Algebra and Trigonometry
Algebra and Trigonometry
John Wiley & Sons Inc
11/2017
1296
Loose-leaf
Inglês
9781119445135
2285
Descrição não disponível.
[0] Prerequisites and Review 2 0.1 REAL NUMBERS 4 0.2 INTEGER EXPONENTS AND SCIENTIFIC NOTATION 17 0.3 POLYNOMIALS: BASIC OPERATIONS 27 0.4 FACTORING POLYNOMIALS 36 0.5 RATIONAL EXPRESSIONS 46 0.6 RATIONAL EXPONENTS AND RADICALS 60 0.7 COMPLEX NUMBERS 70 Review 77 Review Exercises 79 Practice Test 81 [1] Equations and Inequalities 82 1.1 LINEAR EQUATIONS 84 1.2 APPLICATIONS INVOLVING LINEAR EQUATIONS 93 1.3 QUADRATIC EQUATIONS 107 1.4 OTHER TYPES OF EQUATIONS 121 1.5 LINEAR INEQUALITIES 129 1.6 POLYNOMIAL AND RATIONAL INEQUALITIES 139 1.7 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 149 Review 157 Review Exercises 158 Practice Test 162 Cumulative Test 163 [2] Graphs 164 2.1 BASIC TOOLS: CARTESIAN PLANE, DISTANCE, AND MIDPOINT 166 2.2 GRAPHING EQUATIONS, POINT-PLOTTING, INTERCEPTS, AND SYMMETRY 173 2.3 LINES 186 2.4 CIRCLES 202 2.5 LINEAR REGRESSION: BEST FIT 209 Review 231 Review Exercises 232 Practice Test 234 Cumulative Test 235 [3] Functions and Their Graphs 236 3.1 FUNCTIONS 238 3.2 GRAPHS OF FUNCTIONS; PIECEWISE-DEFINED FUNCTIONS; INCREASING AND DECREASING FUNCTIONS; AVERAGE RATE OF CHANGE 255 3.3 GRAPHING TECHNIQUES: TRANSFORMATIONS 274 3.4 OPERATIONS ON FUNCTIONS AND COMPOSITION OF FUNCTIONS 287 3.5 ONE-TO-ONE FUNCTIONS AND INVERSE FUNCTIONS 298 3.6 MODELING FUNCTIONS USING VARIATION 312 Review 322 Review Exercises 324 Practice Test 328 Cumulative Test 329 [4] Polynomial and Rational Functions 330 4.1 QUADRATIC FUNCTIONS 332 4.2 POLYNOMIAL FUNCTIONS OF HIGHER DEGREE 349 4.3 DIVIDING POLYNOMIALS: LONG DIVISION AND SYNTHETIC DIVISION 363 4.4 THE REAL ZEROS OF A POLYNOMIAL FUNCTION 372 4.5 COMPLEX ZEROS: THE FUNDAMENTAL THEOREM OF ALGEBRA 388 4.6 RATIONAL FUNCTIONS 396 Review 416 Review Exercises 418 Practice Test 422 Cumulative Test 423 [5] Exponential and Logarithmic Functions 424 5.1 EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 426 5.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS 440 5.3 PROPERTIES OF LOGARITHMS 456 5.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS 464 5.5 EXPONENTIAL AND LOGARITHMIC MODELS 474 Review 485 Review Exercises 487 Practice Test 490 Cumulative Test 491 [6] Trigonometric Functions 492 6.1 ANGLES, DEGREES, AND TRIANGLES 494 6.2 DEFINITION 1 OF TRIGONOMETRIC FUNCTIONS:RIGHT TRIANGLE RATIOS 511 6.3 APPLICATIONS OF RIGHT TRIANGLE TRIGONOMETRY:SOLVING RIGHT TRIANGLES 525 6.4 DEFINITION 2 OF TRIGONOMETRIC FUNCTIONS: CARTESIAN PLANE 538 6.5 TRIGONOMETRIC FUNCTIONS OF NONACUTE ANGLES 552 6.6 