College Algebra with Trigonometry

Cover......Page 1
Title Page......Page 4
ISBN-13: 9780073519500......Page 5
Contents......Page 13
Preface......Page 15
Features......Page 18
Applications Index......Page 29
CHAPTER R: Basic Algebraic Operations......Page 34
R-1 Algebra and Real Numbers......Page 35
R-2 Exponents and Radicals......Page 44
R-3 Polynomials: Basic Operations and Factoring......Page 54
R-4 Rational Expressions: Basic Operations......Page 65
Chapter R: Review......Page 72
Chapter R: Review Exercises......Page 73
CHAPTER 1 Equations and Inequalities......Page 76
1-1 Linear Equations and Applications......Page 77
1-2 Linear Inequalities......Page 89
1-3 Absolute Value in Equations and Inequalities......Page 98
1-4 Complex Numbers......Page 107
1-5 Quadratic Equations and Applications......Page 117
1-6 Additional Equation-Solving Techniques......Page 130
Chapter 1 Review......Page 137
Chapter 1 Review Exercises......Page 139
Chapter 1 Group Activity: Solving a Cubic Equation......Page 141
CHAPTER 2 Graphs......Page 142
2-1 Cartesian Coordinate Systems......Page 143
2-2 Distance in the Plane......Page 155
2-3 Equation of a Line......Page 165
2-4 Linear Equations and Models......Page 180
Chapter 2 Review......Page 190
Chapter 2 Review Exercises......Page 191
Chapter 2 Group Activity: Average Speed......Page 193
CHAPTER 3 Functions......Page 194
3-1 Functions......Page 195
3-2 Graphing Functions......Page 208
3-3 Transformations of Functions......Page 221
3-4 Quadratic Functions......Page 236
3-5 Operations on Functions; Composition......Page 256
3-6 Inverse Functions......Page 268
Chapter 3 Review......Page 283
Chapter 3 Review Exercises......Page 285
Chapter 3 Group Activity: Mathematical Modeling: Choosing a Cell Phone Plan......Page 290
CHAPTER 4 Polynomial and Rational Functions......Page 292
4-1 Polynomial Functions, Division, and Models......Page 293
4-2 Real Zeros and Polynomial Inequalities......Page 311
4-3 Complex Zeros and Rational Zeros of Polynomials......Page 321
4-4 Rational Functions and Inequalities......Page 331
4-5 Variation and Modeling......Page 348
Chapter 4 Review......Page 354
Chapter 4 Review Exercises......Page 356
Chapter 4 Group Activity: Interpolating Polynomials......Page 359
CHAPTER 5 Exponential and Logarithmic Functions......Page 360
5-1 Exponential Functions......Page 361
5-2 Exponential Models......Page 373
5-3 Logarithmic Functions......Page 387
5-4 Logarithmic Models......Page 398
5-5 Exponential and Logarithmic Equations......Page 405
Chapter 5 Review......Page 412
Chapter 5 Review Exercises......Page 413
Chapter 5 Group Activity: Comparing Regression Models......Page 416
CHAPTER 6 Trigonometric Functions......Page 418
6-1 Angles and Their Measure......Page 419
6-2 Right Triangle Trigonometry......Page 428
6-3 Trigonometric Functions: A Unit Circle Approach......Page 437
6-4 Properties of Trigonometric Functions......Page 447
6-5 More General Trigonometric Functions and Models......Page 461
6-6 Inverse Trigonometric Functions......Page 474
Chapter 6 Review......Page 486
Chapter 6 Review Exercises......Page 489
Chapter 6 Group Activity: A Predator–Prey Analysis Involving Mountain Lions and Deer......Page 493
CHAPTER 7 Trigonometric Identities and Conditional Equations......Page 494
7-1 Basic Identities and Their Use......Page 495
7-2 Sum, Difference, and Cofunction Identities......Page 504
7-3 Double-Angle and Half-Angle Identities......Page 513
7-4 Product–Sum and Sum–Product Identities......Page 521
7-5 Trigonometric Equations......Page 526
Chapter 7 Review......Page 537
Chapter 7 Review Exercises......Page 538
Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C)—A Harmonic Analysis Tool......Page 540
CHAPTER 8 Additional Topics in Trigonometry......Page 542
8-1 Law of Sines......Page 543
8-2 Law of Cosines......Page 552
8-3 Vectors in the Plane......Page 560
8-4 Polar Coordinates and Graphs......Page 573
8-5 Complex Numbers and De Moivre's Theorem......Page 586
Chapter 8 Review......Page 596
Chapter 8 Review Exercises......Page 600
Chapter 8 Group Activity: Polar Equations of Conic Sections......Page 603
CHAPTER 9 Additional Topics in Analytic Geometry......Page 604
9-1 Conic Sections; Parabola......Page 605
9-2 Ellipse......Page 614
9-3 Hyperbola......Page 624
9-4 Translation and Rotation of Axes......Page 637
Chapter 9 Review......Page 653
Chapter 9 Review Exercises......Page 656
Chapter 9 Group Activity: Focal Chords......Page 657
CHAPTER 10 Systems of Equations and Matrices......Page 658
10-1 Systems of Linear Equations......Page 659
10-2 Solving Systems of Linear Equations Using Gauss-Jordan Elimination......Page 676
10-3 Matrix Operations......Page 692
10-4 Solving Systems of Linear Equations Using Matrix Inverse Methods......Page 705
10-5 Determinants and Cramer's Rule......Page 722
Chapter 10 Review......Page 731
Chapter 10 Review Exercises......Page 733
Chapter 10 Group Activity: Modeling with Systems of Linear Equations......Page 736
CHAPTER 11 Sequences, Induction, and Probability......Page 738
11-1 Sequences and Series......Page 739
11-2 Mathematical Induction......Page 746
11-3 Arithmetic and Geometric Sequences......Page 755
11-4 Multiplication Principle, Permutations, and Combinations......Page 766
11-5 Sample Spaces and Probability......Page 778
11-6 The Binomial Formula......Page 793
Chapter 11 Review......Page 799
Chapter 11 Review Exercises......Page 801
Chapter 11 Group Activity: Sequences Specified by Recursion Formulas......Page 803
Appendix A: Cumulative Review Exercises......Page 804
Appendix B: Special Topics......Page 820
Appendix C: Geometric Formulas......Page 840
Student Answers SA1 Instructor Answers......Page 844
Subject Index......Page 888