I1 definition of, 972 under the graph of a function, 968–972 of a parallelogram, 672–673 of a triangle, 577–583 SAS, 577–578 SSS, 578–579 Arguments of a function, 66 of z, 628 Arithmetic calculator, A10 Arithmetic mean, A86 Arithmetic sequences (progressions), 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 Ars Conjectandi (Bernoulli), 932 Ars Magna (Cardano), 226 ASA (angle-side-angle) triangles, A17 Associative property of matrix addition, 797 of matrix multiplication, 802 of vector addition, 638 Asymptotes of a hyperbola, 710–712 rational functions and, 238–244 horizontal, 239, 241–244 oblique, 239, 241–244 vertical, 239, 240–241 Average rate of change, 33 definition of, 94 of a function, 93–96 identifying linear functions using, 139–142 limits of, 951 Axis/axes conjugate, of a hyperbola, 705 coordinate, 2 imaginary, in complex plane, 627 major, of an ellipse, 693, 729 minor, of an ellipse, 693 polar, 600 of a quadratic function, 160–161 real, in complex plane, 627 of a right circular cone, 681 rotation of analyzing equations using, 724–725 identifying conics without, 726 rotation formulas and, 722 to transform equations of conics, 721–723 of symmetry, of a parabola, 159, 160, 161–163, 682 transverse, of a hyperbola, 705, 729 x-axis, 2 projection of P on, 584 reflections about, graphing functions using, 117–118 testing equations for symmetry with respect to, 21, 22, 23 y-axis, 2 projection of P on, 584 reflections about, graphing functions using, 117–118 testing equations for symmetry with respect to, 21, 22, 23 Azimuth, 553n Back-substitution, 758 Base of an exponent (power), A8 Basic trigonometric identities, 504 Berners-Lee, Tim, 755 Bernoulli, Jakob, 624, 932 Abel, Niels, 226, 903 Abscissa, 2 Absolute maximum and minimum of functions, 91–93 Absolute value, solving inequalities involving, A82–A83 Absolute value equations, solving, A54 Absolute value functions, 101–102, 104 computing, A5 definition of, A5 of z, 628 Accumulated value, 346 Acute angles definition of, 546 finding value of functions of, using right triangles, 546–548 Addition. See also Sum(s); Sum and Difference Formulas of complex numbers, A59 matrix associative property of, 797 commutative property of, 797 of rational expressions, A37–A39 of vectors, 662 algebraic, 641–642 geometric, 638 Addition principle of counting, 912 Addition property of inequalities, A78 Adjacency matrix, 811 Airfoil, 599 Algebra, A1–A13 domain of a variable, A7 evaluating algebraic expressions and, A6–A7 Fundamental Theorem of, 230 graphing inequalities and, A4–A5 Laws of Exponents and, A7–A9 linear, 795 matrix, 795–812 real number line and, A4 distance on, A5–A6 relations expressed using, 62 sets and, A1–A4 solving geometry problems using, 15–16 square roots and, A9–A10 Algebraic expressions evaluating, A6–A7 writing trigonometric expressions as, 490 Algebraic vectors, 640 Algorithms, 215n Ambiguous case, 561 Amortization formula, 864 Amplitude of an object in simple harmonic motion, 584 of a sinusoidal function, 431–432, 452–454 Analytic geometry, 680–753 Analytic trigonometry, 471–544 Double-angle Formulas and establishing identities using, 525–528 finding exact values using, 525 Half-angle Formulas and, 528–530 inverse functions and. See Inverse trigonometric functions Product-to-Sum Formulas and, 535–536 Sum and Difference Formulas and, 511–524 for cosine function, 511–512 establishing identities using, 516–517 finding exact values using, 512–515 involving inverse trigonometric functions, 517–518 solving trigonometric equations linear in sine and cosine and, 518–520 Sum-to-Product Formulas and, 536–537 trigonometric equations and, 493–503 inverse, solving, 482–483 involving a single trigonometric function, solving, 493–496 linear in sine and cosine, solving, Sum and Difference Formulas and, 518–520 quadratic in form, solving, 496–497 solutions of, 493 solving using a calculator, 496 solving using a graphing utility, 498 solving using fundamental identities, 497–498 solving using identities, 527–528 trigonometric identities and, 503–511 basic, 504 establishing, 505–508, 516–517, 525–528 even-odd, 504 Pythagorean, 504 quotient, 504 reciprocal, 504 simplifying using algebra, 504–505 writing trigonometric expressions as algebraic expressions and, 490 Angles acute definition of, 546 finding value of functions of, using right triangles, 546–548 complementary, 548 direction, of a vector, 644 finding, 664–666 elongation, 568 quadrantal, exact values of the trigonometric functions of, 399–401 of repose, 492 right, A14 transformation, 723 between two vectors, finding, 652–653 viewing, 485 Angle-side-angle (ASA) triangles, A17 Annuities, 862–864 amount of, 863 ordinary, 863 Annuity formula, 863 Annus, Adrian, 468 Aphelion, 703, 734, 753 Apothem, 523 Applied problems. See also Applications Index constant rate job problems as, A71–A73 interest problems as, A67–A68 involving ellipses, 700 involving hyperbolas, 714–716 involving parabolas, 688–689 mixture problems as, A69 steps for solving, A67 translating verbal descriptions into mathematical expressions and, A67 uniform motion problems as, A70–A71 using Law of Cosines, 572–573 using Law of Sines, 563–565 Approximation of area under the graph of a function, 969–972 of f x ex ( ) = , 813 of integrals, using a graphing utility, 972–974 of intercepts, 9–10 of local maxima and minima of functions, 93 of logarithms whose base is neither 10 nor e, 331–332 of real zeros of a polynomial function, 228 of roots, A88 of solutions to equations, 29–31 of the value of a trigonometric function, 405–406 of the value of inverse trigonometric functions, 488–489 Araybhata the Elder, 407 Area, 968–972 Subject Index
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