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More About This Textbook
Overview
Editorial Reviews
From The Critics
Sullivan (Chicago State U.) presents the sixth edition of this college textbook designed for students with little mathematical background and possibly a fear of mathematics, as well as for highly motivated students who will go on to further their mathematical education. A major change in the sixth edition is that each chapter demonstrates the relevance of mathematics to everyday life by connecting principles from the chapter to a reallife business< >Motorola—including a brief description of a situation at the company, interviews at the company, a biographical sketch of an employee, and an employeedesigned problem at Motorola and accompanying student exercises. The content and organization of the text have also undergone a number of revisions and additions. Annotation c. Book News, Inc., Portland, OR (booknews.com)Booknews
New edition of a text that helps the student to master the terminology and basic concepts of algebra and trigonometry. Each of the 13 chapters begins with an Internet Excursion involving a real world problem utilizing the material in the chapter and information found on the Web. Sections begin with a list of objectives to add further focus to important concepts. Annotation c. by Book News, Inc., Portland, Or.Product Details
Related Subjects
Meet the Author
Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between a home in Oak Lawn IL and a condo in Naples FL.
Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.
Mike has been writing textbooks for more than 35 years and currently has 15 books in print, twelve with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.
Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his coauthor on two precalculus series; Dan works in publishing; and Colleen teaches middleschool and secondary school mathematics. Twelve grandchildren round out the family.
Table of Contents
R. Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents
1. Equations and Inequalities
1.1 Linear Equations
1.2 Quadratic Equations
1.3 Complex Numbers; Quadratic Equations in the Complex Number System
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
1.5 Solving Inequalities
1.6 Equations and Inequalities Involving Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs Applications
2. Graphs
2.1 The Distance and Midpoint Formulas
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
2.3 Lines
2.4 Circles
2.5 Variation
3. Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewisedefined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions
4. Linear and Quadratic Functions
4.1 Linear Functions and Their Properties
4.2 Linear Models: Building Linear Functions from Data
4.3 Quadratic Functions and Their Properties
4.4 Building Quadratic Models from Data
4.5 Inequalities Involving Quadratic Functions
5. Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 Properties of Rational Functions
5.3 The Graph of a Rational Function
5.4 Polynomial and Rational Inequalities
5.5 The Real Zeros of a Polynomial Function
5.6 Complex Zeros: Fundamental Theorem of Algebra
6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 OnetoOne Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data
7. Trigonometric Functions
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Computing the Values of Trigonometric Functions of Acute Angles
7.4 Trigonometric Functions of Any Angle
7.5 Unit Circle Approach; Properties of the Trigonometric Functions
7.6 Graphs of the Sine and Cosine Functions
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8 Phase Shift; Sinusoidal Curve Fitting
8. Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions
8.2 The Inverse Trigonometric Functions (continued)
8.3 Trigonometric Equations
8.4 Trigonometric Identities
8.5 Sum and Difference Formulas
8.6 DoubleAngle and HalfAngle Formulas
8.7 ProducttoSum and SumtoProduct Formulas
9. Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
9.2 Law of Sines
9.3 Law of Cosines
9.4 Area of a Triangle
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
10. Polar Coordinates; Vectors
10.1 Polar Coordinates
10.2 Polar Equations and Graphs
10.3 The Complex Plane; DeMoivre’s Theorem
10.4 Vectors
10.5 The Dot Product
11. Analytic Geometry
11.1 Conics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Rotation of Axes; General Form of a Conic
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations
12. Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination
12.2 Systems of Linear Equations: Matrices
12.3 Systems of Linear Equations: Determinants
12.4 Matrix Algebra
12.5 Partial Fraction Decomposition
12.6 Systems of Nonlinear Equations
12.7 Systems of Inequalities
12.8 Linear Programming
13. Sequences; Induction; The Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences; Geometric Series
13.4 Mathematical Induction
13.5 The Binomial Theorem
14. Counting and Probability
14.1 Sets and Counting
14.2 Permutations and Combinations
14.3 Probability
Appendix: Graphing Utilities
1. The Viewing Rectangle
2. Using a Graphing Utility to Graph Equations
3. Using a Graphing Utility to Graph Equations Locating Intercepts and Checking for Symmetry
4. Using a Graphing Utility to Solve Equations
5. Square Screens
6. Using a Graphing Utility to Graph Inequalities
7. Using a Graphing Utility to Solve Systems of Linear Equations
8. Using a Graphing Utility to Graph a Polar Equation
9. Using a Graphing Utility to Graph Parametric Equations
Preface
To the Instructor
As a professor at an urban public university for over 30 years, I am aware of the varied needs of algebra and trigonometry students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education. I have written this text for both groups. As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four college graduates, I also understand the realities of college life. I have taken great pains to insure that the text contains solid, studentfriendly examples and problems, as well as a clear, seamless, writing style. I encourage you to share with me your experiences teaching from this text.
