Algebra and Trigonometry / Edition 6

by Robert Blitzer

Overview

For courses in College Algebra.

Show students that our world is profoundly mathematical

Bob Blitzer continues to inspire students with his engaging approach to mathematics, making this beloved series the #1 in the market year after year. Blitzer draws on his unique background in mathematics and behavioral science to present a wide range of vivid applications in real-life situations. Students of all majors stay engaged because Blitzer uses pop-culture and up-to-date references to connect math to students’ lives, showing that our world is profoundly mathematical.

With the new edition, Blitzer takes student engagement with the mathematical world to a whole new level drawing from applications across all fields as well as topics that are of interest to any college student (e.g., student loan debt, grade inflation, sleep hours of college students). Applications are also brought to life online in a new, assignable video series that explore the entertaining and mathematical Blitzer Bonus boxes. The new edition also aims to help more students to succeed in the course with just-in-time support in the text—such as Brief Review of prerequisite topics, Achieving Success boxes, and Retain the Concepts exercises—as well as support within MyLabTM Math such as new concept-level videos, assignable tools to enhance visualization, and more.

Also available with MyLab Math

MyLabTM Math 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 new edition continues to expand the comprehensive auto-graded exercise options. In addition, MyLab Math includes new options designed to help students of all levels and majors to stay engaged and succeed in the course.

Note: You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyLab, search for:

0134765508 / 9780134765501 Algebra and Trigonometry Plus MyMathLab with eText — Title-Specific Access Card Package, 6/e

Package consists of:

• 0134463218 / 9780134463216 Algebra and Trigonometry
• 0134758846 / 9780134758848 MyLab Math with Pearson eText - Standalone Access Card - for Algebra and Trigonometry

Product Details

ISBN-13:	9780134463216
Publisher:	Pearson Education
Publication date:	01/01/2017
Edition description:	Older Edition
Pages:	1296
Product dimensions:	8.70(w) x 10.90(h) x 1.80(d)

About the Author

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to College Algebra, Bob has written textbooks covering developmental mathematics, introductory algebra, intermediate algebra, trigonometry, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

Read an Excerpt

PREFACE:

Preface

Today's college algebra and trigonometry students are a diverse group. Some are going on into calculus or other math sequences, whereas others will complete their math requirements with this course. This text is designed and written to help both sets of students succeed. The book has three fundamental goals: First, to help students acquire a solid foundation in algebra and trigonometry, preparing them for other college courses such as calculus, business calculus, finite mathematics, and computer science; second, to show students how algebra and trigonometry can model and solve authentic real-world problems; and third, to enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

• "I cannot follow the explanations."
• "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Algebra & Trigonometry have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most aboutteaching in a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting algebra and trigonometry to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-089785-X); (8978E-0). Includes fully worker out solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-089384-6); (8938D-2). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website specifically designed to accompany this text. This product combines the series' key supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-by-section reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly why is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-089387-0); (89386-5). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et al. (013-010954-1); (1095D-6). A three year NSF-funded project integrates an applied approach to the topics in the Pre; calculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-089784-1); (8978D-3). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-089386-2); (8938F-7). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQI is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-089783-3); (8978C-5). A hard-copy version of materials derived from the TestGen-EQ program.

Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.2 Exponents and Scientific Notation

P.3 Radicals and Rational Exponents

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

1. Equations and Inequalities

1.1 Graphs and Graphing Utilities

1.2 Linear Equations and Rational Equations

1.3 Models and Applications

1.4 Complex Numbers

1.5 Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities and Absolute Value Inequalities

2. Functions and Graphs

2.1 Basics of Functions and Their Graphs

2.2 More on Functions and Their Graphs

2.3 Linear Functions and Slope

2.4 More on Slope

2.5 Transformations of Functions

2.6 Combinations of Functions; Composite Functions

2.7 Inverse Functions

2.8 Distance and Midpoint Formulas; Circles

3. Polynomial and Rational Functions

3.1 Quadratic Functions

3.2 Polynomial Functions and Their Graphs

3.3 Dividing Polynomials; Remainder and Factor Theorems

3.4 Zeros of Polynomial Functions

3.5 Rational Functions and Their Graphs

3.6 Polynomial and Rational Inequalities

3.7 Modeling Using Variation

4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Exponential and Logarithmic Equations

4.5 Exponential Growth and Decay; Modeling Data

5. Trigonometric Functions

5.1 Angles and Radian Measure

5.2 Right Triangle Trigonometry

5.3 Trigonometric Functions of Any Angle

5.4 Trigonometric Functions of Real Numbers; Periodic Functions

5.5 Graphs of Sine and Cosine Functions

5.6 Graphs of Other Trigonometric Functions

5.7 Inverse Trigonometric Functions

5.8 Applications of Trigonometric Functions

6. Analytic Trigonometry

6.1 Verifying Trigonometric Identities

6.2 Sum and Difference Formulas

6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas

6.4 Product-to-Sum and Sum-to-Product Formulas

6.5 Trigonometric Equations

7. Additional Topics in Trigonometry

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Polar Coordinates

7.4 Graphs of Polar Equations

7.5 Complex Numbers in Polar Form; DeMoivre's Theorem

7.6 Vectors

7.7 The Dot Product

8. Systems of Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Partial Fractions

8.4 Systems of Nonlinear Equations in Two Variables

8.5 Systems of Inequalities

8.6 Linear Programming

9. Matrices and Determinants

9.1 Matrix Solutions to Linear Systems

9.2 Inconsistent and Dependent Systems and Their Applications

9.3 Matrix Operations and Their Applications

9.4 Multiplicative Inverses of Matrices and Matrix Equations

9.5 Determinants and Cramer's Rule

10. Conic Sections and Analytic Geometry

10.1 The Ellipse

10.2 The Hyperbola

10.3 The Parabola

10.4 Rotation of Axes

10.5 Parametric Equations

10.6 Conic Sections in Polar Coordinates

11. Sequences, Induction, and Probability

11.1 Sequences and Summation Notation

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles, Permutations, and Combinations

11.7 Probability

Preface

Preface

Today's college algebra and trigonometry students are a diverse group. Some are going on into calculus or other math sequences, whereas others will complete their math requirements with this course. This text is designed and written to help both sets of students succeed. The book has three fundamental goals: First, to help students acquire a solid foundation in algebra and trigonometry, preparing them for other college courses such as calculus, business calculus, finite mathematics, and computer science; second, to show students how algebra and trigonometry can model and solve authentic real-world problems; and third, to enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

• "I cannot follow the explanations."
• "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Algebra & Trigonometry have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most about teachingin a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting algebra and trigonometry to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-089785-X); (8978E-0). Includes fully worker out solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-089384-6); (8938D-2). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website specifically designed to accompany this text. This product combines the series' key supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-by-section reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly why is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-089387-0); (89386-5). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et al. (013-010954-1); (1095D-6). A three year NSF-funded project integrates an applied approach to the topics in the Pre; calculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-089784-1); (8978D-3). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-089386-2); (8938F-7). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQI is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-089783-3); (8978C-5). A hard-copy version of materials derived from the TestGen-EQ program.