RADIAN MEASURE AND APPLICATIONS 567 6.7 DEFINITION 3 OF TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH 584 6.8 GRAPHS OF SINE AND COSINE FUNCTIONS 594 6.9 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS 623 Review 641 Review Exercises 647 Practice Test 650 Cumulative Test 651 [7] Analytic Trigonometry 652 7.1 BASIC TRIGONOMETRIC IDENTITIES 654 7.2 VERIFYING TRIGONOMETRIC IDENTITIES 665 7.3 SUM AND DIFFERENCE IDENTITIES 675 7.4 DOUBLE-ANGLE IDENTITIES 689 7.5 HALF-ANGLE IDENTITIES 697 7.6 PRODUCT-TO-SUM AND SUM-TO-PRODUCT IDENTITIES 708 7.7 INVERSE TRIGONOMETRIC FUNCTIONS 716 7.8 TRIGONOMETRIC EQUATIONS 737 Review 754 Review Exercises 757 Practice Test 762 Cumulative Test 763 [8] Additional Topics in Trigonometry 764 8.1 OBLIQUE TRIANGLES AND THE LAW OF SINES 766 8.2 THE LAW OF COSINES 780 8.3 THE AREA OF A TRIANGLE 791 8.4 VECTORS 798 8.5 THE DOT PRODUCT 813 8.6 POLAR (TRIGONOMETRIC) FORM OF COMPLEX NUMBERS 821 8.7 PRODUCTS, QUOTIENTS, POWERS, AND ROOTS OF COMPLEX NUMBERS;DE MOIVRE'S THEOREM 829 8.8 POLAR EQUATIONS AND GRAPHS 841 Review 856 Review Exercises 859 Practice Test 862 Cumulative Test 863 [9] Systems of Linear Equations and Inequalities 864 9.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES 866 9.2 SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES 881 9.3 PARTIAL FRACTIONS 892 9.4 SYSTEMS OF LINEAR INEQUALITIES IN TWO VARIABLES 903 9.5 THE LINEAR PROGRAMMING MODEL 914 Review 921 Review Exercises 922 Practice Test 924 Cumulative Test 925 [10] Matrices 926 10.1 MATRICES AND SYSTEMS OF LINEAR EQUATIONS 928 10.2 MATRIX ALGEBRA 950 10.3 MATRIX EQUATIONS; THE INVERSE OF A SQUARE MATRIX 964 10.4 THE DETERMINANT OF A SQUARE MATRIX AND CRAMER'S RULE 976 Review 990 Review Exercises 993 Practice Test 996 Cumulative Test 997 [11] Analytic Geometry and Systems of Nonlinear Equations and Inequalities 998 11.1 CONIC BASICS 1000 11.2 THE PARABOLA 1003 11.3 THE ELLIPSE 1015 11.4 THE HYPERBOLA 1028 11.5 SYSTEMS OF NONLINEAR EQUATIONS 1039 11.6 SYSTEMS OF NONLINEAR INEQUALITIES 1049 11.7 ROTATION OF AXES 1057 11.8 POLAR EQUATIONS OF CONICS 1067 11.9 PARAMETRIC EQUATIONS AND GRAPHS 1078 Review 1086 Review Exercises 1089 Practice Test 1093 Cumulative Test 1095 [12] Sequences, Series, and Probability 1096 12.1 SEQUENCES AND SERIES 1098 12.2 ARITHMETIC SEQUENCES AND SERIES 1109 12.3 GEOMETRIC SEQUENCES AND SERIES 1117 12.4 MATHEMATICAL INDUCTION 1128 12.5 THE BINOMIAL THEOREM 1133 12.6 COUNTING, PERMUTATIONS, AND COMBINATIONS 1141 12.7 PROBABILITY 1151 Review 1160 Review Exercises 1162 Practice Test 1166 Cumulative Test 1167 Answers to Odd-Numbered Exercises 1169 Applications Index 1261 Subject Index 1265
