Higher Education

Precalculus: With Unit Circle Trigonometry, 4th Edition

  • includes Interactive Video Skillbuilder CD-ROM
  • David Cohen late of University of California, Los Angeles
  • ISBN-10: 0534402305  |  ISBN-13: 9780534402303
  • 1200 Pages
  • Previous Editions: 1998, 1994
  • © 2006 | Published
  • College Bookstore Wholesale Price = $173.25
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About

Overview

David Cohen's PRECALCULUS, WITH UNIT-CIRCLE TRIGONOMETRY, Fourth Edition, focuses on teaching mathematics, using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.

Features and Benefits

  • The author has a remarkable writing style that is student friendly and yet mathematically honest.
  • The "Graphical Perspective" feature uses graphs to supplement the text discussion and encourage students to produce their own pictures of a graph.
  • There is a strong emphasis on graphs and visualization, with numerical, graphical, and algebraic viewpoints tightly linked throughout the text, to help students understand the material.
  • Coordinates and graphs are developed in Chapter 1.
  • Iteration is covered from numerical, graphical, and algebraic viewpoints.
  • Optional "Graphing Utility" exercises are available throughout the text.
  • Exercises range in difficulty from simple to more complex and are designated with an "A," "B," or "C" rating.

Table of Contents

1. FUNDAMENTALS.
Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS.
The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION.
Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
6. THE TRIGONOMETRIC FUNCTIONS.
Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry.
7. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS.
Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
8. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
9. ADDITIONAL TOPICS IN TRIGONOMETRY.
Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
10. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
11. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
12. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
13. ADDITIONAL TOPICS.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem.
Appendix 1: Using a Graphing Utility.
Appendix 2: Significant Digits and Calculators.
Tables.
Answers to Selected Exercises.
Index.

What's New

  • The role of the graphing utility has been expanded in this edition, with graphing utility material carefully integrated throughout the text. Graphing utility exercises are now integrated into the exercise sets with an icon to identify them. Reviewers praised Cohen's thoughtful approach to the optional use of technology, lauding his realistic use of modern technologies while maintaining a solid foundation in algebraic concepts.
  • Exercises have been rewritten, updating real data and applications throughout.
  • In addition to the "Writing Mathematics" sections, there are now "Projects" and "Mini Projects" at the ends of many sections. These give the students additional opportunities to discuss, explore, learn, and write mathematics.
  • The material on long division of polynomials has been moved to Chapter 12, preceding synthetic division.
  • Chapter 3 includes an expanded introduction to the function concept. Functions are introduced at length using algebraic, verbal, tabular, and graphical forms. Functions as models are introduced and used in examples and exercises. Implicit functions are introduced in the section "Project." Material on the average rate of change of a function (previously in section 3.2) has been expanded and there is an increased emphasis on applications.
  • New material includes: a discussion on the use of spreadsheets in generating scatter plots and regression lines, modeling real-life data with quadratic functions (Chapter 4); discussion on the use of graphing calculators and spreadsheets in computing matrix products and matrix inverses, including new examples and exercises using matrices to code and decode messages (Chapter 10); and new material in Chapter 11 on the perihelion and aphelion for an elliptical orbit.
  • Every new copy of this text is packaged with iLrn Tutorial, our suite of online, dynamic, customizable tutorial resources that puts tools for students' content mastery at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one online help from an experienced mathematics tutor. For instructors, iLrn offers highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power the course.
  • Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction and includes MathCue Tutorial Software.
  • Preloaded with content and available FREE via PIN code when packaged with this text, WebTutor ToolBox pairs all the content of this text's rich Book Companion Web Site with all the sophisticated course management functionality of a WebCT or Blackboard product. It's an ideal solution for online and distance learning needs.
  • A Book Companion Web Site accompanies this text and features a variety of teaching and learning resources. This Web site features everything from book-specific resources to newsgroups. It's a great way to make teaching and learning an interactive and intriguing experience.

Efficacy and Outcomes

Reviews

"The quantity and quality of the exercises are the reasons why I think that Cohen’s book is my favorite algebra and precalculus book ever…. Both the quantity and quality of the exercises of Cohen’s book are first class and the problems in each section are reflective of the concepts being taught. As far as I am concerned, the quality of both his algebra text and precalculus text are way above anything on the market that I’ve seen."

— Fred M. Schifando, Pennsylvania State University

"The mini projects are excellent and can be used for collaborative learning…. I think the writing style of an already well-written book has been improved."

