Table of Contents
Volume II
Chapter 7 Trigonometric Functions
7.1 Angles and Their Measure .................................................................................................... 708
7.2 Right Triangle Trigonometry ................................................................................................ 715
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 728
7.4 Trigonometric Functions of Any Angle ................................................................................ 740
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 754
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 761
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 780
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 788
Chapter Review ............................................................................................................................ 800
Chapter Test ................................................................................................................................. 815
Cumulative Review ...................................................................................................................... 819
Chapter Projects ........................................................................................................................... 823
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 827
8.2 The Inverse Trigonometric Functions (continued) ................................................................ 837
8.3 Trigonometric Equations ....................................................................................................... 848
8.4 Trigonometric Identities ........................................................................................................ 867
8.5 Sum and Difference Formulas............................................................................................... 878
8.6 Double-Angle and Half-Angle Formulas .............................................................................. 900
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 923
Chapter Review ............................................................................................................................ 933
Chapter Test ................................................................................................................................. 957
Cumulative Review ...................................................................................................................... 961
Chapter Projects ........................................................................................................................... 966
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ................................................................................ 970
9.2 The Law of Sines .................................................................................................................. 976
9.3 The Law of Cosines .............................................................................................................. 989
9.4 Area of a Triangle ................................................................................................................. 998
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves........................................ 1005
Chapter Review .......................................................................................................................... 1013
Chapter Test ............................................................................................................................... 1022
Cumulative Review .................................................................................................................... 1025
Chapter Projects ......................................................................................................................... 1032
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1036
10.2 Polar Equations and Graphs .............................................................................................. 1043
10.3 The Complex Plane; DeMoivre’s Theorem ...................................................................... 1071
10.4 Vectors .............................................................................................................................. 1081
10.5 The Dot Product ................................................................................................................ 1091
Chapter Review .......................................................................................................................... 1095
Chapter Test ............................................................................................................................... 1111
Cumulative Review .................................................................................................................... 1114
Chapter Projects ......................................................................................................................... 1116
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
,Chapter 11 Analytic Geometry
11.2 The Parabola ..................................................................................................................... 1120
11.3 The Ellipse ........................................................................................................................ 1134
11.4 The Hyperbola................................................................................................................... 1149
11.5 Rotation of Axes; General Form of a Conic...................................................................... 1167
11.6 Polar Equations of Conics ................................................................................................. 1179
11.7 Plane Curves and Parametric Equations............................................................................ 1186
Chapter Review .......................................................................................................................... 1197
Chapter Test ............................................................................................................................... 1215
Cumulative Review .................................................................................................................... 1220
Chapter Projects ......................................................................................................................... 1222
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1226
12.2 Systems of Linear Equations: Matrices ............................................................................. 1245
12.3 Systems of Linear Equations: Determinants ..................................................................... 1267
12.4 Matrix Algebra .................................................................................................................. 1279
12.5 Partial Fraction Decomposition ......................................................................................... 1296
12.6 Systems of Nonlinear Equations ....................................................................................... 1309
12.7 Systems of Inequalities ..................................................................................................... 1336
12.8 Linear Programming ......................................................................................................... 1350
Chapter Review .......................................................................................................................... 1361
Chapter Test ............................................................................................................................... 1387
Cumulative Review .................................................................................................................... 1396
Chapter Projects ......................................................................................................................... 1400
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1402
13.2 Arithmetic Sequences........................................................................................................ 1411
13.3 Geometric Sequences; Geometric Series .......................................................................... 1417
13.4 Mathematical Induction .................................................................................................... 1427
13.5 The Binomial Theorem ..................................................................................................... 1434
Chapter Review .......................................................................................................................... 1439
Chapter Test ............................................................................................................................... 1446
Cumulative Review .................................................................................................................... 1449
Chapter Projects ......................................................................................................................... 1452
Chapter 14 Counting and Probability
14.1 Sets and Counting ............................................................................................................. 1455
14.2 Permutations and Combinations........................................................................................ 1456
14.3 Probability ......................................................................................................................... 1460
