Subject Index I11 denoting, A1–A2 disjoint, A2, A3 elements of, A1 empty (null), A1 equal, 911 finite, 911n infinite, 911n intersection of, A2, A3 union of, A2, A3 universal, A2 Set-builder notation, A1–A2 Setting the viewing window (rectangle), 3 Shannon’s diversity index, 324 Shifts, vertical and horizontal, graphing functions using, 112–114 Side(s) of an equation, 4, A44 of an inequality, A5 Side-angle-side (SAS) triangles, A17 Side-side-side (SSS) triangles, A17 Similar triangles, A17–A18 definition of, A17 determining, A18 using, A18–A19 Simple harmonic motion analyzing, 585–586 model for an object in, 583–585 Simple interest, A67–A68 Simple interest formula, 345, A67 Simplex method, 840n Simplification of expressions with rational exponents, A91–A92 of nth roots, A87 of radicals, A88 of a rational expression, A35–A36 complex, A40–A42 of trigonometric identities, using algebra, 504–505 Simpson’s Rule, 178–179 Sine function, 398 of best fit, 458–459 graphs/graphing of, 427 historical feature on, 407 inverse definition of, 472–473 exact value of, 474–475 name of, 407 properties of, 428 Sines, Law of, 560–565 applied problems using, 563–565 historical feature on, 573 proof of, 565 solving SAA or ASA triangles using, 560–561 solving SSA triangles using, 561–563 Sinusoidal functions, 430–432 amplitude, period, and phase shift of, 452–454 amplitude and period of, 431–432 graphing the sum of, 589 graphs/graphing of, 451–455 using key points, 432–435 Sinusoidal graphs, 431 finding an equation for, 436 Sinusoidal models from data, 455–459 Slope of a line, 32–35 finding, 38 graphing a line given a point and, 35 undefined, 33 of a line perpendicular to another line, 42–43 m as symbol for, 47 Slope-intercept form of a line, 37–38 Solutions of an equation, A44 extraneous, A90 of an inequality, A80 to a linear programming problem definition of, 842 location of, 842 repeated, A48 rotation formulas and, 722 to transform equations of conics, 721–723 analyzing equations using, 724–725 identifying conics without, 726 Row echelon form, 773–779 reduced, 776 Row index of a matrix, 770, 795 Row operations, 771–772 Row vectors, product of a column vector and, 799 Ruffini, P., 226 Run, 32 Sample space, 925–926 SAS (side-angle-side) triangles, A17, A18 Satisfying an equation, 4, A44 Scalar(s), 638–639 Scalar multiples of matrices, 798–799 of vectors, 638 finding, 642 Scalar multiplication, 798–799 properties of, 799 Scalar products. See also Dot product finding, 662 Scale of real number line, A4 Scatter plots, 149–150 Schroeder, E., 932 Scientific calculators, A10 Secant function, 398 graphs/graphing of, 447–448 inverse definition of, 487 exact value of, 487–489 Secant line, 95–96 Second-degree equations, A48 Sequences, 855–889 amortization and, 864 annuity problems and, 862–864 arithmetic, 869–875 common difference and, 869 definition of, 869 determining, 869–870 formula for, finding, 870–871 nth term of, 870–871 recursive formula for, 871 sum of, 871–873 convergence of, 888 definition of, 855 determining from a pattern, 858 divergence of, 888–889 Fibonacci, 859–860 geometric, 875–879 common ratio and, 875–876 definition of, 875–876 determining, 876 formula for, finding, 877 nth term of, 877 sum of, finding, 878–879 historical feature on, 883 limit of, 887–889 of partial sums, 891 recursively defined, terms of, 858–859 summation notation and, 859–860 sum of, 861–862 terms of, 855–859 first several, listing, 855–858 general, 856 of a recursively defined sequence, 858–859 Series convergence of, 891 divergence of, 891 geometric, 879–881, 892–893 definition of, 892 sum of, 893 infinite, 889–891 definition of, 890 terms of, 890 Set(s), A1–A4 complement of, A2, A3 in space, 660 transforming equations between polar and rectangular forms and, 606–607 Rectangular coordinate system, 2 Rectangular equations converting polar equations of conics to, 733 identifying and graphing polar equations by converting to, 611–612 for a plane curve defined parametrically, 738–740 plane curves defined by, parametric equations for, 743–745 Rectangular form, converting complex numbers between polar form or exponential form and, 628–631 Recursive formulas for an arithmetic sequence, 871 sequences defined by, terms of, 858–859 solving annuity and amortization problems using, 862–864 Reduced row echelon form, 776 Reflections about the x-axis or y-axis, graphing functions using, 117–118 Regiomontanus, 392 Regression, 174 Relations, 61–65 definition of, 61 domain of, 61 input and output of, 61 linear vs. nonlinear, 150–152 mapping, 61, 63–64 range of, 61 representing a function, 63–65 Remainder, 215 Remainder Theorem, 215–216, A25 Repeated solutions, A48 Repeating decimals, A3 Resonance, 588 Rest position, 584 Resultant force, 644 Rhaeticus, 392 Rhind papyrus, 883 Richter scale, 325 Right angles, A14 Right circular cones, 681 Right endpoint, A77 Right-hand limit, 954 Right-hand rule, 660 Right triangles definition of, 546 finding values of functions of acute angles using, 546–548 hypotenuse of, 546, A14 properties of, 549 Pythagorean Theorem and, A14–A15 solving, 548–549 verifying, A14–A15 Right triangle trigonometry, 546–559 Complementary Angle Theorem and, 548 finding value of functions of acute angles using right triangles and, 546–548 solving right triangles and, 548–549 Rise, 32 Roots. See also Real zeros (roots) complex, 632–634 cube, A87 complex, 632, 633–634 double, A48 of an equation, A44 limits of, 949–950 of multiplicity 2 (double), A48 nth, A87–88 perfect, A87 square, A9–A10, A87 complex, 632 evaluating, A9–A10 principal, A9, A63 Rose curves, 620 Ross, Mary Golda, 190 Roster method, A1–A2 Rotation of axes
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