I-6 INDEX eccentricity of, 1019–1020 equations of, 1017 foci of, 1014 forming, 723 fundamental rectangle of, 1016 geometric definition of, 1014 geometric interpretation of, 992 translations of, 1018 transverse axis of, 1015 vertices of, 1015 Hypotenuse of a right triangle, 143, 549 Hypotrochoids, 854 I i definition of, 123 powers of, 128–129 i, j unit vectors, 814 Identities, 682 – 683. See also Trigonometric identities Identity equations, 108, 109 Identity function, 268 Identity matrix, 965 Identity property for addition, 32 for multiplication, 32 Imaginary axis, 821 Imaginary numbers, 123 Imaginary part of a complex number, 123 Imaginary unit, 123 Impedance, 831 Impossible events, 1100 Improper fractions converting between mixed numbers and, 3 explanation of, 2 Inclination, angle of, 804 Inconsistent systems, 874, 896 Increasing function, 230 Independent equations, 874 Independent events, 1088 Independent variable, 221, 223 Index of a radical, 82, 85 of summation, 1044 Induction, mathematical, 1080–1085 Inequalities absolute value, 182–183 definition of, 24, 168 graphing, 939, 941 linear, 168 – 170, 939 – 942 nonlinear, 402 nonstrict, 173, 940 polynomial, 402 – 405 properties of, 168 quadratic, 171 – 174 rational, 174–176, 406 strict, 173, 940 symbols indicating, 24 three-part, 170 – 171 Infinite discontinuity, 391 Infinite geometric sequence definition of sum of terms, 1063 – 1066 formula for sum of terms of, 1066 stretching and shrinking, 279–280 summary of, 290 symmetry, 282 – 284 translations, 286 – 290 Greatest common factor (GCF) definition of, 61 explanation of, 2 Greatest integer function, 272 Groundspeed, 805 Grouping, factoring by, 62–63 Grouping symbols, 29 H Half-angle identities definition of, 717 general statement about, 718 simplifying expressions using, 719 verifying, 720 Half-life, 503 Half-plane boundary of, 939 definition of, 939 Harmonic motion, 662 Height of a projected object, 144, 150 Heron of Alexandria, 791 Heron’s formula application of, 792 derivation of, 792–794 statement of, 791 Heron triangle, 799 Hipparchus, 565 Holding time, 50 Hooke’s Law, 417 Horizontal asymptote definition of, 381, 385 determining, 385 Horizontal axis, 821 Horizontal component of a vector, 811 Horizontal line equation of, 256, 259 graph of, 239 slope of, 242 Horizontal line test for one-to-one functions, 435 Horizontal parabola definition of, 992 graph of, 993 Horizontal shrinking of the graph of a function, 280 Horizontal stretching of the graph of a function, 280 Horizontal translations of cosine function, 635 of cotangent function, 649 of a graph, 287 graphing, 633 – 635 of a graph of a polynomial function, 360 of sine function, 634 Hubble constant, 264 Hyperbola(s) asymptotes of, 1015 center of, 1015 definition of, 1014 of polar coordinates, 840 of polar equations, 842–846 of polynomial functions, 359–360 of quadratic functions, 324–326 of rational functions, 383–384 of the reciprocal function, 382 reflecting across a line, 281 reflecting across an axis, 281 of a relation, 222 of secant function, 654 shrinking of, 279–280 of sine function, 621 solving polynomial equations or inequalities using, 403 stretched, 623 stretching of, 279–280 summary of polar, 847 symmetry of, 282 of systems of inequalities, 941–942 of tangent function, 645 translations of, 286, 360 of a vertical line, 239 vertical translation of, 286, 360 Graphing calculator(s) analyzing the path of a projectile, 856 converting from trigonometric form to rectangular form, 822 decimal window on, 382 degree mode in, 537, 538, 556 finding magnitude and direction angle of vectors, 811 finding trigonometric function values with, 556 – 557 for fitting exponential curves to scatter diagrams, 458 graphing a cycloid, 854 graphing a plane curve defined parametrically, 852 graphing of polar equations, 842 – 846 performing row operations, 896 sine regression feature, 638–639 solving problems involving angles of elevation, 573 solving trigonometric equations by linear methods, 740 square viewing window on, 214 standard viewing window on, 209 ZTrig viewing window, 623 Graphing calculator method for circles, 214 finding the determinant of a matrix, 907 for rational functions, 382–384, 392 for the reciprocal function, 381–382 for solving linear equations in one variable, 260 – 261 for solving nonlinear systems, 928 for solving systems of equations using matrix inverses, 970 for solving systems of linear equations in two variables, 875, 877 Graphing techniques even and odd functions, 285 reflecting, 281 Graph(s) (continued)
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