I-12 INDEX of a geometric sequence, 1063 – 1064 of an infinite geometric sequence, 1066 of an infinite geometric series, 1064 – 1066 Sum-to-product identities, 716–717 Superelevation, 563 Supplementary angles, 527 Supply and demand, 891 Swokowski, Earl, 715 Symbols grouping, 29 inequality, 24 of order on the number line, 24 radical, 82 Symmetry example of, 201 graphing techniques for, 282–284 of graphs, 282 with respect to origin, 283–284 with respect to x-axis, 282 – 283 with respect to y-axis, 282 – 283 tests for, 282–284 Synthetic division for polynomials, 341 – 342 Systems of equations definition of, 874 solutions of, 874 Systems of inequalities definition of, 941 graphing, 941 – 942 Systems of linear equations in three variables applications of, 883 Cramer’s rule for solving, 914 elimination method for solving, 880 Gauss-Jordan method for solving, 895 geometric interpretation of, 879 matrix inverses method for solving, 970 – 972 modeling with, 881 solving, 879 – 880 Systems of linear equations in two variables applications of, 878–879 consistent, 874 Cramer’s rule for solving, 912–913 elimination method for solving, 875 – 876 equivalent, 875 Gauss-Jordan method for solving, 893 graphing calculator method for solving, 875, 877 inconsistent, 874 matrix method for solving, 893 solution set for, 874 substitution method for solving, 874 – 875 transformations of, 875 Systolic pressure, 630 T Tangent function characteristics of, 645 definition of, 534–535 Spherical trigonometry, 565 Spiral of Archimedes, 845–846 Square(s) of a binomial, 54 completing the, 133, 326 difference of, 54, 65–66 Square matrix, 951 Square root function, 270 Square root method for solving quadratic equations, 132, 133 Square root property, 132 Square viewing window on graphing calculators, 214 Squaring function, 269 Standard form of a complex number, 124, 821 of the equation of a line, 253 of a linear equation, 239, 259 of a quadratic equation, 131 Standard position of an angle, 529 Standard viewing window on graphing calculators, 209 Statute mile, 606 Stefan-Boltzmann law, 419 Step function, 273 Stirling’s formula, 1080 Straight angle, 526 Stretching graphs graphing techniques for, 279–280 horizontal, 280 vertical, 280 Strict inequalities, 173, 940 Subscripts, 1044 Subset, 17 Substitution method definition of, 874 for solving linear systems, 875 Substitution method for factoring, 67 Subtend an angle, 604 Subtense bar method, 572 Subtraction of complex numbers, 126 of decimals, 7 of fractions, 5–6 of functions, 297 of matrices, 953 order of operations for, 29 of polynomials, 52–53 of radicals, 87–88 of rational expressions, 75–77 of real numbers, 26–27 of vectors, 802 Sum, definition of, 26 Sum identity application of, 702–704 for cosine, 697–698 for sine, 700–701 for tangent, 700–701 Summation, index of, 1044 Summation notation definition of, 1044 with subscripts, 1044 Summation properties, 1045 Summation rules, 1046 Sum of cubes, 65 Sum of terms of an arithmetic sequence, 1055 Sine function amplitude of, 623 characteristics of, 621 definition of, 534–535 difference identity for, 700–701 domain of, 621 double-angle identity for, 711–712 graph of, 621 half-angle identity for, 718 horizontal translation of, 634 inverse of, 725–727 period of, 621, 625 range of, 542, 621 steps to graph, 626, 637 sum identity for, 700–701 translating graphs of, 634, 637 Sine regression, 638–639 Sines, law of ambiguous case of, 776 applications of, 774–775 derivation of, 773 Sine wave, 621 Singular matrix, 970 Sinusoid, 621 Sinusoidal function, 638 Size of a matrix, 892 Slope(s) of a curve at a point, 241 definition of, 240 formula for, 241 of a horizontal line, 242 of a line, 240–244 negative, 243 of parallel lines, 256 of perpendicular lines, 256 point-slope form, 253, 259 positive, 243 slope-intercept form, 254, 259 undefined, 241–242, 243 of a vertical line, 241–242 zero, 242, 243 Slope-intercept form of the equation of a line, 254, 259 Snell’s law, 767–768 Solar constant, 632 Solution(s) of an equation, 106 double, 132 of a polynomial function, 344, 365 proposed, 154 Solution set, 106 Solving applied problems, 112 Solving for a specified variable, 109, 137 Solving triangles, 567 – 568, 774 – 775, 777 – 779, 789 – 791 Sound waves, 632, 709 Special angles finding angle measures with, 556 reference angles as, 554–556 trigonometric function values of, 551 – 552 Special products of polynomials, 54 Speed angular, 612 – 614 linear, 612 – 614 in motion problems, 113
RkJQdWJsaXNoZXIy NjM5ODQ=