College algebra & trigonometry 9780134112527, 1292151951, 9781292151953, 0134112520, 9781292151977, 1292151978

Table of contents :
Cover......Page 1
Title Page......Page 6
Copyright Page......Page 7
Contents......Page 9
Preface......Page 18
Resources for Success......Page 23
Acknowledgments......Page 25
R. Review of Basic Concepts......Page 28
R.1. Sets......Page 29
R.2. Real Numbers and Their Properties......Page 36
R.3. Polynomials......Page 51
R.4. Factoring Polynomials......Page 63
R.5. Rational Expressions......Page 73
R.6. Rational Exponents......Page 82
R.7. Radical Expressions......Page 93
Test Prep......Page 104
Review Exercises......Page 108
Test......Page 112
1. Equations and Inequalities......Page 114
1.1. Linear Equations......Page 115
1.2. Applications and Modeling with Linear Equations......Page 121
1.3. Complex Numbers......Page 132
1.4. Quadratic Equations......Page 140
Chapter 1: Quiz (Sections 1.1–1.4)......Page 150
1.5. Applications and Modeling with Quadratic Equations......Page 151
1.6. Other Types of Equations and Applications......Page 163
Summary Exercises on Solving Equations......Page 176
1.7. Inequalities......Page 177
1.8. Absolute Value Equations and Inequalities......Page 189
Test Prep......Page 197
Review Exercises......Page 202
Test......Page 208
2. Graphs and Functions......Page 210
2.1. Rectangular Coordinates and Graphs......Page 211
2.2. Circles......Page 222
2.3. Functions......Page 230
2.4. Linear Functions......Page 246
Chapter 2: Quiz (Sections 2.1–2.4)......Page 260
2.5. Equations of Lines and Linear Models......Page 261
Summary Exercises on Graphs, Circles, Functions, and Equations......Page 274
2.6. Graphs of Basic Functions......Page 275
2.7. Graphing Techniques......Page 287
Chapter 2: Quiz (Sections 2.5–2.7)......Page 303
2.8. Function Operations and Composition......Page 304
Test Prep......Page 319
Review Exercises......Page 323
Test......Page 328
3. Polynomial and Rational Functions......Page 330
3.1. Quadratic Functions and Models......Page 331
3.2. Synthetic Division......Page 347
3.3. Zeros of Polynomial Functions......Page 354
3.4. Polynomial Functions: Graphs, Applications, and Models......Page 366
Summary Exercises on Polynomial Functions, Zeros, and Graphs......Page 385
3.5. Rational Functions: Graphs, Applications, and Models......Page 387
Summary Exercises on Solving Equations and Inequalities......Page 408
3.6. Variation......Page 410
Test Prep......Page 419
Review Exercises......Page 424
Test......Page 429
4. Inverse, Exponential, and Logarithmic Functions......Page 432
4.1. Inverse Functions......Page 433
4.2. Exponential Functions......Page 446
4.3. Logarithmic Functions......Page 462
Summary Exercises on Inverse, Exponential, and Logarithmic Functions......Page 475
4.4. Evaluating Logarithms and the Change-of-Base Theorem......Page 476
4.5. Exponential and Logarithmic Equations......Page 488
4.6. Applications and Models of Exponential Growth and Decay......Page 500
Summary Exercises on Functions: Domains and Defining Equations......Page 512
Test Prep......Page 515
Review Exercises......Page 518
Test......Page 522
5. Trigonometric Functions......Page 524
5.1. Angles......Page 525
5.2. Trigonometric Functions......Page 533
5.3. Trigonometric Function Values and Angle Measures......Page 548
Chapter 5: Quiz (Sections 5.1–5.3)......Page 563
5.4. Solutions and Applications of Right Triangles......Page 564
Test Prep......Page 582
Review Exercises......Page 586
Test......Page 589
6. The Circular Functions and Their Graphs......Page 592
6.1. Radian Measure......Page 593
6.2. The Unit Circle and Circular Functions......Page 605
6.3. Graphs of the Sine and Cosine Functions......Page 619
6.4. Translations of the Graphs of the Sine and Cosine Functions......Page 632
6.5. Graphs of the Tangent and Cotangent Functions......Page 643
6.6. Graphs of the Secant and Cosecant Functions......Page 652
6.7. Harmonic Motion......Page 660
Test Prep......Page 667
Review Exercises......Page 670
Test......Page 677
7. Trigonometric Identities and Equations......Page 680
7.1. Fundamental Identities......Page 681
7.2. Verifying Trigonometric Identities......Page 687
7.3. Sum and Difference Identities......Page 696
7.4. Double-Angle and Half-Angle Identities......Page 710
7.5. Inverse Circular Functions......Page 723
7.6.Trigonometric Equations......Page 739
7.7. Equations Involving Inverse Trigonometric Functions......Page 752
Test Prep......Page 759
Review Exercises......Page 763
Test......Page 767
8. Applications of Trigonometry......Page 770
8.1. The Law of Sines......Page 771
8.2. The Law of Cosines......Page 786
Chapter 8: Quiz (Sections 8.1–8.2)......Page 799
8.3. Geometrically Defined Vectors and Applications......Page 800
8.4. Algebraically Defined Vectors and the Dot Product......Page 810
Summary Exercises on Applications of Trigonometry and Vectors......Page 818
8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients......Page 820
8.6. De Moivre’s Theorem; Powers and Roots of Complex Numbers......Page 831
8.7. Polar Equations and Graphs......Page 838
8.8. Parametric Equations, Graphs, and Applications......Page 851
Test Prep......Page 859
Review Exercises......Page 864
Test......Page 870
9. Systems and Matrices......Page 872
9.1. Systems of Linear Equations......Page 873
9.2. Matrix Solution of Linear Systems......Page 891
9.3. Determinant Solution of Linear Systems......Page 903
9.4. Partial Fractions......Page 916
Chapter 9: Quiz (Sections 9.1–9.4)......Page 923
9.5. Nonlinear Systems of Equations......Page 924
Summary Exercises on Systems of Equations......Page 934
9.6. Systems of Inequalities and Linear Programming......Page 935
9.7. Properties of Matrices......Page 947
9.8. Matrix Inverses......Page 961
Test Prep......Page 973
Review Exercises......Page 978
Test......Page 984
10. Analytic Geometry......Page 986
10.1. Parabolas......Page 987
10.2. Ellipses......Page 996
10.3. Hyperbolas......Page 1008
10.4. Summary of the Conic Sections......Page 1018
Test Prep......Page 1025
Review Exercises......Page 1027
Test......Page 1030
11. Further Topics in Algebra......Page 1032
11.1. Sequences and Series......Page 1033
11.2. Arithmetic Sequences and Series......Page 1044
11.3. Geometric Sequences and Series......Page 1054
Summary Exercises on Sequences and Series......Page 1065
11.4. The Binomial Theorem......Page 1066
11.5. Mathematical Induction......Page 1073
Chapter 11: Quiz (Sections 11.1–11.5)......Page 1080
11.6. Basics of Counting Theory......Page 1081
11.7. Basics of Probability......Page 1092
Test Prep......Page 1104
Review Exercises......Page 1108
Test......Page 1112
Appendix A: Polar Form of Conic Sections......Page 1114
Appendix B: Rotation of Axes......Page 1118
Appendix C: Geometry Formulas......Page 1122
Answers to Selected Exercises......Page 1124
Photo Credits......Page 1182
Index......Page 1184
Back Cover......Page 1202