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[0] Prerequisites and Review 2 0.1 REAL NUMBERS 4 0.2 INTEGER EXPONENTS AND SCIENTIFIC NOTATION 17 0.3 POLYNOMIALS: BASIC OPERATIONS 27 0.4 FACTORING POLYNOMIALS 36 0.5 RATIONAL EXPRESSIONS 46 0.6 RATIONAL EXPONENTS AND RADICALS 60 0.7 COMPLEX NUMBERS 70 Review 77 Review Exercises 79 Practice Test 81 [1] Equations and Inequalities 82 1.1 LINEAR EQUATIONS 84 1.2 APPLICATIONS INVOLVING LINEAR EQUATIONS 93 1.3 QUADRATIC EQUATIONS 107 1.4 OTHER TYPES OF EQUATIONS 121 1.5 LINEAR INEQUALITIES 129 1.6 POLYNOMIAL AND RATIONAL INEQUALITIES 139 1.7 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 149 Review 157 Review Exercises 158 Practice Test 162 Cumulative Test 163 [2] Graphs 164 2.1 BASIC TOOLS: CARTESIAN PLANE, DISTANCE, AND MIDPOINT 166 2.2 GRAPHING EQUATIONS, POINT-PLOTTING, INTERCEPTS, AND SYMMETRY 173 2.3 LINES 186 2.4 CIRCLES 202 2.5 LINEAR REGRESSION: BEST FIT 209 Review 231 Review Exercises 232 Practice Test 234 Cumulative Test 235 [3] Functions and Their Graphs 236 3.1 FUNCTIONS 238 3.2 GRAPHS OF FUNCTIONS; PIECEWISE-DEFINED FUNCTIONS; INCREASING AND DECREASING FUNCTIONS; AVERAGE RATE OF CHANGE 255 3.3 GRAPHING TECHNIQUES: TRANSFORMATIONS 274 3.4 OPERATIONS ON FUNCTIONS AND COMPOSITION OF FUNCTIONS 287 3.5 ONE-TO-ONE FUNCTIONS AND INVERSE FUNCTIONS 298 3.6 MODELING FUNCTIONS USING VARIATION 312 Review 322 Review Exercises 324 Practice Test 328 Cumulative Test 329 [4] Polynomial and Rational Functions 330 4.1 QUADRATIC FUNCTIONS 332 4.2 POLYNOMIAL FUNCTIONS OF HIGHER DEGREE 349 4.3 DIVIDING POLYNOMIALS: LONG DIVISION AND SYNTHETIC DIVISION 363 4.4 THE REAL ZEROS OF A POLYNOMIAL FUNCTION 372 4.5 COMPLEX ZEROS: THE FUNDAMENTAL THEOREM OF ALGEBRA 388 4.6 RATIONAL FUNCTIONS 396 Review 416 Review Exercises 418 Practice Test 422 Cumulative Test 423 [5] Exponential and Logarithmic Functions 424 5.1 EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 426 5.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS 440 5.3 PROPERTIES OF LOGARITHMS 456 5.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS 464 5.5 EXPONENTIAL AND LOGARITHMIC MODELS 474 Review 485 Review Exercises 487 Practice Test 490 Cumulative Test 491 [6] Trigonometric Functions 492 6.1 ANGLES, DEGREES, AND TRIANGLES 494 6.2 DEFINITION 1 OF TRIGONOMETRIC FUNCTIONS:RIGHT TRIANGLE RATIOS 511 6.3 APPLICATIONS OF RIGHT TRIANGLE TRIGONOMETRY:SOLVING RIGHT TRIANGLES 525 6.4 DEFINITION 2 OF TRIGONOMETRIC FUNCTIONS: CARTESIAN PLANE 538 6.5 TRIGONOMETRIC FUNCTIONS OF NONACUTE ANGLES 552 6.6 RADIAN MEASURE AND APPLICATIONS 567 6.7 DEFINITION 3 OF TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH 584 6.8 GRAPHS OF SINE AND COSINE FUNCTIONS 594 6.9 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS 623 Review 641 Review Exercises 647 Practice Test 650 Cumulative Test 651 [7] Analytic Trigonometry 652 7.1 BASIC TRIGONOMETRIC IDENTITIES 654 7.2 VERIFYING TRIGONOMETRIC IDENTITIES 665 7.3 SUM AND DIFFERENCE IDENTITIES 675 7.4 DOUBLE-ANGLE IDENTITIES 689 7.5 HALF-ANGLE IDENTITIES 697 7.6 PRODUCT-TO-SUM AND SUM-TO-PRODUCT IDENTITIES 708 7.7 INVERSE TRIGONOMETRIC FUNCTIONS 716 7.8 TRIGONOMETRIC EQUATIONS 737 Review 754 Review Exercises 757 Practice Test 762 Cumulative Test 763 [8] Additional Topics in Trigonometry 764 8.1 OBLIQUE TRIANGLES AND THE LAW OF SINES 766 8.2 THE LAW OF COSINES 780 8.3 THE AREA OF A TRIANGLE 791 8.4 VECTORS 798 8.5 THE DOT PRODUCT 813 8.6 POLAR (TRIGONOMETRIC) FORM OF COMPLEX NUMBERS 821 8.7 PRODUCTS, QUOTIENTS, POWERS, AND ROOTS OF COMPLEX NUMBERS;DE MOIVRE'S THEOREM 829 8.8 POLAR EQUATIONS AND GRAPHS 841 Review 856 Review Exercises 859 Practice Test 862 Cumulative Test 863 [9] Systems of Linear Equations and Inequalities 864 9.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES 866 9.2 SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES 881 9.3 PARTIAL FRACTIONS 892 9.4 SYSTEMS OF LINEAR INEQUALITIES IN TWO VARIABLES 903 9.5 THE LINEAR PROGRAMMING MODEL 914 Review 921 Review Exercises 922 Practice Test 924 Cumulative Test 925 [10] Matrices 926 10.1 MATRICES AND SYSTEMS OF LINEAR EQUATIONS 928 10.2 MATRIX ALGEBRA 950 10.3 MATRIX EQUATIONS; THE INVERSE OF A SQUARE MATRIX 964 10.4 THE DETERMINANT OF A SQUARE MATRIX AND CRAMER'S RULE 976 Review 990 Review Exercises 993 Practice Test 996 Cumulative Test 997 [11] Analytic Geometry and Systems of Nonlinear Equations and Inequalities 998 11.1 CONIC BASICS 1000 11.2 THE PARABOLA 1003 11.3 THE ELLIPSE 1015 11.4 THE HYPERBOLA 1028 11.5 SYSTEMS OF NONLINEAR EQUATIONS 1039 11.6 SYSTEMS OF NONLINEAR INEQUALITIES 1049 11.7 ROTATION OF AXES 1057 11.8 POLAR EQUATIONS OF CONICS 1067 11.9 PARAMETRIC EQUATIONS AND GRAPHS 1078 Review 1086 Review Exercises 1089 Practice Test 1093 Cumulative Test 1095 [12] Sequences, Series, and Probability 1096 12.1 SEQUENCES AND SERIES 1098 12.2 ARITHMETIC SEQUENCES AND SERIES 1109 12.3 GEOMETRIC SEQUENCES AND SERIES 1117 12.4 MATHEMATICAL INDUCTION 1128 12.5 THE BINOMIAL THEOREM 1133 12.6 COUNTING, PERMUTATIONS, AND COMBINATIONS 1141 12.7 PROBABILITY 1151 Review 1160 Review Exercises 1162 Practice Test 1166 Cumulative Test 1167 Answers to Odd-Numbered Exercises 1169 Applications Index 1261 Subject Index 1265
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