Algebra and Trigonometry With Analytic

This latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY (CLASSIC EDITION), Eleventh Edition, effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets.

PREFACE

x

CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA

1

(52)

1.1 Real Numbers

2

(13)

1.2 Exponents and Radicals

15

(12)

1.3 Algebraic Expressions

27

(13)

1.4 Fractional Expressions

40

(9)

CHAPTER 1 REVIEW EXERCISES

49

(2)

CHAPTER 1 DISCUSSION EXERCISES

51

(2)

CHAPTER 2 EQUATIONS AND INEQUALITIES

53

(70)

2.1 Equations

54

(8)

2.2 Applied Problems

62

(12)

2.3 Quadratic Equations

74

(12)

2.4 Complex Numbers

86

(6)

2.5 Other Types of Equations

92

(9)

2.6 Inequalities

101

(9)

2.7 More on Inequalities

110

(7)

CHAPTER 2 REVIEW EXERCISES

117

(3)

CHAPTER 2 DISCUSSION EXERCISES

120

(3)

CHAPTER 3 FUNCTIONS AND GRAPHS

123

(114)

3.1 Rectangular Coordinate Systems

124

(7)

3.2 Graphs of Equations

131

(13)

3.3 Lines

144

(17)

3.4 Definition of Function

161

(15)

3.5 Graphs of Functions

176

(13)

3.6 Quadratic Functions

189

(14)

3.7 Operations on Functions

203

(10)

3.8 Inverse Functions

213

(10)

3.9 Variation

223

(6)

CHAPTER 3 REVIEW EXERCISES

229

(5)

CHAPTER 3 DISCUSSION EXERCISES

234

(3)

CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS

237

(56)

4.1 Polynomial Functions of Degree Greater Than 2

238

(8)

4.2 Properties of Division

246

(8)

4.3 Zeros of Polynomials

254

(13)

4.4 Complex and Rational Zeros of Polynomials

267

(8)

4.5 Rational Functions

275

(15)

CHAPTER 4 REVIEW EXERCISES

290

(2)

CHAPTER 4 DISCUSSION EXERCISES

292

(1)

CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

293

(60)

5.1 Exponential Functions

294

(11)

5.2 The Natural Exponential Function

305

(10)

5.3 Logarithmic Functions

315

(15)

5.4 Properties of Logarithms

330

(8)

5.5 Exponential and Logarithmic Equations

338

(10)

CHAPTER 5 REVIEW EXERCISES

348

(2)

CHAPTER 5 DISCUSSION EXERCISES

350

(3)

CHAPTER 6 THE TRIGONOMETRIC FUNCTIONS

353

(96)

6.1 Angles

354

(9)

6.2 Trigonometric Functions of Angles

363

(16)

6.2 Trigonometric Functions of Real Numbers

379

(19)

6.4 Values of the Trigonometric Functions

398

(7)

6.5 Trigonometric Graphs

405

(15)

6.6 Additional Trigonometric Graphs

420

(9)

6.7 Applied Problems

429

(13)

CHAPTER 6 REVIEW EXERCISES

442

(6)

CHAPTER 6 DISCUSSION EXERCISES

448

(1)

CHAPTER 7 ANALYTIC TRIGONOMETRY

449

(64)

7.1 Verifying Trigonometric Identities

450

(5)

7.2 Trigonometric Equations

455

(12)

7.3 The Addition and Subtraction Formulas

467

(11)

7.4 Multiple-Angle Formulas

478

(10)

7.5 Product-to-Sum and Sum-to-Product Formulas

488

(5)

7.6 The Inverse Trigonometric Functions

493

(15)

CHAPTER 7 REVIEW EXERCISES

508

(3)

CHAPTER 7 DISCUSSION EXERCISES

511

(2)

CHAPTER 8 APPLICATIONS OF TRIGONOMETRY

513

(60)

8.1 The Law of Sines

514

(10)

8.2 The Law of Cosines

524

(10)

8.3 Trigonometric Form for Complex Numbers

534

(5)

8.4 De Moivre's Theorem and nth Roots of Complex Numbers

539

(5)

8.5 Vectors

544

(14)

8.6 The Dot Product

558

(10)

CHAPTER 8 REVIEW EXERCISES

568

(3)

CHAPTER 8 DISCUSSION EXERCISES

571

(2)

CHAPTER 9 SYSTEMS OF EQUATIONS AND INEQUALITIES

573

(90)

9.1 Systems of Equations

574

(9)

9.2 Systems of Linear Equations in Two Variables

583

(8)

9.3 Systems of Linear Equations in More Than Two Variables

591

(15)

9.4 Partial Fractions

606

(6)

9.5 Systems of Inequalities

612

(7)

9.6 Linear Programming

619

(9)

9.7 The Algebra of Matrices

628

(9)

9.8 The Inverse of a Matrix

637

(6)

9.9 Determinants

643

(7)

9.10 Properties of Determinants

650

(8)

CHAPTER 9 REVIEW EXERCISES

658

(3)

CHAPTER 9 DISCUSSION EXERCISES

661

(2)

CHAPTER 10 SEQUENCES, SERIES, AND PROBABILITY

663

(72)

10.1 Infinite Sequences and Summation Notation

664

(9)

10.2 Arithmetic Sequences

673

(7)

10.3 Geometric Sequences

680

(9)

10.4 Mathematical Induction

689

(6)

10.5 The Binomial Theorem

695

(9)

10.6 Permutations

704

(7)

10.7 Distinguishable Permutations and Combinations

711

(7)

10.8 Probability

718

(12)

CHAPTER 10 REVIEW EXERCISES

730

(3)

CHAPTER 10 DISCUSSION EXERCISES

733

(2)

CHAPTER 11 TOPICS AND ANALYTIC GEOMETRY

735

(69)

11.1 Parabolas

736

(10)

11.2 Ellipses

746

(13)

11.3 Hyperbolas

759

(13)

11.4 Plane Curves and Parametric Equations

772

(10)

11.5 Polar Coordinates

782

(12)

11.6 Polar Equations of Conics

794

(7)

CHAPTER II REVIEW EXERCISES

801

(2)

CHAPTER II DISCUSSION EXERCISES

803

(1)

APPENDIXES

804

I Using a TI-82/83 Graphing Calculator

804

(38)

II Common Graphs and Their Equations

842

(2)

III A Summary of Graph Transformations

844

(2)

IV Graphs of Trigonometric Functions and Their Inverses

846

ANSWERS TO SELECTED EXERCISES

A1

(88)

INDEX OF APPLICATIONS

A89

(6)

INDEX

A95

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Algebra and Trigonometry With Analytic Geometry

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