## College Algebra and Trigonometry, Global Edition

(2016)

### Abstract

For courses in college algebra and trigonometry .

The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. With this latest edition, the authors respond to the challenges of new student expectations and new classroom models.

MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features support College Algebra students in a variety of classroom formats (traditional, hybrid, and online).

Section Title Page Action Price
Cover Cover
Title Page 5
Contents 8
Preface 17
Resources for Success 22
Acknowledgments 24
R. Review of Basic Concepts 27
R.1. Sets 28
R.2. Real Numbers and Their Properties 35
R.3. Polynomials 50
R.4. Factoring Polynomials 62
R.5. Rational Expressions 72
R.6. Rational Exponents 81
Test Prep 103
Review Exercises 107
Test 111
1. Equations and Inequalities 113
1.1. Linear Equations 114
1.2. Applications and Modeling with Linear Equations 120
1.3. Complex Numbers 131
Chapter 1: Quiz (Sections 1.1–1.4) 149
1.5. Applications and Modeling with Quadratic Equations 150
1.6. Other Types of Equations and Applications 162
Summary Exercises on Solving Equations 175
1.7. Inequalities 176
1.8. Absolute Value Equations and Inequalities 188
Test Prep 196
Review Exercises 201
Test 207
2. Graphs and Functions 209
2.1. Rectangular Coordinates and Graphs 210
2.2. Circles 221
2.3. Functions 229
2.4. Linear Functions 245
Chapter 2: Quiz (Sections 2.1–2.4) 259
2.5. Equations of Lines and Linear Models 260
Summary Exercises on Graphs, Circles, Functions, and Equations 273
2.6. Graphs of Basic Functions 274
2.7. Graphing Techniques 286
Chapter 2: Quiz (Sections 2.5–2.7) 302
2.8. Function Operations and Composition 303
Test Prep 318
Review Exercises 322
Test 327
3. Polynomial and Rational Functions 329
3.1. Quadratic Functions and Models 330
3.2. Synthetic Division 346
3.3. Zeros of Polynomial Functions 353
3.4. Polynomial Functions: Graphs, Applications, and Models 365
Summary Exercises on Polynomial Functions, Zeros, and Graphs 384
3.5. Rational Functions: Graphs, Applications, and Models 386
Chapter 3: Quiz (Sections 3.1–3.5) 407
Summary Exercises on Solving Equations and Inequalities 407
3.6. Variation 409
Test Prep 418
Review Exercises 423
Test 428
4. Inverse, Exponential, and Logarithmic Functions 431
4.1. Inverse Functions 432
4.2. Exponential Functions 445
4.3. Logarithmic Functions 461
Summary Exercises on Inverse, Exponential, and Logarithmic Functions 474
4.4. Evaluating Logarithms and the Change-of-Base Theorem 475
Chapter 4: Quiz (Sections 4.1–4.4) 487
4.5. Exponential and Logarithmic Equations 487
4.6. Applications and Models of Exponential Growth and Decay 499
Summary Exercises on Functions: Domains and Defining Equations 511
Test Prep 514
Review Exercises 517
Test 521
5. Trigonometric Functions 523
5.1. Angles 524
5.2. Trigonometric Functions 532
5.3. Trigonometric Function Values and Angle Measures 547
Chapter 5: Quiz (Sections 5.1–5.3) 562
5.4. Solutions and Applications of Right Triangles 563
Test Prep 581
Review Exercises 585
Test 588
6. The Circular Functions and Their Graphs 591
6.2. The Unit Circle and Circular Functions 604
6.3. Graphs of the Sine and Cosine Functions 618
6.4. Translations of the Graphs of the Sine and Cosine Functions 631
Chapter 6: Quiz (Sections 6.1–6.4) 642
6.5. Graphs of the Tangent and Cotangent Functions 642
6.6. Graphs of the Secant and Cosecant Functions 651
Summary Exercises on Graphing Circular Functions 659
6.7. Harmonic Motion 659
Test Prep 666
Review Exercises 669
Test 676
7. Trigonometric Identities and Equations 679
7.1. Fundamental Identities 680
7.2. Verifying Trigonometric Identities 686
7.3. Sum and Difference Identities 695
Chapter 7: Quiz (Sections 7.1–7.3) 709
7.4. Double-Angle and Half-Angle Identities 709
Summary Exercises on Verifying Trigonometric Identities 722
7.5. Inverse Circular Functions 722
7.6.Trigonometric Equations 738
Chapter 7: Quiz (Sections 7.5–7.6) 751
7.7. Equations Involving Inverse Trigonometric Functions 751
Test Prep 758
Review Exercises 762
Test 766
8. Applications of Trigonometry 769
8.1. The Law of Sines 770
8.2. The Law of Cosines 785
Chapter 8: Quiz (Sections 8.1–8.2) 798
8.3. Geometrically Defined Vectors and Applications 799
8.4. Algebraically Defined Vectors and the Dot Product 809
Summary Exercises on Applications of Trigonometry and Vectors 817
8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 819
8.6. De Moivre’s Theorem; Powers and Roots of Complex Numbers 830
Chapter 8: Quiz (Sections 8.3–8.6) 837
8.7. Polar Equations and Graphs 837
8.8. Parametric Equations, Graphs, and Applications 850
Test Prep 858
Review Exercises 863
Test 869
9. Systems and Matrices 871
9.1. Systems of Linear Equations 872
9.2. Matrix Solution of Linear Systems 890
9.3. Determinant Solution of Linear Systems 902
9.4. Partial Fractions 915
Chapter 9: Quiz (Sections 9.1–9.4) 922
9.5. Nonlinear Systems of Equations 923
Summary Exercises on Systems of Equations 933
9.6. Systems of Inequalities and Linear Programming 934
9.7. Properties of Matrices 946
9.8. Matrix Inverses 960
Test Prep 972
Review Exercises 977
Test 983
10. Analytic Geometry 985
10.1. Parabolas 986
10.2. Ellipses 995
Chapter 10: Quiz (Sections 10.1–10.2) 1007
10.3. Hyperbolas 1007
10.4. Summary of the Conic Sections 1017
Test Prep 1024
Review Exercises 1026
Test 1029
11. Further Topics in Algebra 1031
11.1. Sequences and Series 1032
11.2. Arithmetic Sequences and Series 1043
11.3. Geometric Sequences and Series 1053
Summary Exercises on Sequences and Series 1064
11.4. The Binomial Theorem 1065
11.5. Mathematical Induction 1072
Chapter 11: Quiz (Sections 11.1–11.5) 1079
11.6. Basics of Counting Theory 1080
11.7. Basics of Probability 1091
Test Prep 1103
Review Exercises 1107
Test 1111
Appendices 1113
Appendix A: Polar Form of Conic Sections 1113
Appendix B: Rotation of Axes 1117
Appendix C: Geometry Formulas 1121