I12 Subject Index Tangent line to a circle, 55 definition of, 961 to graph of a function, finding equation of, 961–962 Tangent problem, 960–962 Tangents, Law of, historical feature on, 573 Tartaglia, 226, 634 Tautochrone, 745 Term(s) of an arithmetic sequence, finding, 870–871 in a binomial expansion, 902 general, of an infinite series, 890 of a geometric sequence, finding, 877 of an infinite series, 890 leading, of a polynomial, A22 like, A22 lowest rational functions in, 237 reducing a rational expression to, A35–A36 of a polynomial, A22 of a polynomial function, 190 of a sequence first several, listing, 855–858 of a recursively defined sequence, 858–859 sequences, general of, 856 Terminal point of a geometric vector, 637 Terminating decimals, A3 3 by 3 determinant, 669 determinants, 787–789 Thrust, 599 Time as parameter in parametric equations, 740–742 required to double a lump sum, 350–351 Transformation(s), 112–126 compressions and stretches as, 115–117 graphing cosine function using, 430 graphing exponential functions using, 302, 303–304 graphing polynomial functions using, 194 graphing quadratic functions using, 158–160 graphing rational functions using, 238 graphing sine function using, 428–429 reflections about the x-axis or y-axis as, 117–118 vertical and horizontal shifts as, 112–114 Transformation angle, 723 Transverse axis of a hyperbola, 705, 729 Tree diagrams, 914 Trejo, JoAnn, 855 Triangles area of, 577–583 ASA, solving, 561 congruent, A16–A17 definition of, A16 error, 19 oblique, 559–560 right definition of, 546 finding values of functions of acute angles using, 546–548 hypotenuse of, 546 properties of, 549 solving, 548–549 SAA, solving, 560–561 SAS area of, 577–578 solving using the Law of Cosines, 571 similar, A17–A18 definition of, A17 determining, A18 using, A18–A19 SSA, solving, 561–563 SSS area of, 578–579 solving using the Law of Cosines, 571–572 Triangular numbers, 868 Trigonometric equations, 493–503 inverse, solving, 482–483 involving a single trigonometric function, solving, 493–496 solving trigonometric equations linear in sine and cosine and, 518–520 Sum function, 71, 72 Summation notation, 859–860 properties of, 861 Sum-to-Product Formulas, 536–537 Sylvester, James J., 808 Symmetry, testing equations for, 21–23 polar equations and, 615–616 Synthetic division, A31–A35 Systems of equations consistent, 756 definition of, 755 dependent, Cramer’s Rule with, 790 equivalent, rules for obtaining, 759 examples of, 755–756 inconsistent, 756 Cramer’s Rule with, 790 linear. See Systems of linear equations nonlinear, 821–831 elimination method to solve, 822–826 historical feature on, 827 substitution method to solve, 821–822 solutions of, 756, 762 Systems of inequalities in two variables, 834–840 graphs/graphing of, 834–837 Systems of linear equations, 757–795 consistent, 757 definition of, 757 determinants and, 784–795 Cramer’s Rule to solve a system of three equations containing three variables, 789–790 Cramer’s Rule to solve a system of two equations containing two variables and, 785–787 expanding across a row or column and, 788 properties of, 791–792 ×3 3, 787–789 ×2 2, 784 inconsistent, 757 containing three variables, identifying, 763 containing two variables, identifying, 760 identifying, 760 matrices for identifying, 777–778 inverse matrices to solve, 807 matrices and, 769–783 row operations on, 771–772 solving a system using, 773–779 writing the augmented matrix of a system, 770–771 writing the system from the augmented matrix, 771 solving by elimination, 758–760 by substitution, 758 system of dependent equations containing two variables, 760–761 systems of dependent equations containing three variables, 763–765 systems of three equations containing three variables, 761–763 using a graphing utility, 757 solving using inverse matrices, 807 Systems of nonlinear equations, 821–831 elimination method to solve, 822–826 historical feature on, 827 substitution method to solve, 821–822 Systolic pressure, 441 Tables creating using a graphing utility, 8–9 investigating limits using, 941–943 Tangent function, 398 graphs/graphing of, 443–444, 445–447 inverse definition of, 477–478 exact value of, 478–479 name of, 407 properties of, 444 Solution sets of an equation, A44 Special products FOIL and, A24 formulas for, A24–A25 Spheres center of, 668 radius of, 668 Spheroids, prolate, 703 Spirals, 621–622 logarithmic, 622 Square(s) of binomials, formula for, A25 completing, A29 difference of, formula for, A24 perfect, formula for, A25 Square matrices, 796 diagonal entries in, 803 identity matrix In, 803 inverse, 804 main diagonal in, 803 Square root(s), A9–A10, A87 complex, 632 evaluating, A9–A10 principal, definition of, A9 Square root functions, 100, 103 of a negative number, evaluating, A63 Square Root Method, solving quadratic equations using, A49 Square screen, 34–35 SSS (side-side-side) triangles, A17, A18 Standard deviation, A86 Standard form complex numbers in, A59 of equation of a circle, 48–49 of a polynomial, A22 of a polynomial function, 190 powers of a complex number in, A62 quadratic equations in, A48 of rational functions, 246 reciprocal functions of a complex number in, A61 reciprocal of complex numbers in, A61 Static equilibrium, 645–646 Step functions, 104 Stretches, graphing functions using, 115–117 Strict inequalities, A5 Subsets, 911, A2 proper, 911 Substitution solving a system of linear equations using, 758 solving systems of nonlinear equations using, 821–822 Subtraction. See also Difference(s); Sum and Difference Formulas of rational expressions, A37–A39 of vectors, algebraic, 641–642 Sum(s). See also Addition of an arithmetic sequence, 871–873 expressing as products, 536–537 expressing products as, 535–536 of a geometric sequence, 878–879 of a geometric series, 893 index of, 860 of an infinite series, 891 limits of, 947 of logarithms, writing logarithmic expressions as, 39–330 partial, sequences of, 891 of a sequence, finding, 861–862 summation notation and, 859–860 of two cubes, formula for, A25 of two functions, graphs/graphing of, 588–589 of two matrices, 796, 797–798 of vectors, 638 Sum and Difference Formulas, 511–524 for cosine function, 511–512 establishing identities using, 516–517 finding exact values using, 512–515 involving inverse trigonometric functions, 517–518
RkJQdWJsaXNoZXIy NjM5ODQ=