I-3 INDEX expansion of, 909 of a 2 * 2 matrix, 907 of a 3 * 3 matrix, 908 theorems for, 911 Determinant equation, 918 Diagonal form of a matrix, 893 Diastolic pressure, 630 Difference of cubes, 65, 66 definition of, 26 of squares, 54, 65–66 Difference identity application of, 702–705 for cosine, 697–698 for sine, 700–701 for tangent, 700–701 Difference quotient, 301 Difference tones, 752 Differential equations, 501 Differentiation, 305 Digits, significant, 566–567 Dimensions of a matrix, 892 Direction angle of a vector, 811 Directly proportional definition of, 411 as nth power, 412 Directrix of a parabola, 994 Direct variation definition of, 411 as nth power, 412 Discontinuity of the graph of a function, 268, 381, 391 Discriminant, 137 – 138 Disjoint interval, 173 Disjoint sets, 18 Distance, rate, and time problems, 113 – 114 Distance between points, 35 Distance formula, 203–205 Distributive property, 32–33, 957 Divergent sequence, 1041 Division of complex numbers, 128 of decimals, 8–9 of fractions, 4–5 of functions, 297 order of operations for, 29 of polynomials, 56–57, 340 by powers of ten, 8–9 of rational expressions, 74–75 of real numbers, 26, 28 synthetic, 341 – 342 by zero, 27 Division algorithm for polynomials, 340 special case of, 343 Domain(s) agreement on, 224 of circular functions, 609 of a function, 226, 297 of inverse circular functions, 731 of a rational expression, 72 of a relation, 223 Dominating term, 324, 362 Dot product of vectors definition of, 814 geometric interpretation of, 815 properties of, 814 D Damped oscillatory motion, 663 Dantzig, George, 942 Decibels, 479 Decimal(s) addition of, 7 division of, 8–9 equivalents, 10 explanation of, 6, 20 multiplication of, 8–9 operations with, 7–9 place value in, 6 repeating, 9 rounding of, 8 subtraction of, 7 terminating, 9 writing as fractions, 7 writing as percents, 10 writing fractions as, 9 writing percents as, 10 Decimal degrees, 528 Decimal places, 8–9 Decimal window, 382 Decomposition into partial fractions, 920, 925 of rational expressions, 920 Decreasing function, 230 De Fermat, Pierre, 202 Definite integral, 113, 329, 1045 Degree measure converting to radian measure, 594 – 595 definition of, 526 Degree mode, calculators in, 537, 538, 556 Degree of a polynomial, 51–52 Degree of a term, 51 Degree of curvature, 605 Degree/radian relationship converting measures, 594–595 table of, 596 Delta x, 240 Delta y, 240 De Moivre, Abraham, 832 De Moivre’s theorem, 832 Denominator(s) addition of fractions with same, 5 common, 5 – 6 least common, 5–6, 75 rationalizing, 89–90, 536, 540, 543, 545 Dependent equations, 874 Dependent variable, 221, 223 Depression, angle of, 569–570 Derivative of a function, 242, 301, 305, 348 of a parametric equation, 568 power rule for, 84 of a trigonometric function, 689 Descartes, René, 202, 203 Descartes’ rule of signs, 354 Descending order, 53, 56 Determinant(s) definition of, 907 evaluating, 909 – 910 Correlation coefficient, 369 Cosecant function characteristics of, 655 definition of, 534–535 domain of, 655 graph of, 655 inverse of, 730 period of, 655 range of, 542, 655 steps to graph, 656 Cosine function amplitude of, 623 characteristics of, 622 definition of, 534–535 difference identity for, 697–698 domain of, 622 double-angle identity for, 711–712 graph of, 622 half-angle identity for, 718 horizontal translation of, 635 inverse of, 728–729 period of, 622, 625 range of, 542, 622 steps to graph, 626, 637 sum identity for, 697–698 translating graphs of, 635, 636, 637 vertical translation of, 636 Cosines, law of applications of, 789–790 applying to solve a triangle, 787, 789 – 790 derivation and statement of, 788 Heron’s formula and, 792–794 Cost fixed, 245 per item, 245 Cost-benefit model, 82 Cost function, 245 Cotangent function characteristics of, 646 definition of, 534–535 domain of, 646 graph of, 646 horizontal translation of, 649 inverse of, 730 period of, 646 range of, 542, 646 steps to graph, 647 vertical translation of, 649 Coterminal angles, 529 Counting numbers, 15 Counting theory, 1088–1094 Cramer’s rule for solving linear systems derivation of, 912 general form of, 913 Critical angle, 767 Cryptography, 442 Cube root function, 270 Cubes difference of, 65 sum of, 65 Cubic equation, 136 Cubing function, 269 Curvature, degree of, 605 Cycloid calculator graphing of, 854 definition of, 854
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