Chapter Review .......................................................................................................................... 1465
Chapter Test ............................................................................................................................... 1467
Cumulative Review .................................................................................................................... 1469
Chapter Projects ......................................................................................................................... 1472
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1474
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1475
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1479
Section 5 Square Screens .......................................................................................................... 1481
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
, Table of Contents
Volume I
Preface
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ................................................................................................................ 11
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division ................................................................................................................... 28
R.7 Rational expressions ............................................................................................................... 29
R.8 nth Roots; Rational Exponents ............................................................................................... 39
Chapter 1 Equations and Inequalities
1.1 Linear Equations ..................................................................................................................... 48
1.2 Quadratic Equations ................................................................................................................ 65
1.3 Complex Numbers; Quadratic Equations in the Complex Number System ........................... 82
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 88
1.5 Solving Inequalities ............................................................................................................... 107
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 118
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications 127
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 149
Chapter Projects ........................................................................................................................... 150
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 152
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 163
2.3 Lines ...................................................................................................................................... 175
2.4 Circles ................................................................................................................................... 192
2.5 Variation................................................................................................................................ 202
Chapter Review ............................................................................................................................ 207
Chapter Test ................................................................................................................................. 218
Cumulative Review ...................................................................................................................... 220
Chapter Projects ........................................................................................................................... 222
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 224
3.2 The Graph of a Function ....................................................................................................... 238
3.3 Properties of Functions ......................................................................................................... 245
3.4 Library of Functions; Piecewise-defined Functions ............................................................... 260
3.5 Graphing Techniques: Transformations ................................................................................ 271
3.6 Mathematical Models: Building Functions ........................................................................... 287
Chapter Review ............................................................................................................................ 293
Chapter Test ................................................................................................................................. 306
Cumulative Review ...................................................................................................................... 310
Chapter Projects ........................................................................................................................... 313
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
, Chapter 4 Linear and Quadratic Functions
4.1 Linear Functions and Their Properties .................................................................................. 315
4.2 Linear Models: Building Linear Functions from Data .......................................................... 325
4.3 Quadratic Functions and Their Properties ............................................................................. 330
4.4 Quadratic Models; Building Quadratic Functions from Verbal Descriptions and
From Data ........................................................................................................................... 348
4.5 Inequalities Involving Quadratic Functions .......................................................................... 356
Chapter Review ............................................................................................................................ 374
Chapter Test ................................................................................................................................. 387
Cumulative Review ...................................................................................................................... 388
Chapter Projects ........................................................................................................................... 391
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions and Models ........................................................................................ 394
5.2 Properties of Rational Functions ........................................................................................... 416
5.3 The Graph of a Rational Function ......................................................................................... 423
5.4 Polynomial and Rational Inequalities ................................................................................... 470
5.5 The Real Zeros of a Polynomial Function ............................................................................ 486
5.6 Complex Zeros; Fundamental Theorem of Algebra.............................................................. 513
Chapter Review ............................................................................................................................ 520
Chapter Test ................................................................................................................................. 549
Cumulative Review ...................................................................................................................... 553
Chapter Projects ........................................................................................................................... 558
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 560
6.2 One-to-One Functions; Inverse Functions ............................................................................ 576
6.3 Exponential Functions ........................................................................................................... 595
6.4 Logarithmic Functions .......................................................................................................... 614
6.5 Properties of Logarithms ....................................................................................................... 634
6.6 Logarithmic and Exponential Equations ............................................................................... 642
6.7 Financial Models ................................................................................................................... 659
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 666
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 673
Chapter Review ............................................................................................................................ 678
Chapter Test ................................................................................................................................. 698
Cumulative Review ...................................................................................................................... 702
Chapter Projects ........................................................................................................................... 706
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Volume II
Chapter 7 Trigonometric Functions
7.1 Angles and Their Measure .................................................................................................... 708
7.2 Right Triangle Trigonometry ................................................................................................ 715
