I-11 INDEX convergent, 1041 definition of, 1040 divergent, 1041 explicitly defined, 1041 Fibonacci, 1039, 1042 finite, 1040 general term of, 1040 geometric. See Geometric sequence infinite, 1040 infinite geometric, 1064–1066 nth term of, 1040, 1052, 1061 recursively defined, 1041 terms of, 1040 Series arithmetic, 1055 definition of, 1043–1044 finite, 1043 – 1044 geometric, 1063 infinite, 1043 – 1044 infinite geometric, 1064–1066 power, 182 Set(s) complement of, 17, 18, 19 definition of, 15 disjoint, 18 elements of, 15 empty, 16, 108 equal, 17 finite, 15 infinite, 15 intersection of, 18, 19, 1100 members of, 15 notation, 16, 169 null, 16 of numbers, 19–21 operations on, 17–19 subset of, 17 summary of operations on, 19 union of, 18, 19, 173, 1100 universal, 16 Set braces, 15 Set-builder notation, 16, 169 Shrinking graphs graphing techniques for, 279 – 280 horizontally, 280 vertically, 280 Side adjacent to an angle, 549 Side-Angle-Angle (SAA) axiom, 772 Side-Angle-Side (SAS) axiom, 772 Side opposite an angle, 549 Side-Side-Side (SSS) axiom, 772 Sigma notation definition of, 1044 symbol for, 1044 Sign array for matrices, 910 Significant digits, 566–567 Signs of trigonometric function values, 540 Simple harmonic motion, 662 Simple interest formula, 109 Simplifying complex fractions, 77–78 fractions, 2 radicals, 86 – 87 rational expressions with negative exponents, 78 – 79 Remainder theorem, 343 Removable discontinuity, 391 Repeating decimals, 9 Resistance, grade, 558 Resultant vectors, 802, 821 Revenue function, 245 Right angle, 526 Right triangle(s) hypotenuse of, 143, 549 legs of, 143 in Pythagorean theorem, 143 solving, 567 – 568 Right-triangle-based definitions of trigonometric functions, 549 Rise, 240 Root(s) of an equation, 106 in an expression, 29 of a complex number, 833–836 evaluating for radicals, 83 of polynomial functions, 344 using absolute value to find, 84 Rose curve, 844, 847 Rotation angles of, 1126 of axes, 1125–1127 definition of, 1125 Rounding, of decimals, 8 Row-echelon form, 898–899 Row matrix, 951 Row of a matrix, 892 Row transformations, 892 Rules for exponents, 40–45, 47 – 48 Rules for odds, 1102 Run, 240 Rutherford, Ernest, 1022 S Sample space, 1099 Saturation constant, 1050 Scalar, 954 Scalar multiplication definition of, 954 properties of, 954 Scalars, 801 Scatter diagrams, 259, 458 Secant function characteristics of, 654 definition of, 534–535 domain of, 654 graph of, 654 inverse of, 730 period of, 654 range of, 542, 654 steps to graph, 656 Secant line, 301 Second, 528 Second-degree equation, 131 Sector of a circle area of, 599–600 definition of, 599 Segment of a line, 526 Semiperimeter, 791 Sequence(s) arithmetic, 1051, 1052, 1055 Real numbers addition of, 26–27 additive inverse of, 26, 32 definition of, 20 division of, 26, 28 multiplication of, 26, 28 multiplicative inverse of, 26, 32, 966 negative of, 32 operations on, 26–28 properties of, 32–33 reciprocals of, 26, 32 sign rules for operations on, 26 subtraction of, 26–27 summary of properties of, 32 Real part of a complex number, 123 Reciprocal(s) definition of, 539 explanation of, 4 of fractions, 4 of a real number, 26, 32 Reciprocal functions graphing by calculator, 381 graph of, 382 important features of, 382 Reciprocal identities, 539–540, 683 Rectangular coordinates, converting to polar coordinates, 840 Rectangular coordinate system, 202 Rectangular equations converting polar equations to, 846 definition of, 842 Rectangular form of a complex number converting to trigonometric form, 823 definition of, 821 Recursively defined sequence, 1041 Reduced row-echelon form of a matrix, 893 Reduction formula, 710 Reference angles definition of, 552 special angles as, 554–556 table of, 554 Reference arc, 607 Reflection of a graph across a line, 281 across an axis, 281 Reflective property of an ellipse, 1010 of a parabola, 997 Region of feasible solutions corner point of, 944 definition of, 943 vertex of, 944 Regression linear, 260 quadratic, 332 Regression, sine, 638–639 Related rates, 568 Relation definition of, 221 domain of, 223 graph of, 222 range of, 223 Relatively prime integers, 239
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