9780072368697

Raymond A. Barnett received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing postdoctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science Karl E. Byleen received his B.S., M.A., and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics, and Computer Science of Marquette University

Preface

ix

Chapter Dependencies

xx

To the Student

xxiv

Basic Algebraic Operations

1

(72)

Algebra and Real Numbers

2

(10)

Polynomials: Basic Operations

12

(11)

Polynomials: Factoring

23

(10)

Rational Expressions: Basic Operations

33

(9)

Integer Exponents

42

(9)

Rational Exponents

51

(6)

Radicals

57

(16)

Rational Number Representations

67

(1)

Review

67

(6)

Equations and Inequalities

73

(100)

Linear Equations and Applications

74

(15)

Systems of Linear Equations and Applications

89

(9)

Linear Inequalities

98

(11)

Absolute Value in Equations and Inequalities

109

(10)

Complex Numbers

119

(11)

Quadratic Equations and Applications

130

(15)

Equations Reducible to Quadratic Form

145

(8)

Polynomial and Rational Inequalities

153

(20)

Rates of Change

162

(1)

Review

163

(5)

Cumulative Review Exercise

168

(5)

Graphs and Functions

173

(110)

Basic Tools; Circles

174

(17)

Straight Lines

191

(16)

Functions

207

(16)

Graphing Functions

223

(18)

Combining Functions

241

(17)

Inverse Functions

258

(25)

Mathematical Modeling in Business

274

(2)

Review

276

(7)

Polynomial and Rational Functions

283

(70)

Polynomial Functions and Graphs

285

(12)

Finding Rational Zeros of Polynomials

297

(13)

Approximating Real Zeros of Polynomials

310

(12)

Rational Functions

322

(15)

Partial Fractions

337

(16)

Interpolating Polynomials

345

(2)

Review

347

(6)

Exponential and Logarithmic Functions

353

(60)

Exponential Functions

354

(11)

The Exponential Function with Base e

365

(11)

Logarithmic Functions

376

(9)

Common and Natural Logarithms

385

(10)

Exponential and Logarithmic Equations

395

(18)

Growth of Increasing Functions

405

(1)

Review

405

(3)

Cumulative Review Exercise

408

(5)

Trigonometric Functions

413

(110)

Angles and Their Measure

414

(9)

Acute Angle Domains

423

(12)

General Angle and Real Number Domains

435

(9)

Exact Values for Special Angles and Real Numbers

444

(10)

Circular Functions

454

(12)

Graphing Basic Trigonometric Functions

466

(11)

Graphing y = k + A sin (Bx + C) and y = k + A cos (Bx + C)

477

(16)

Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions

493

(8)

Inverse Trigonometric Functions

501

(22)

A Predator-Prey Analysis Involving Mountain Lions and Deer

514

(1)

Review

515

(8)

Trigonometric Identities and Conditional Equations

523

(54)

Basic Identities and Their Use

524

(9)

Sum, Difference, and Cofunction Identities

533

(10)

Double-Angle and Half-Angle Identities

543

(9)

Product-Sum and Sum-Product Identities

552

(5)

Trigonometric Equations

557

(20)

From M sin Bt + N cos Bt to A sin (Bt + C)---A Harmonic Analysis Tool

569

(2)

Review

571

(6)

Additional Topics in Trigonometry

577

(80)

Law of Sines

578

(10)

Law of Cosines

588

(8)

Geometric Vectors

596

(7)

Algebraic Vectors

603

(10)

Polar Coordinates and Graphs

613

(14)

Complex Numbers in Rectangular and Polar Forms

627

(8)

De Moivre's Theorem

635

(22)

Conic Sections and Planetary Orbits

641

(3)

Review

644

(7)

Cumulative Review Exercise

651

(6)

Systems of Equations and Inequalities

657

(74)

Systems of Linear Equations and Augmented Matrices

658

(18)

Gauss-Jordan Elimination

676

(14)

Systems Involving Second-Degree Equations

690

(9)

Systems of Linear Inequalities in Two Variables

699

(13)

Linear Programming

712

(19)

Modeling with Systems of Linear Equations

723

(2)

Review

725

(6)

Matrices and Determinants

731

(64)

Matrices: Basic Operations

732

(14)

Inverse of a Square Matrix

746

(10)

Matrix Equations and Systems of Linear Equations

756

(10)

Determinants

766

(8)

Properties of Determinants

774

(7)

Cramer's Rule

781

(14)

Using Matrices to Find Cost, Revenue and Profit

786

(1)

Review

787

(5)

Cumulative Review Exercise

792

(3)

Sequences and Series

795

(54)

Sequences and Series

796

(8)

Mathematical Induction

804

(8)

Arithmetic and Geometric Sequences

812

(13)

Binomial Formula

825

(8)

Multiplication Principle, Permutations, and Combinations

833

(16)

Sequences Specified by Recursion Formulas

845

(1)

Review

845

(4)

Additional Topics in Analytic Geometry

849

Conic Sections; Parabola

850

Ellipse

860

Hyperbola

871

Translation of Axes

883

Parametric Equations

893

Focal Chords

900

Review

901

Cumulative Review Exercise

907

Appendices

Appendix A Significant Digits

A-1

Appendix B Geometric Formulas

A-4

Answers

A-7

Applications Index

I-1

Subject Index

I-3

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College Algebra With Trigonometry

College Algebra With Trigonometry

0072368691

Author Biography

Table of Contents

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