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9780130914651

Algebra and Trigonometry (6th Edition)

Sullivan, Michael Author

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A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of any reader. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Includes Case Studies; New design that utilizes multiple colors to enhance accessibility; Multiple source applications; Numerous graduated examples and exercises; Discussion, writing, and research problems; Important formulas, theorems, definitions, and objectives; and more. For anyone interested in algebra and trigonometry.

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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, student-friendly 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 broad-based 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 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 just-in-time 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 just-in-time 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

  • The Appendix, Graphing Utilities, has been updated and expanded to include the latest features of the graphing calculator. While the graphing calculator remains an option, identified by a graphing icon, references to the Appendix occur at appropriate places in the text for those inclined to use the graphing calculator features of the text.
  • The Area of a Sector is now included as part of the section Angles and Their Measure.
  • A discussion of combining waves was added to the section on Harmonic Motion.

Organization

  • The discussion on Rational Functions now appears in two sections, Rational Functions I and Rational Functions II: Analyzing Graphs. This division should allow the sections to be covered in one teaching period each.
  • The discussion of Polynomial and Rational Inequalities now appears after Polynomial and Rational Functions. This allows us to use information obtained about the graphs to solve the inequalities. Students and instructors will appreciate how easy this usually tough concept is now handled.
  • Zeros of a Polynomial Function now appears in a separate chapter following Polynomial and Rational Functions to provide more flexibility in teaching and testing.
  • The chapter on Trigonometric Functions now has a single section devoted to the graphs of the sine and cosine functions, including a discussion of sinusoidal graphs. Separate sections follow on Graphs of the Remaining Trigonometric Functions and Phase Shift; Sinusoidal Curve Fitting. These changes will allow the material of each section to be taught in a single period and provide flexibility in choice of content.
  • The chapter on Analytic Trigonometry now begins with two sections that discuss the inverse trigonometric functions. The chapter concludes with two sections devoted to Trigonometric Equations. These changes will allow each section to be taught in a single period.
  • Separate chapters on Sequences; Induction; the Binomial Theorem and Counting and Probability also provide more flexibility in coverage.

FEATURES IN THE 6TH EDITION

  • Section OBJECTIVES appear in a numbered list to begin each section.
  • NOW WORK PROBLEM XX appears after a concept has been introduced. This directs the student to a problem in the exercises that tests the concept, insuring that the concept has been mastered before moving on. The Now Work problems are identified in the exercises using yellow numbers and a pencil icon.
  • Optional Comments, Explorations, Seeing the Concept, Examples, and Exercises that utilize the graphing calculator are clearly marked with a calculator icon. Calculator exercises are also identified by the icon and green numbers.
  • References to Calculus are identified by a calculus icon.
  • Historical Perspectives, sometimes with exercises, are presented in context and provide interesting anecdotal information.
  • Varied applications are abundant both in Examples and in Exercises. Many contain sourced data.
  • Discussion, Writing, and Research problems appear in each exercise set, identified by an icon and red numbers. These provide the basis for class discussion, writing projects, and collaborative learning experiences.
  • An extensive Chapter Review provides a list of important formulas, definitions, theorems, and objectives, as well as a complete set of Review Exercises, with sample test questions identified by blue numbers.

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 just-in-time 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 6.1-6.5 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 10.1-10.3 and Sections 10.4-10.5 are independent and may be covered separately or in sequence, depending on the course syllabus.

Chapter 11 - Analytic Geometry

Sections 11.1-11.4 follow in sequence. Sections 11.5,11.6, and 11.7 are independent of each other, but do depend on Sections 11.1-11.4.

Chapter 12 - Systems of Equations and Inequalities

Sections 12.1-12.2 follow in sequence; Sections 12.3-12.8 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 13.1-13.3,13.4, and 13.5.

Chapter 14 - Counting and Probability

Sections 14.1-14.3 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 read-so 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 odd-numbered problems have answers in the back of the book and worked-out solutions in the Student Solutions Manual supplement. Be sure you have made an honest effort before looking at a worked-out 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 "Fill-in-the-Blank" 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

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