Precalculus: A Unit Circle Approach, 3rd edition

For courses in Precalculus.

Providing the rigor of solid mathematics with an engaging and friendly approach

As teachers, Ratti and McWaters saw firsthand where their Precalculus and Calculus students struggled, where they needed help making connections, and what material they needed to be successful in calculus. They decided to partner and write this text with the primary goal of preparing students to be successful in calculus and future STEM courses. Their experience in the classroom shows in each chapter. The focus on conceptual development, real-life applications, and extensive exercises, encourages a deeper understanding of the mathematics. Precalculus: A Unit Circle Approach, 3rd Edition, includes thorough coverage of topics as preparation for calculus, including; trig identities, difference quotient, functional composition, decomposition and emphasizes graphing techniques/transformations.

Also available with MyLab Math

MyLab™ 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. At University of South Florida, the authors’ school, student results improved when using this book with MyLab Math. Published results are available at Pearsonmylabandmastering.com on the Results page. For the new edition, MyLab Math continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over time. In addition, MyLab Math includes new options to support conceptual learning, visualization, and student preparedness.

Students, if interested in purchasing this title with MyLab Math, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

Precalculus: A Unit Circle Approach offers rigorous topics ideal for students heading for calculus, in a friendly, “teacherly” tone.

• Functions are presented in Chapter 1, building a foundation for a strong preparation for calculus.
• Trigonometric functions are introduced in Chapter 4 with a unit circle approach, before developing the right triangle.
• Right triangle applications (height and distance) are covered in Chapter 6, Applications of Trigonometric Functions.

• Student-friendly support features in Ratti/McWaters are designed to help students to see not only what they are going to learn, but also why, so that every concept is given the proper context.
• NEW! Additional Review Material.  We have provided additional review material in Chapters 1 and 2 that users of the previous editions identified as material they had to supplement or as requiring reference to the appendix.
• Topics for review help students refresh their memories on essential topics before beginning each chapter, listing specific page references to make it easy to find those concepts.
• Clear Objectives preview the key points of the section ahead, providing easy reference points when studying for exams. These Objectives appear again at the appropriate places in the section, putting each new topic into context.
• Every section opens with an engaging Application that is revisited later in the section through examples and exercises. The Application ties key ideas together and provides motivation for students to read and study.
• Work it out: As you would in your own class, Ratti and McWaters encourage students to practice the material frequently, and give them ample opportunities to master the material by solving problems and applying their understanding.
• Procedure in Action is a special feature which introduces procedure steps within the context of a worked-out example. Important multistep procedures, such as the steps for finding the inverse of a one-to-one function, are presented in a two-column format. The numbered steps of the procedure are given in the left column, and an example is worked out step-by-step, aligned with and numbered as the procedure steps, in the right column. This approach provides students with a clear solution model when encountering difficulty in their work.
• Examples include a wide range of computational, conceptual, and modern applied problems carefully selected to build condence, competency, and understanding. Every example has a title indicating its purpose, and a detailed solution containing annotated steps. All examples are followed by a Practice Problem for students to try so that they can check their understanding of the concept covered. Answers to the Practice Problems are provided just before the section exercises.
• Exercises are plentiful and each section ends with three levels of exercises for students to practice the math and apply their understanding:
• NEW! Graph and Data Related Examples and Exercises demonstrate how to extract information about real world situations from a graphic representation of that situation as well as how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph.
• New! Concepts and Vocabulary exercises begins each exercise set with exercises that assess the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section.
• Basics Skills exercises develop fundamental skills–each odd-numbered exercise is closely paired with its consecutive even-numbered exercise.
• Applying the Concepts use the section’s material to solve real-world problems–all are titled and relevant to the topics of the section.
• Beyond the Basics provide more challenging exercises that give students an opportunity to reach beyond the material covered in the section–these are generally more theoretical in nature and are suitable for honors students, special assignments, or extra credit.
• Critical Thinking/Discussion/Writing exercises, appearing as appropriate, are designed to develop students’ higher-level thinking skills. Calculator problems, identied by  are included where needed.
• Preparing for the Next Section exercises ends each exercise set with exercises that provide a review of concepts and skills that will be used in the following section.  
• Help along the way: These integrated study aids give students hints and tips at strategic places in the text, addressing some of the most frequent issues and questions that occur in office hours.
• Recall notes, located in the margins, periodically remind students of a key idea they learned earlier in the text that will help them with the current problem at hand.
• Warning notes point out commonly-made errors in thinking and calculations, with specific examples and detailed guidance.
• Side Notes provide hints for handling newly introduced concepts.
• Do You Know? marginal notes keeps students engaged with interesting facts and information.
• Historical Notes cover key people and ideas in the history and development of mathematics.
• Technology Connections, although optional, give students tips on using their calculators to solve problems, check answers, and reinforce concepts.
• Preparation and review–end-of-chapter material includes all of the following items to help students prepare for exams and make the most of their study time.
• Summary of Definitions, Concepts, and Formulas lists key ideas from the chapter and encourage students to reread sections rather than memorize definitions out of context.
• Review Exercises provide students with an opportunity to practice what they have learned in the chapter. Then students are given two chapter test options.
• Two full Practice Tests,  Practice Test A in the usual open-ended format and/or Practice Test B, covering the same topics, in multiple-choice format, help students prepare for any exam format and verify that students have mastered the skills and concepts in the chapter.
• Cumulative Review exercises: Starting in Chapter 2, these exercises remind students that math isn’t modular. What they learn in the first part of book is the foundation for later concepts.

