I-1 Index A Abscissa, 658 Absolute value of a complex number, 822 definition of, 24, 180 evaluating, 25, 34 finding roots using, 84 properties of, 25 Absolute value equations, 181–182 Absolute value function definition of, 270–271 modeling with, 184 Absolute value inequalities, 181, 182–183 Acute angles definition of, 526 trigonometric functions of, 535 – 536, 549 Acute triangle, 773 Addition of complex numbers, 126 of decimals, 7 of fractions, 5 of functions, 297 identity property for, 32 of matrices, 951 order of operations for, 29 of ordinates method, 658 of polynomials, 52–53 of radicals, 87–88 of rational expressions, 75–77 of real numbers, 26–27 Addition property of equality, 106 Additive inverse definition of, 26 of a matrix, 953 of a real number, 26, 32 Adjacent side to an angle, 549 Aerial photography, 786 Agreement on domain, 224 Airspeed, 805 Algebraic expressions, 28 Algorithm for division, 56 Alternating current, 705, 752 Ambiguous case of the law of sines, 776 Amplitude of cosine function, 623 definition of, 623 of sine function, 623 Analytic geometry, 203 Angle(s) acute, 526, 549 adjacent side to an, 549 complementary, 527 coterminal, 529 critical, 767 definition of, 526 of depression, 569 direction angle for vectors, 811 of elevation, 569, 573 nth term of, 1052 sum of terms of, 1055 Arithmetic series, 1055 Array of signs for matrices, 910 Arrhenius, Svante, 481 Associative properties, 32–33, 957 Asymptote, vertical, 644 Asymptotes determining, 385 horizontal, 381, 385 of a hyperbola, 1015 oblique, 385, 387 vertical, 381, 385, 390 Atanasoff, John, 906 Augmented matrix, 892 Average rate of change, 243 – 244 Axis of a coordinate system, 202 horizontal, 821 imaginary, 821 polar, 839 real, 821 rotation of, 1125–1127 of symmetry of a parabola, 325 symmetry with respect to, 282 vertical, 821 B Babbage, Charles, 471 Base of a logarithm, 463 Base of an exponent, 28 Basics of probability, 1099–1106 Bearing, 570–572, 805 Beats, 751 Binomial(s) definition of, 51 expansion of, 1073 factoring, 65 – 66 multiplication of, 53–55 square of, 54–55 Binomial coefficient, 1075 Binomial expansion pattern explanation of, 1073 kth term of, 1078 Binomial experiment, 1105 Binomial probability, 1105 Binomial theorem explanation of, 1076 proof of, 1084–1085 Blood alcohol concentration (BAC), 38 Blood pressure, 34, 38 Body mass index (BMI), 418 Boundary of a half-plane, 939 Boundedness theorem, 368 Brackets, 29 Break-even point, 170, 251 British nautical mile, 768 of inclination, 804 initial side of, 526 measure of, 526, 556, 557–558 negative, 526 obtuse, 526 opposite side to an, 549 phase, 674 positive, 526 quadrantal, 529 reference, 552 – 554 right, 526 of rotation, 1126 side adjacent to, 549 side opposite, 549 significant digits for, 566–567 special, 551 – 552, 554 – 556 standard position of, 529 straight, 526 subtend an, 604 supplementary, 527 terminal side of, 526 types of, 526 between vectors, 816 vertex of, 526 Angle-Side-Angle (ASA) axiom, 772 Angular speed applications of, 613–614 definition of, 612 formula for, 612 Annuity definition of, 1066 future value of, 1066–1067 Applied problems solving, 112 steps to solve, 112 Applied trigonometry problems, steps to solve, 569 Approximating real zeros of polynomials, 369 Arccos x, 728 Arccot x, 730 Arccsc x, 730 Archimedes, spiral of, 845–846 Arc length, 597 Arcsec x, 730 Arcsin x, 726 Arctan x, 729 Area of a sector, 599–600 Area of a triangle deriving formula for, 780 Heron’s formula for, 791 Argument of an absolute value function, 514 of a complex number, 822 of a function, 633, 685 of a logarithm, 463 Arithmetic progression, 1051 Arithmetic sequence common difference of, 1051 definition of, 1051
RkJQdWJsaXNoZXIy NjM5ODQ=