— Richard Riggs, New Jersey City University

"This text is one of the most challenging precalculus books I have seen, but I like that because it gives students the opportunity to be very well prepared for calculus. The presentations are rigorous, precise, and detailed, but written in a way that students can follow fairly well. The exercises range from simple to complex and include not only applications to other disciplines but to other areas of mathematics as well." "One of the main reasons I continue to use this author’s texts is that I receive more compliments from my students on his books than I have on any other texts."

— Greg S. Deitrich, Florida Community College at Jacksonville

"Overall, the quantity and quality of the exercises in Cohen’s texts are outstanding. The different levels of exercises--A, B, and C levels--make an excellent transition from skill development to concept development."

— John Gosselin, University of Georgia

"One of the strengths of the series has been David’s ability to make simple, clear, and reasoned arguments about the mathematical assertions…. David did a very subtle and powerful thing when he included difficult problems broken down into small, manageable steps." "The new authors have done a nice job in reorganizing the material in Chapter 6. Instructors familiar with earlier editions of Cohen’s books will find the transition seamless."

— Thomas J. Walters, University of California Los Angeles (retired)/Wilson High School

Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

ExamView  (ISBN-10: 0495018147 | ISBN-13: 9780495018148)

iLrn Tutorial Student Version Website  (ISBN-10: 0534402364 | ISBN-13: 9780534402365)

List Price = $80.00  | CengageBrain Price = $80.00  | College Bookstore Wholesale Price = $80.00

iLrn Instructor Version Website  (ISBN-10: 0534402356 | ISBN-13: 9780534402358)

Instructor's Resource CD-ROM  (ISBN-10: 0495106402 | ISBN-13: 9780495106401)

Complete Solutions Manual  (ISBN-10: 0534402348 | ISBN-13: 9780534402341)

The complete solutions manual provides worked-out solutions to all of the problems in the text.

Student Solutions Manual  (ISBN-10: 0534402321 | ISBN-13: 9780534402327)

Provides detailed and complete solutions to the odd-numbered exercises and test questions.

List Price = $102.95  | CengageBrain Price = $102.95  | College Bookstore Wholesale Price = $77.25

Test Bank  (ISBN-10: 0534402380 | ISBN-13: 9780534402389)

The test bank includes six tests per chapter as well as three final exams. The tests are made up of a combination of multiple-choice, free-response, true/false, and fill-in-the-blank questions.

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.

List Price = $50.95  | CengageBrain Price = $50.95  | College Bookstore Wholesale Price = $38.25

Student Supplements

Interactive Video Skillbuilder CD-ROM  (ISBN-10: 0534402399 | ISBN-13: 9780534402396)

Think of it as portable office hours! AUTOMATICALLY PACKAGED WITH THE TEXT, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction. The problems worked during each video lesson are shown on the viewing screen so that students can try working them before watching the solution. To help students evaluate their progress, each section contains a 10-question Web quiz (the results of which can be emailed to the instructor) and each chapter contains a chapter test, with the answer to each problem on each test. This CD-ROM also includes MathCue tutorial and quizzing software, featuring a Skill Builder that presents problems to solve and evaluates answers with step-by-step explanations; a Quiz function that enables students to generate quiz problems keyed to problem types from each section of the book; a Chapter Test that provides many problems keyed to problem types from each chapter; and a Solution Finder that allows students to enter their own basic problems and receive step-by-step help as if they were working with a tutor. Also included is a new graphing calculator tutorial learning tool, which features examples, exercises, and video tutorials.

List Price = $44.95  | CengageBrain Price = $44.95  | College Bookstore Wholesale Price = $34.00

iLrn Tutorial Student Version Website  (ISBN-10: 0534402364 | ISBN-13: 9780534402365)

With iLrn: Heinle Learning Center, everything students need to master the skills and concepts of the course is built right in to this dynamic audio- and video-enhanced learning environment, including: An audio- and video-enhanced eBook Assignable, integrated textbook activities Companion videos with pre- and post-viewing activities Assignable, partnered voice-recorded activities An online workbook and lab manual with audio Interactive enrichment activities, and A diagnostic study tool to better prepare students for exams.

List Price = $80.00  | CengageBrain Price = $80.00  | College Bookstore Wholesale Price = $80.00

Student Solutions Manual  (ISBN-10: 0534402321 | ISBN-13: 9780534402327)

Provides detailed and complete solutions to the odd-numbered exercises and test questions.

List Price = $102.95  | CengageBrain Price = $102.95  | College Bookstore Wholesale Price = $77.25

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = $50.95  | CengageBrain Price = $50.95  | College Bookstore Wholesale Price = $38.25

Meet the Author

Author Bio

David Cohen

David Cohen, a senior lecturer at UCLA, was the original author of the successful, well-respected precalculus series--COLLEGE ALGEBRA, ALGEBRA AND TRIGONOMETRY, PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, and PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY.