College Algebra with Trigonometry

Description

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