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 728
7.4 Trigonometric Functions of Any Angle ................................................................................ 740
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 754
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 761
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 780
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 788
Chapter Review ............................................................................................................................ 800
Chapter Test ................................................................................................................................. 815
Cumulative Review ...................................................................................................................... 819
Chapter Projects ........................................................................................................................... 823
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 827
8.2 The Inverse Trigonometric Functions (continued) ................................................................ 837
8.3 Trigonometric Equations ....................................................................................................... 848
8.4 Trigonometric Identities ........................................................................................................ 867
8.5 Sum and Difference Formulas............................................................................................... 878
8.6 Double-Angle and Half-Angle Formulas .............................................................................. 900
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 923
Chapter Review ............................................................................................................................ 933
Chapter Test ................................................................................................................................. 957
Cumulative Review ...................................................................................................................... 961
Chapter Projects ........................................................................................................................... 966
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles ................................................................................ 970
9.2 The Law of Sines .................................................................................................................. 976
9.3 The Law of Cosines .............................................................................................................. 989
9.4 Area of a Triangle ................................................................................................................. 998
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves........................................ 1005
Chapter Review .......................................................................................................................... 1013
Chapter Test ............................................................................................................................... 1022
Cumulative Review .................................................................................................................... 1025
Chapter Projects ......................................................................................................................... 1032
Chapter 10 Polar Coordinates; Vectors
10.1 Polar Coordinates .............................................................................................................. 1036
10.2 Polar Equations and Graphs .............................................................................................. 1043
10.3 The Complex Plane; DeMoivre’s Theorem ...................................................................... 1071
10.4 Vectors .............................................................................................................................. 1081
10.5 The Dot Product ................................................................................................................ 1091
Chapter Review .......................................................................................................................... 1095
Chapter Test ............................................................................................................................... 1111
Cumulative Review .................................................................................................................... 1114
Chapter Projects ......................................................................................................................... 1116
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
,Chapter 11 Analytic Geometry
11.2 The Parabola ..................................................................................................................... 1120
11.3 The Ellipse ........................................................................................................................ 1134
11.4 The Hyperbola................................................................................................................... 1149
11.5 Rotation of Axes; General Form of a Conic...................................................................... 1167
11.6 Polar Equations of Conics ................................................................................................. 1179
11.7 Plane Curves and Parametric Equations............................................................................ 1186
Chapter Review .......................................................................................................................... 1197
Chapter Test ............................................................................................................................... 1215
Cumulative Review .................................................................................................................... 1220
Chapter Projects ......................................................................................................................... 1222
Chapter 12 Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 1226
12.2 Systems of Linear Equations: Matrices ............................................................................. 1245
12.3 Systems of Linear Equations: Determinants ..................................................................... 1267
12.4 Matrix Algebra .................................................................................................................. 1279
12.5 Partial Fraction Decomposition ......................................................................................... 1296
12.6 Systems of Nonlinear Equations ....................................................................................... 1309
12.7 Systems of Inequalities ..................................................................................................... 1336
12.8 Linear Programming ......................................................................................................... 1350
Chapter Review .......................................................................................................................... 1361
Chapter Test ............................................................................................................................... 1387
Cumulative Review .................................................................................................................... 1396
Chapter Projects ......................................................................................................................... 1400
Chapter 13 Sequences; Induction; the Binomial Theorem
13.1 Sequences .......................................................................................................................... 1402
13.2 Arithmetic Sequences........................................................................................................ 1411
13.3 Geometric Sequences; Geometric Series .......................................................................... 1417
13.4 Mathematical Induction .................................................................................................... 1427
13.5 The Binomial Theorem ..................................................................................................... 1434
Chapter Review .......................................................................................................................... 1439
Chapter Test ............................................................................................................................... 1446
Cumulative Review .................................................................................................................... 1449
Chapter Projects ......................................................................................................................... 1452
Chapter 14 Counting and Probability
14.1 Sets and Counting ............................................................................................................. 1455
14.2 Permutations and Combinations........................................................................................ 1456
14.3 Probability ......................................................................................................................... 1460