Also available with MyLabMath.

MyLab™ 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. At University of South Florida, the authors’ school, student results improved when using this book with MyLab Math. Published results are available at Pearsonmylabandmastering.com on the Results page. For the new edition, MyLab Math continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over time. In addition, MyLab Math includes new options to support conceptual learning, visualization, and student preparedness. 

• Two MyLab Math course options are now available for Ratti: a standard course and an Integrated Review course:
• Standard MyLab Math courses allow instructors to build their courses their way, offering maximum flexibility and complete control over all aspects of assignment creation.
• The new Integrated Review provide a full suite of supporting resources for the main course content plus additional assignments and study aids for students who will benefit from remediation. Assignments for the integrated review content are preassigned in MyLab Math, making it easier than ever to create your course!
• NEW! MyLab Math Question Types  enable students to develop and gauge their conceptual understanding.
• New!  Concept and Vocabulary exercises start each section by assessing the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section and are assignable in Pearson MyLab Math and Learning Catalytics.
• New!  Video Assessment questions are assignable MyLab Math exercises tied to Example Solutions videos.  The questions are designed to check students’ understanding of the important math concepts covered in the video.  The videos and Video Assessment questions provide an active learning environment where students can work at their own pace.
• New! The Video Notebook with Worksheets is a guide that gives students a structured place to take notes and work on the example problems as they watch the Example Solution videos.  Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way.  Integrated Review worksheets are included to help students practice needed prerequisite skills. The notebook is also available in MyLab Math for download.
• NEW! Set Up & Solve exercises require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution
• New! Exercises Preparing Students for Material in the Next Section. Each exercise section ends with a set of exercises that provide a review of concepts and skills that will be used in the following section.
• Students enter the course with widely varying skill levels, so MyLab Math includes personalized support and targeted practice to help all students succeed.
• Integrated Review MyLab Math courses provide a full suite of supporting resources for the main course content, plus additional prerequisite review for students who will benefit from remediation. Personalized assignments for the integrated review content are preassigned in MyLab Math, making it easier than ever to create your course and meet individualized student needs!
• NEW! Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
• NEW! Workspace Assignments allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.
• Getting Ready material provides  just-in-time review, integrated throughout the course as needed to prepare students with prerequisite material to succeed. From a quick quiz, a personalized, just-in-time review assignment is generated for each student, allowing them to refresh forgotten concepts.
• Develop visualization skills and leverage those skills to deepen students’ understanding of the concepts
• Guided Visualizations enable users to interact with and manipulate figures to bring hard-to-convey math concepts to life. These are assignable in MyLab Math, integrated into the eText, and available to show in-class with accompanying as Exploratory Exercises in the Multimedia Library.
• Enhanced Graphing Utility allows students to graph 3-point quadratic, 4-point cubic, and transformation graphs (which include sine, cosine, logarithmic, and exponential functions). These new graphing questions are assignable in MyLab Math.
• Easier course set-up for instructors
• NEW! Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the author, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic. The included video assessment questions can also be used alongside the Video Notebook with Worksheets.
• Foster student engagement and peer-to-peer learning
• NEW! Learning Catalytics^™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.
• Upload a full PowerPoint^® deck for easy creation of slide questions.
• Team names are no longer case sensitive.
• Help your students develop critical thinking skills.
• Monitor responses to find out where your students are struggling.
• Rely on real-time data to adjust your teaching strategy.
• Automatically group students for discussion, teamwork, and peer-to-peer learning.

Features of the Ratti/McWaters program help students be successful in their endeavor to move on to calculus and into their chosen profession.

• Student-friendly support features in Ratti/McWaters are designed to help students to see not only what they are going to learn, but also why, so that every concept is given the proper context.
• Additional Review Material.  We have provided additional review material in Chapters 1 and 2 that users of the previous editions identified as material they had to supplement or as requiring reference to the appendix.

• Exercises are plentiful and each section ends with three levels of exercises for students to practice the math and apply their understanding:
• Graph and Data Related Examples and Exercises demonstrate how to extract information about real world situations from a graphic representation of that situation as well as how to recover algebraic or trigonometric formulations of a graph by using key characteristics of that graph.
• Concepts and Vocabulary exercises begins each exercise set with exercises that assess the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section.

• Section on Modeling Data, using linear regression was added in Chapter 1, as well as a section in Chapter 3 on building linear, exponential, logarithmic, and power models from data.
• Section Polynomial and Rational Inequalities was added in Chapter 2.
• Section Trigonometric Equations was completely rewritten and is now placed as the last section of Chapter 5.
• Section Systems of Inequalities in Chapter 7 was relocated to follow the section on systems of linear equations in three variables.
• Identifying Material Particularly Useful for Calculus includes concepts and exercises with a new symbol and added a new Chapter “An Introduction to Calculus” introducing the basic concepts of limit, derivative, and integral.

