I-9 INDEX Phase shift, 633 Phelps, Phlash, 220 Photographic coordinates, 786 Pi (p), 594 Piecewise-defined function, 271–272 Place value in decimals, 6 Plane curve, 852 Plane trigonometry, 565 Plimpton 322 (tablet), 565 Points collinear, 205 distance between, 35 Point-slope form of the equation of a line, 253, 259 Poiseuille’s law, 418 Polar axis, 839 Polar coordinates of a point definition of, 620, 839 graph of, 840 Polar coordinate system definition of, 839 polar axis of, 839 pole of, 839 Polar equations calculator graphing of, 842–846 classifying, 846 – 847 converting to rectangular equations, 846 definition of, 842 graphs of, 842–846 Polar form of a complex number, 822 of conic sections, 1121–1123 of lines and circles, 842–843 Polar grid, 843 Pole of a polar coordinate system, 839 Polynomial(s) addition of, 52–53 classifying expressions as, 52 definition of, 51 degree of, 51–52 descending order of, 53, 56 division algorithm for, 340 division of, 56–57 factored form of, 61 factoring of, 61 multiplication of, 53–55 prime, 61 special products of, 54 subtraction of, 52–53 synthetic division for, 341 term of, 51 in x, 51 zero, 324 Polynomial functions approximating real zeros of, 369 boundedness theorem for, 368 comprehensive graph of, 364 conjugate zeros theorem for, 352 definition of, 324 of degree n, 324 derivative of, 348 dominating term of, 324, 362 end behavior of graph of, 362, 363 of even degree, 361 factors of, 365 factor theorem for, 347 graph of, 359–360 axis of, 325 definition of, 269, 324 directrix of, 994 eccentricity of, 1007, 1020 equations of, 992 focus of, 994 geometric definition of, 994 geometric interpretation of, 992 graphing by completing the square, 326 – 327 graph of, 269, 993 horizontal, 992, 993, 995 maximum point of, 328 minimum point of, 327 reflective property of, 997 translations of, 996 vertex formula for, 329 vertex of, 269, 325, 329, 992 vertical, 994 Parallel lines definition of, 256 slope of, 256 Parallelogram rule for vectors, 802 Parallelograms, properties of, 802 Parametric equations definition of, 633, 852 derivatives of, 568 of a plane curve, 852 Parentheses, 29 Partial fraction decomposition, 920 – 925 Pascal, Blaise, 471, 1074 Pascal’s triangle, 1073–1074 Path of a projectile, 856 Pendulum, period of, 104 Percents and percentages equivalents, 10 explanation of, 10 writing as decimals, 10 writing as fractions, 11 writing decimals as, 10 writing fractions as, 11 Perfect square trinomial, 54, 64–65 Perfect triangle, 799 Period of cosecant function, 655 of cosine function, 622, 625 of cotangent function, 646 definition of, 620, 625 of secant function, 654 of sine function, 621, 625 of tangent function, 645 Periodic function definition of, 620 period of, 620 Period life table, 1109 Period of a pendulum, 104 Permutations definition of, 1089 distinguishing from combinations, 1093 – 1094 formula for, 1089 Perpendicular lines definition of, 256 slope of, 256 pH, 478 Phase angle, 674 distance between points on, 35 order on, 24 Number of zeros theorem, 350–351 Numerator definition of, 2 rationalizing, 90 Numerical coefficient, 51 O Objective function, 943 Oblique asymptote definition of, 385, 387 determining, 385 Oblique triangle(s) congruency and, 772–773 data required for solving, 772 definition of, 772 finding area of, 780 Obtuse angle, 526 Obtuse triangle, 773 Odd-degree polynomial functions, 361, 363 Odd function, 285, 621, 682 Odds definition of, 1101 in favor of an event, 1101–1102 rules for, 1102 One-sided limits, 385 One-to-one functions definition of, 434, 724 horizontal line test for, 435 tests to determine, 436 Open interval, 169 Operations on complex numbers, 125–129 with decimals, 7–9 on fractions, 3–6 on functions, 297 order of, 29–31 with radicals, 87–89 on rational expressions, 74–77 on real numbers, 26–28 on sets, 17–19 Opposite of a vector, 802 Opposite side to an angle, 549 Orbital period of a satellite, 850 Order descending, 53, 56 of a matrix, 892 on a number line, 24 of operations, 29–31 Ordered pair, 202, 207 Ordered triple(s), 204, 880 Order symbols, 24 Ordinates, addition of, 658 Origin of rectangular coordinate system, 202 symmetry with respect to, 283–284 Orthogonal vectors, 816 Outcomes of an experiment, 1099 P Pair, ordered, 202, 207 Parabola(s) application of, 997
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