipse, 1002 of a hyperbola, 1015 Center-radius form of the equation of a circle, 213 Certain events, 1100 Chain rule, 305 Change in x, 240 Change in y, 240 Change-of-base theorem for logarithms, 482 Chords, table of, 565 Circadian rhythm, 666 Circle(s) applications of, 216–217 arc length of, 597 center, 213 circumference of, 594 definition of, 213 eccentricity of, 1008, 1020 equations of, 213–216 general form of the equation of, 214 – 215 geometric interpretation of, 992 graphing by calculator, 214 graph of, 214 polar form of, 842–843, 847 radius of, 213 sector of, 599 tangent line to, 219 unit, 213, 607 Circular function(s) definition of, 607 domains of, 609 evaluating, 609 finding numbers with a given circular function value, 611 interpreting in calculus, 213 inverse, 727 Circumference of a circle, 594 Cis u, 822 Cissoid graphing, 849 with a loop, 849 Clinometer, 578 Closed interval, 169 Closure properties, 32 Cloud ceiling, 578 Coefficient binomial, 1075 correlation, 369 definition of, 51 leading, 324 Cofactor of an element of a matrix, 908 – 909 Cofunction identities, 550, 699 – 700
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