Chapter Review .......................................................................................................................... 1465
Chapter Test ............................................................................................................................... 1467
Cumulative Review .................................................................................................................... 1469
Chapter Projects ......................................................................................................................... 1472
Appendix Graphing Utilities
Section 1 The Viewing Rectangle ............................................................................................. 1474
Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1475
Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1479
Section 5 Square Screens .......................................................................................................... 1481
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
, Table of Contents
Volume I
Preface
Chapter R Review
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ................................................................................................................ 11
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division ................................................................................................................... 28
R.7 Rational expressions ............................................................................................................... 29
R.8 nth Roots; Rational Exponents ............................................................................................... 39
Chapter 1 Equations and Inequalities
1.1 Linear Equations ..................................................................................................................... 48
1.2 Quadratic Equations ................................................................................................................ 65
1.3 Complex Numbers; Quadratic Equations in the Complex Number System ........................... 82
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 88
1.5 Solving Inequalities ............................................................................................................... 107
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 118
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications 127
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 149
Chapter Projects ........................................................................................................................... 150
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................... 152
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 163
2.3 Lines ...................................................................................................................................... 175
2.4 Circles ................................................................................................................................... 192
2.5 Variation................................................................................................................................ 202
Chapter Review ............................................................................................................................ 207
Chapter Test ................................................................................................................................. 218
Cumulative Review ...................................................................................................................... 220
Chapter Projects ........................................................................................................................... 222
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................... 224
3.2 The Graph of a Function ....................................................................................................... 238
3.3 Properties of Functions ......................................................................................................... 245
3.4 Library of Functions; Piecewise-defined Functions ............................................................... 260
3.5 Graphing Techniques: Transformations ................................................................................ 271
3.6 Mathematical Models: Building Functions ........................................................................... 287
Chapter Review ............................................................................................................................ 293
Chapter Test ................................................................................................................................. 306
Cumulative Review ...................................................................................................................... 310
Chapter Projects ........................................................................................................................... 313
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
, Chapter 4 Linear and Quadratic Functions
4.1 Linear Functions and Their Properties .................................................................................. 315
4.2 Linear Models: Building Linear Functions from Data .......................................................... 325
4.3 Quadratic Functions and Their Properties ............................................................................. 330
4.4 Quadratic Models; Building Quadratic Functions from Verbal Descriptions and
From Data ........................................................................................................................... 348
4.5 Inequalities Involving Quadratic Functions .......................................................................... 356
Chapter Review ............................................................................................................................ 374
Chapter Test ................................................................................................................................. 387
Cumulative Review ...................................................................................................................... 388
Chapter Projects ........................................................................................................................... 391
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions and Models ........................................................................................ 394
5.2 Properties of Rational Functions ........................................................................................... 416
5.3 The Graph of a Rational Function ......................................................................................... 423
5.4 Polynomial and Rational Inequalities ................................................................................... 470
5.5 The Real Zeros of a Polynomial Function ............................................................................ 486
5.6 Complex Zeros; Fundamental Theorem of Algebra.............................................................. 513
Chapter Review ............................................................................................................................ 520
Chapter Test ................................................................................................................................. 549
Cumulative Review ...................................................................................................................... 553
Chapter Projects ........................................................................................................................... 558
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ............................................................................................................. 560
6.2 One-to-One Functions; Inverse Functions ............................................................................ 576
6.3 Exponential Functions ........................................................................................................... 595
6.4 Logarithmic Functions .......................................................................................................... 614
6.5 Properties of Logarithms ....................................................................................................... 634
6.6 Logarithmic and Exponential Equations ............................................................................... 642
6.7 Financial Models ................................................................................................................... 659
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 666
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 673
Chapter Review ............................................................................................................................ 678
Chapter Test ................................................................................................................................. 698
Cumulative Review ...................................................................................................................... 702
Chapter Projects ........................................................................................................................... 706
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