THE SIXTH EDITION
The Sixth Edition builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. A huge benefit of authoring a successful series is the broadbased feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used previous editions. I am sincerely grateful for this feedback andhave tried to make changes that improve the flow and usability of the text.
NEW TO THE SIXTH EDITION
Real Mathematics at Motorola
Each chapter begins with Field Trip to Motorola, a brief description of a current situation at Motorola, followed by Interview at Motorola, a biographical sketch of a Motorola employee. At the end of each chapter is Project at Motorola, written by the Motorola employee, that contains a description, with exercises, of a problem at Motorola that relates to the mathematics found in the chapter. It doesn't get more REAL than this.
Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a justintime review for students.
Chapter R Review
This chapter, a revision of the old Chapter 1, has been renamed to more accurately reflect its content. It may be used as the first part of the course or as a justintime review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.
Content
Organization
FEATURES IN THE 6TH EDITION
USING THE 6TH EDITION EFFECTIVELY AND EFFICIENTLY WITH YOUR SYLLABUS
To meet the varied needs of diverse syllabi, this book contains more content than expected in a college algebra course. This book has been organized with flexibility of use in mind. Even within a given chapter, certain sections can be skipped without fear of future problems.
Chapter R  Review
This chapter, a revision of the old Chapter 1, has been renamed to more accurately reflect its content. It may be used as the first part of the course or as a justintime review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.
Chapter 1  Equations and Inequalities
Primarily a review of Intermediate Algebra topics, this material is prerequisite for later topics. For those who prefer to treat complex numbers and negative discriminants early, Section 5.3 can be covered at any time after Section 1.3.
Chapter 2  Graphs
This chapter lays the foundation. Sections 2.5 and 2.6 may be skipped without adverse effects.
Chapter 3  Functions and Their Graphs
Perhaps the most important chapter. Section 3.6 can be skipped without adverse effects.
Chapter 4  Polynomial and Rational Functions
Topic selection is dependent on your syllabus.
Chapter 5  The Zeros of a Polynomial Function
Topic selection is dependent on your syllabus. Section 5.1 is not absolutely necessary, but its coverage makes some computations easier.
Chapter 6  Exponential and Logarithmic Functions
Sections 6.16.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.
Chapter 7  Trigonometric Functions
The sections follow in sequence.
Chapter 8  Analytic Trigonometry
The sections follow in sequence. Sections 8.2, 8.6, and 8.8 may be skipped in a brief course.
Chapter 9 Application Trigonometric
The sections follow in sequence. Sections 9.4 and 9.5 may be skipped in a brief course.
Chapter 10  Polar Coordinates; Vectors
Sections 10.110.3 and Sections 10.410.5 are independent and may be covered separately or in sequence, depending on the course syllabus.
Chapter 11  Analytic Geometry
Sections 11.111.4 follow in sequence. Sections 11.5,11.6, and 11.7 are independent of each other, but do depend on Sections 11.111.4.
Chapter 12  Systems of Equations and Inequalities
Sections 12.112.2 follow in sequence; Sections 12.312.8 require Sections 12.1 and 12.2, and may be covered in any order. Section 12.9 depends on Section 12.8.
Chapter 13  Sequences; Induction; the Binomial Theorem
There are three independent parts: Sections 13.113.3,13.4, and 13.5.
Chapter 14  Counting and Probability
Sections 14.114.3 follow in order.
To the Student
As you begin your study of Algebra and Trigonometry you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Algebra and Trigonometry are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, just the first in a series of many. Either way, this text was written with you in mind. I have taught algebra and trigonometry courses for over thirty years. I am also the father of four college students who called home from time to time, frustrated and with questions. I know what you're going through. So I have written a text that doesn't overwhelm, or unnecessarily complicate Algebra and Trigonometry, but at the same time it gives you the skills and practice you need to be successful.
This text is designed to help you, the student, master the terminology and basic concepts of Algebra and Trigonometry. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," one that can help you focus your efforts and get the most from the time and energy you invest.
HOW TO USE THIS BOOK EFFECTIVELY AND EFFICIENTLY
First, and most important, this book is meant to be readso please, begin by reading the material assigned. You will find that the text has additional explanation and examples that will help you. Also, it is best to read the section before the lecture, so you can ask questions right away about anything you didn't understand.
Many sections begin with "Preparing for This Section," a list of concepts that will be used in the section. Take the short amount of time required to refresh your memory. This will make the section easier to understand and will actually save you time and effort.
