College Algebra With Trigonometry

by Barnett, Raymond A.; Byleen, Karl E.

• ISBN13: 9780072867404
• ISBN10: 007286740X
• Edition: 8th
• Format: Hardcover
• Copyright: 2007-02-16
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

The Barnett/Ziegler/Byleen College Algebra series is designed to give students a solid grounding in pre-calculus topics in a user-friendly manner. The series emphasizes computational skills, ideas, and problem solving rather than theory. Explore/Discuss boxes integrated throughout each text encourage students to think critically about mathematical concepts. All worked examples are followed by Matched Problems that reinforce the concepts being taught. New to these editions, Technology Connections illustrate how concepts that were previously explained in an algebraic context may also be solved using a graphing calculator. Students are always shown the underlying algebraic methods first so that they do not become calculator-dependent. In addition, each text in the series contains an abundance of exercises - including numerous calculator-based and reasoning and writing exercises - and a wide variety of real-world applications illustrating how math is useful. College Algebra with Trigonometry 8/e employs a right-angle approach and can be used in one- or two-semester College Algebra with Trig or Precalculus courses.

Author Biography

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

Table of Contents

Chapter R: Basic Algebraic Operations

R-1 Algebra and Real Numbers

R-2 Exponents

R-3 Radicals

R-4 Polynomials: Basic Operations

R-5 Polynomials: Factoring

R-6 Rational Expressions: Basic Operations

Chapter R Review

Chapter R Group Activity: Rational Number Representations

Chapter 1: Equations and Inequalities

1-1 Linear Equations and Applications

1-2 Linear Inequalities

1-3 Absolute Value

1-4 Complex Numbers

1-5 Quadratic Equations and Applications

1-6 Equations Involving Radicals

Chapter 1 Review

Chapter 1 Group Activity: Solving a Cubic Equation

Chapter 2: Graphs

2-1 Cartesian Coordinate system

2-2 Distance in the Plane

2-3 Equations of a line

2-4 Linear Equations and Models

Chapter 2 Review

Chapter 2 Group Activity: Rates of Change

Chapter 3: Functions

3-1 Functions

3-2 Graphing Functions

3-3 Transformations of Functions

3-4 Quadratic Functions

3-5 Combining Functions; Composition

3-6 Inverse Functions

Chapter 3 Review

Chapter 3 Group Activity: Mathematical Modeling: Choosing a Long-Distance Calling Plan

Chapters 1-3 Cumulative Review Exercises

Chapter 4: Polynomials and Rational Functions

4-1 Polynomial Functions and Models

4-2 Real Zeros and Polynomial Inequalities

4-3 Complex Zeros and Rational Zeros of Polynomials

4-4 Rational Functions and Inequalities

4-5 Variation and Modeling

Chapter 4 Review

Chapter 4 Group Activity: Interpolating Polynomials

Chapter 5: Exponential and Logarithmic Functions

5-1 Exponential Functions

5-2 Exponential Models

5-3 Logarithmic Functions

5-4 Logarithmic Models

5-5 Exponential and Logarithmic Equations

Chapter 5 Review

Chapter 5 Group Activity: Growth of Increasing Functions

Chapters 4-5 Cumulative Review Exercises

Chapter 6: Trigonometric Functions

6-1 Angles and Their Measure

6-2 Right-Triangle Trigonometry

6-3 Trigonometric Functions: A Unit Circle Approach

6-4 Trigonometric Functions: Properties and Graphs

6-5 More General Trigonometric Functions

6-6 Inverse Trigonometric Functions

Chapter 6 Review

Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer

Chapter 7: Trigonometric Identities and Conditional Equations

7-1 Basic Identities and Their Use

7-2 Sum, Difference, and Cofunction Identities

7-3 Double-Angle and Half-Angle Identities

7-4 Product-Sum and Sum-Product Identities

7-5 Trigonometric Equations

Chapter 7 Review

Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C): A Harmonic Analysis Tool

Chapter 8: Additional Topics in Trigonometry

8-1 Law of Sines

8-2 Law of Cosines

8-3 Vectors in the Plane

8-4 Polar Coordinates and Graphs

8-5 Complex Numbers and De Moivre's Theorem

Chapter 8 Review

Chapter 8 Group Activity: Conic Sections and Planetary Orbits

Chapters 6-8 Cumulative Review Exercises

Chapter 9: Additional Topics in Analytic Geometry

9-1 Conic Sections; Parabolas

9-2 Ellipses

9-3 Hyperbolas

9-4 Rotation of Axes

Chapter 9 Review

Chapter 9 Group Activity: Focal Chords

Chapter 10: Systems of Equations and Inequalities; Matrices

10-1 Systems of Linear Equations: Graphing and Substitution

10-2 Systems of Linear Equations: Elimination

10-3 Systems of Linear Equations: Gauss-Jordan Elimination

10-4 Matrices: Basic Operations

10-5 Systems of Linear Equations: Matrix Inverse Methods

10-6 Systems of Nonlinear Equations

10-7 Systems of Linear Inequalities in Two Variables

10-8 Linear Programming

Chapter 10 Review

Chapter 10 Group Activity: Modeling With Systems of Linear Equations

Chapter 11: Sequences and Series

11-1 Sequences and Series

11-2 Mathematical Induction

11-3 Arithmetic and Geometric Sequences

11-4 Counting Techniques: Multiplication Principle, Permutations, and Combinations

11-5 Sample Spaces and Probability

11-6 Binomial Formula

Chapter 11 Review

Chapter 11 Group Activity: Sequences Specified by Recursion Formulas

Chapters 9-11 Cumulative Review Exercises

Appendix A: Special Topics

A-1 Scientific Notation and Significant Digits

A-2 Partial Fractions

A-3 Parametric Equations

Appendix B: Geometric Formulas