College Algebra and Trigonometry: A Unit Circle Approach, 6th Edition

Mark Dugopolski

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College Algebra and Trigonometry: A Unit Circle Approach, 6th Edition

By Mark Dugopolski
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Mark Dugopolski
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The Right Tools for Success


With an emphasis on problem solving and critical thinking, Dugopolski’s College Algebra and Trigonometry: A Unit Circle Approach gives students the essential strategies to help them develop the comprehension and confidence they need to be successful in this course. Students will find carefully placed learning aids and review tools to help them do the math.


Mark Dugopolski was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an MS in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign—Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.



STRATEGIES FOR SUCCESS: Learning aids are strategically placed throughout the text giving students guidance right when they need it.

  • Chapter Openers discuss real-world situations that use mathematics from that chapter. Examples and exercises then relate back to the opening scenarios.
  • Try This exercises after every example give students the opportunity to immediately try a problem that is just like the example and to check their work. Solutions to all Try This exercises are in Online Appendix B.
  • Summaries of important concepts are included to help students clarify ideas that have multiple parts.
  • Strategies contain general guidelines for accomplishing tasks and are useful for sharpening students’ problem-solving skills.
  • Procedures are similar to Strategies, but are more specific and more algorithmic, designed to give students a step-by-step approach for problems.
  • Function Galleries show families of functions and their graphs, helping students link the visual aspects with the mathematical properties. These appear throughout the text as appropriate and are also gathered together at the end of the text for easy reference.
  • Graphing calculator discussions throughout the text support and enhance algebraic conclusions but are not used to arrive at those conclusions. These are optional and may be skipped, although students who do not use a graphing calculator may still benefit from the graphs and technology discussions.



MILESTONES ALONG THE WAY: Section exercises and review material include the following exercise types so students can practice and check their progress.

  • Exercises are arranged by difficulty, from easy to challenging. Exercises that require a graphing calculator are marked with an icon and may be skipped.
  • NEW! Data used in examples, exercises, and chapter openers has been updated to make this text relevant for today’s students.
  • NEW! The number of fill-in-the-blank exercises has been increased to help students master the concepts.
  • NEW! The exercise sets now contain new headings that group the exercises by type: Concepts, Skills, and Modeling.
  • NEW! Exercise sets now contain QR codes which link the exercises to solution videos on the Web.
  • NEW! Many new Outside the Box exercises have been added so that there are now two of them at the end of every section.
  • For Thought exercises are ten true/false questions that review the basic concepts in the section, check student understanding before beginning the exercises, and offer opportunities for writing and discussion. Answers are included in the back of the student edition.
  • Hints suggest ways of approaching a problem and give a starting point to solve the application problem. These are given for approximately five application problems in every exercise set.
  • Cumulative review exercises at the end-of-section exercises are designed to keep current the skills learned in previous sections and chapters. These exercises are under the heading “Review.”
  • Writing/Discussion and Cooperative Learning exercises deepen students’ understanding by giving them the opportunity to express mathematical ideas in writing and to their classmates during small group or team discussions.
  • Outside the Box problems are designed to get students (and instructors) to do some mathematics just for fun and encourage students to apply creativity to unique problems. The problems can be used for individual or group work.
  • Linking Concepts are multi-part exercises that require the use of concepts from previous sections to illustrate the links among various ideas. This feature can be found at the end of nearly every exercise set.



TYING IT ALL TOGETHER: Chapter review material contains all of the following features to help students review and synthesise the material as they prepare for the road ahead.

  • Highlights contain an overview of all of the concepts presented in the chapter along with brief examples to illustrate the concept.
  • Chapter Review Exercises give students a comprehensive review of the chapter without reference to individual sections in order to prepare them for the chapter test.
  • Chapter Tests measure the students' readiness for a typical one-hour classroom test. Instructors may also use them as a model for their own end-of-chapter tests.
  • Index of Applications list the many applications contained within the text. The applications are page referenced and grouped by subject matter.


Table of contents
  • P. Prerequisites
  • 1. Equations, Inequalities, and Modeling
  • 2. Functions and Graphs
  • 3. Polynomial and Rational Functions
  • 4. Exponential and Logarithmic Functions
  • 5. The Trigonometric Functions
  • 6. Trigonometric Identities and Conditional Equations
  • 7. Applications of Trigonometry
  • 8. Systems of Equations and Inequalities
  • 9. Matrices and Determinants
  • 10. The Conic Sections
  • 11. Sequences, Series, and Probability