A list of OBJECTIVES is provided at the beginning of each section. Read them. They will help you recognize the important ideas and skills developed in the section.
After a concept has been introduced and an example given, you will see NOW WORK PROBLEM XX. Go to the exercises at the end of the section, work the problem cited, and check your answer in the back of the book. If you get it right, you can be confident in continuing on in the section. If you don't get it right, go back over the explanations and examples to see what you might have missed. Then rework the problem. Ask for help if you miss it again.
If you follow these practices throughout the section, you will find that you have probably done many of your homework problems. In the exercises, every "Now Work Problem" number is in yellow with a pencil icon. All the oddnumbered problems have answers in the back of the book and workedout solutions in the Student Solutions Manual supplement. Be sure you have made an honest effort before looking at a workedout solution.
At the end of each chapter is a Chapter Review. Use it to be sure you are completely familiar with the equations and formulas listed under "Things to Know." If you are unsure of an item here, use the page reference to go back and review it. Go through the Objectives and be sure you can answer "Yes" to the question "I should be able to...." If you are uncertain, a page reference to the objective is provided.
Spend the few minutes necessary to answer the "FillintheBlank" items and the "True/False" items. These are quick and valuable questions to answer.
Lastly, do the problems identified with blue numbers in the Review Exercises. These are my suggestions for a Practice Test. Do some of the other problems in the review for more practice to prepare for your exam.
Please do not hesitate to contact me, through Prentice Hall, with any suggestions or comments that would improve this text. I look forward to hearing from you.
ACKNOWLEDGMENTS
Textbooks are written by authors, but evolve from an idea into final form through the efforts of many people. Special thanks to Don Dellen, who first suggested this book and the other books in this series. Don's extensive contributions to publishing and mathematics are well known; we all miss him dearly.
I would like to thank Motorola and its people who helped make the projects in this new edition possible. Special thanks to Iwona Turlik, Vice President and Director of the Motorola Advanced Technology Center (MATC), for providing the opportunity to share with students examples of their experience in applying mathematics to engineering tasks.
Best Wishes!
Michael Sullivan
Introduction
To the Instructor
As a professor at an urban public university for over 30 years, I am aware of the varied needs of algebra and trigonometry students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education. I have written this text for both groups. As the author of precalculus, engineering calculus, finite math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four college graduates, I also understand the realities of college life. I have taken great pains to insure that the text contains solid, studentfriendly examples and problems, as well as a clear, seamless, writing style. I encourage you to share with me your experiences teaching from this text.
THE SIXTH EDITION
The Sixth Edition builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. A huge benefit of authoring a successful series is the broadbased feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used previous editions. I am sincerely grateful for thisfeedback and have tried to make changes that improve the flow and usability of the text.
NEW TO THE SIXTH EDITION
Real Mathematics at Motorola
Each chapter begins with Field Trip to Motorola, a brief description of a current situation at Motorola, followed by Interview at Motorola, a biographical sketch of a Motorola employee. At the end of each chapter is Project at Motorola, written by the Motorola employee, that contains a description, with exercises, of a problem at Motorola that relates to the mathematics found in the chapter. It doesn't get more REAL than this.
Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a justintime review for students.
Chapter R Review
This chapter, a revision of the old Chapter 1, has been renamed to more accurately reflect its content. It may be used as the first part of the course or as a justintime review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.
Content
Organization
FEATURES IN THE 6TH EDITION
USING THE 6TH EDITION EFFECTIVELY AND EFFICIENTLY WITH YOUR SYLLABUS
To meet the varied needs of diverse syllabi, this book contains more content than expected in a college algebra course. This book has been organized with flexibility of use in mind. Even within a given chapter, certain sections can be skipped without fear of future problems.
Chapter R  Review
This chapter, a revision of the old Chapter 1, has been renamed to more accurately reflect its content. It may be used as the first part of the course or as a justintime review when the content is required in a later chapter. Specific references to this chapter occur throughout the book to assist in the review process.
Chapter 1  Equations and Inequalities
Primarily a review of Intermediate Algebra topics, this material is prerequisite for later topics. For those who prefer to treat complex numbers and negative discriminants early, Section 5.3 can be covered at any time after Section 1.3.
Chapter 2  Graphs
This chapter lays the foundation. Sections 2.5 and 2.6 may be skipped without adverse effects.
Chapter 3  Functions and Their Graphs
Perhaps the most important chapter. Section 3.6 can be skipped without adverse effects.
Chapter 4  Polynomial and Rational Functions
Topic selection is dependent on your syllabus.
Chapter 5  The Zeros of a Polynomial Function
Topic selection is dependent on your syllabus. Section 5.1 is not absolutely necessary, but its coverage makes some computations easier.
Chapter 6  Exponential and Logarithmic Functions
Sections 6.16.5 follow in sequence; Sections 6.6, 6.7, and 6.8 each require Section 6.3.
Chapter 7  Trigonometric Functions
The sections follow in sequence.
Chapter 8  Analytic Trigonometry
The sections follow in sequence. Sections 8.2, 8.6, and 8.8 may be skipped in a brief course.
Chapter 9 Application Trigonometric
The sections follow in sequence. Sections 9.4 and 9.5 may be skipped in a brief course.
Chapter 10  Polar Coordinates; Vectors
Sections 10.110.3 and Sections 10.410.5 are independent and may be covered separately or in sequence, depending on the course syllabus.
Chapter 11  Analytic Geometry
Sections 11.111.4 follow in sequence. Sections 11.5,11.6, and 11.7 are independent of each other, but do depend on Sections 11.111.4.
Chapter 12  Systems of Equations and Inequalities
Sections 12.112.2 follow in sequence; Sections 12.312.8 require Sections 12.1 and 12.2, and may be covered in any order. Section 12.9 depends on Section 12.8.
Chapter 13  Sequences; Induction; the Binomial Theorem
There are three independent parts: Sections 13.113.3,13.4, and 13.5.
Chapter 14  Counting and Probability
Sections 14.114.3 follow in order.
To the Student
As you begin your study of Algebra and Trigonometry you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Algebra and Trigonometry are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, just the first in a series of many. Either way, this text was written with you in mind. I have taught algebra and trigonometry courses for over thirty years. I am also the father of four college students who called home from time to time, frustrated and with questions. I know what you're going through. So I have written a text that doesn't overwhelm, or unnecessarily complicate Algebra and Trigonometry, but at the same time it gives you the skills and practice you need to be successful.
This text is designed to help you, the student, master the terminology and basic concepts of Algebra and Trigonometry. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," one that can help you focus your efforts and get the most from the time and energy you invest.
HOW TO USE THIS BOOK EFFECTIVELY AND EFFICIENTLY
First, and most important, this book is meant to be readso please, begin by reading the material assigned. You will find that the text has additional explanation and examples that will help you. Also, it is best to read the section before the lecture, so you can ask questions right away about anything you didn't understand.
Many sections begin with "Preparing for This Section," a list of concepts that will be used in the section. Take the short amount of time required to refresh your memory. This will make the section easier to understand and will actually save you time and effort.
A list of OBJECTIVES is provided at the beginning of each section. Read them. They will help you recognize the important ideas and skills developed in the section.
After a concept has been introduced and an example given, you will see NOW WORK PROBLEM XX. Go to the exercises at the end of the section, work the problem cited, and check your answer in the back of the book. If you get it right, you can be confident in continuing on in the section. If you don't get it right, go back over the explanations and examples to see what you might have missed. Then rework the problem. Ask for help if you miss it again.
If you follow these practices throughout the section, you will find that you have probably done many of your homework problems. In the exercises, every "Now Work Problem" number is in yellow with a pencil icon. All the oddnumbered problems have answers in the back of the book and workedout solutions in the Student Solutions Manual supplement. Be sure you have made an honest effort before looking at a workedout solution.
At the end of each chapter is a Chapter Review. Use it to be sure you are completely familiar with the equations and formulas listed under "Things to Know." If you are unsure of an item here, use the page reference to go back and review it. Go through the Objectives and be sure you can answer "Yes" to the question "I should be able to...." If you are uncertain, a page reference to the objective is provided.
Spend the few minutes necessary to answer the "FillintheBlank" items and the "True/False" items. These are quick and valuable questions to answer.
Lastly, do the problems identified with blue numbers in the Review Exercises. These are my suggestions for a Practice Test. Do some of the other problems in the review for more practice to prepare for your exam.
Please do not hesitate to contact me, through Prentice Hall, with any suggestions or comments that would improve this text. I look forward to hearing from you.
ACKNOWLEDGMENTS
Textbooks are written by authors, but evolve from an idea into final form through the efforts of many people. Special thanks to Don Dellen, who first suggested this book and the other books in this series. Don's extensive contributions to publishing and mathematics are well known; we all miss him dearly.
I would like to thank Motorola and its people who helped make the projects in this new edition possible. Special thanks to Iwona Turlik, Vice President and Director of the Motorola Advanced Technology Center (MATC), for providing the opportunity to share with students examples of their experience in applying mathematics to engineering tasks.
Best Wishes!
Michael Sullivan