CONTENT UPDATES:

• CHAPTER 1:  In Section 1.2, the two-intercept form of the equation of a line and modeling data using linear regression was added. In Section 1.3 discussion of the range of a function was added. In Section 1.4 an example showing how to write a piecewise function from a set of data points is given. In Section 1.5 a step-by-step process explaining how to graph multiple transformations in sequence was added. In Section 1.6 the explanation of the domain of composite functions was rewritten and a method for computing the average rate of change of a composite function was added. An example of composing a function with a piecewise function was added.
• CHAPTER 2:  In Section 2.1, we added a schematic showing how to solve quadratic inequalities graphically. Exercises using quadratic functions modeling data were added. In Section 2.2, we provide a discussion of the behavior of a polynomial function near it zeros to help understand why a polynomial crosses or bounces off the x-axis in relation to the multiplicity of its zero. We added an example of graphing a polynomial given in factored form. In Section 2.3 we expanded the long division and synthetic division material (this was previously provided in the appendix). Several exercises asking students to sketch a polynomial in non-factored form were added. In Section 2.4 we expanded the discussion of graphing rational functions to include the behavior of a rational function near both its zeros and its vertical asymptotes. Section 2.5 is a new section on polynomial and rational inequalities. The sign of an expression is determined geometrically from its graph (graphic method) or algebraically (test point method).
• CHAPTER 3:  In Section 3.1 a schematic showing various transformation of the graph of f(x) = a^x was added and exercises on graphing transformations of the graph of f(x) = a^x were provided early in the exercises. In Section 3.2 a schematic showing various transformation of the graph of f(x) = log_ax was added and exercises on graphing transformations of the graph of f(x) = log_ax were provided early in the exercises. In Section 3.4 exercises on solving inequalities were added. In Section 3.5, material on building linear, exponential, logarithmic, and power models from data was included.
• CHAPTER 4:  In Section 4.4  we provided an alternative way of graphing trigonometric functions by using transformations of functions and added a subsection on even-odd properties of the Trigonometric functions.
• CHAPTER 5: The section on trigonometric equations was completely rewritten and is now placed as the last section of Chapter 5.
• CHAPTER 7:  The section on systems of inequalities was relocated to follow the section on systems of linear equations in three variables.
• CHAPTER 8:  Sections 8.2, 8.3, 8.4 each have additional examples showing to obtain the equation of the conic discussed in that section from key characteristics of its graph.
• REVIEW APPENDIX: The material on synthetic division has been moved to Section 2.3.

Also available with MyLabMath

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within MyLab Math’s 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. At University of South Florida, the authors’ school, student results improved when using this book with MyLab Math. Published results are available at Pearsonmylabandmastering.com on the Results page. For the new edition, MyLab Math continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over time. In addition, MyLab Math includes new options to support conceptual learning, visualization, and student preparedness. 

• MyLab Math Question Types  enable students to develop and gauge their conceptual understanding.
• Concept and Vocabulary exercises start each section by assessing the student’s grasp of the definitions and ideas introduced in that section. These true/false and fill-in-the-blank exercises help to rapidly identify gaps in comprehension of the material in that section and are assignable in Pearson MyLab Math and Learning Catalytics.
• Video Assessment questions are assignable MyLab Math exercises tied to Example Solutions videos.  The questions are designed to check students’ understanding of the important math concepts covered in the video.  The videos and Video Assessment questions provide an active learning environment where students can work at their own pace.
• The Video Notebook with Worksheets is a guide that gives students a structured place to take notes and work on the example problems as they watch the Example Solution videos.  Definitions, examples, and important concepts are highlighted, and helpful hints are pointed out along the way.  Integrated Review worksheets are included to help students practice needed prerequisite skills. The notebook is also available in MyLab Math for download.
• Set Up & Solve exercises require students to show the setup of the solution for a particular exercise as well as the solution, helping them develop an overall problem-solving strategy before attempting the solution
• Exercises Preparing Students for Material in the Next Section. Each exercise section ends with a set of exercises that provide a review of concepts and skills that will be used in the following section.
  
• Students enter the course with widely varying skill levels, so MyLab Math includes personalized support and targeted practice to help all students succeed.
• Skill Builder offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
• Workspace Assignments allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.
  
• Easier course set-up for instructors
• Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each chapter. Each assignment, handpicked by the author, includes a thoughtful mix of question types (e.g., conceptual, skills, etc.) specific to that topic.   The included video assessment questions can also be used alongside the Video Notebook with Worksheets.

• Foster student engagement and peer-to-peer learning
• Learning Catalytics^™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.
• Upload a full PowerPoint^® deck for easy creation of slide questions.
• Team names are no longer case sensitive.
• Help your students develop critical thinking skills.
• Monitor responses to find out where your students are struggling.
• Rely on real-time data to adjust your teaching strategy.
• Automatically group students for discussion, teamwork, and peer-to-peer learning.