Integrated Review Notebook for Trigonometry

Description

Table of Contents

The table of contents below shows the review topics (bulleted text) that are integrated into the MyLab Math course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.

1. Algebraic Prerequisites
   • P.1 The Cartesian Coordinate System
   • P.2 Functions
   • P.3 Families of Functions, Transformations, and Symmetry
   • P.4 Compositions and Inverses
2. Angles and the Trigonometric Functions
   • 1.1 Angles and Degree Measure
   • 1.2 Radian Measure, Arc Length, and Area
   • 1.3 Angular and Linear Velocity
   • 1.4 The Trigonometric Functions
   • 1.5 Right Triangle Trigonometry
   • 1.6 The Fundamental Identity and Reference Angles
   • Chapter 1 Integrated Review Topics:
     • Multiplying simple rational expressions
     • Using Rational Expressions in Conversions
     • Finding area and circumference of a circle using the standard formula.
     • Simplifying square roots.
     • Performing operations with square roots.
     • Using the Pythagorean theorem to find missing sides of a right triangle.
     • Finding center and radius of a circle given the equation for the circle.
     • Finding the inverse of a function.
3. Graphs of the Trigonometric Functions
   • 2.1 The Unit Circle and Graphing
   • 2.2 The General Sine Wave
   • 2.3 Graphs of the Secant and Cosecant Functions
   • 2.4 Graphs of the Tangent and Cotangent Functions
   • 2.5 Combining Functions
   • Chapter 2 Integrated Review Topics:
     • Shifting graphs of algebraic functions horizontally and vertically.
     • Finding domain and range of algebraic functions; Reflecting, stretching, and shrinking of algebraic functions.
     • Writing equations of horizontal and vertical lines.
     • Performing arithmetic with fractions involving pi.
     • Finding horizontal and vertical asymptotes for rational functions.
     • Identifying domain and range of rational functions.
4. Trigonometric Identities
   • 3.1 Basic Identities
   • 3.2 Verifying Identities
   • 3.3 Sum and Difference Identities for Cosine
   • 3.4 Sum and Difference Identities for Sine and Tangent
   • 3.5 Double-Angle and Half-Angle Identities
   • 3.6 Product and Sum Identities
   • Chapter 3 Integrated Review Topics:
     • Recognizing identities in algebra.
     • Using the Fundamental Identity from Trigonometry to simplify expressions.
     • Using reciprocal identities to simplify expressions.
     • Multiplying binomials.
     • Squaring a binomial.
     • Factoring expressions into a product of two binomials.
     • Finding compositions of algebraic functions.
     • Proving that an equation is not an identity.
     • Operations with rational expressions in algebra.
5. Solving Conditional Trigonometric Equations
   • 4.1 The Inverse Trigonometric Functions
   • 4.2 Basic Sine, Cosine, and Tangent Equations
   • 4.3 Equations Involving Compositions
   • 4.4 Trigonometric Equations of Quadratic Type
   • Chapter 4 Integrated Review Topics:
     • Evaluating a composition of algebraic functions.
     • Identifying identities in trigonometry.
     • Solving proportions for a variable.
     • Solving for a variable in an algebraic equation.
     • Solving quadratic equations by factoring.
     • Solve quadratic equations by using the square root property.
     • Solve quadratic equations by using the quadratic formula.
     • Squaring each side of an equation and getting extraneous roots.
     • Domain and range of the trig functions.
     • Finding the exact values of the sine function.
     • Finding the exact values of secant, cosecant, and cotangent.
6. Applications of Trigonometry
   • 5.1 The Law of Sines
   • 5.2 The Law of Cosines
   • 5.3 Area of a Triangle
   • 5.4 Vectors
   • 5.5 Applications of Vectors
   • Chapter 5 Integrated Review Topics:
     • Solving proportions for x.
     • Solving proportions using the inverse sine function.
     • Finding the area of a triangle using the standard formula.
     • Solving right triangles.
     • Finding the distance between two points with the distance formula.
7. Complex Numbers, Polar Coordinates, and Parametric Equations
   • 6.1 Complex Numbers
   • 6.2 Trigonometric Form of Complex Numbers
   • 6.3 Powers of Roots of Complex Numbers
   • 6.4 Polar Equations
   • 6.5 Parametric Equations
   • New – 6.6 Fun with Polar and Parametric Equations
   • Chapter 6 Integrated Review Topics:
     • Simplifying square roots.
     • Adding and subtracting binomials.
     • Multiplying binomials.
     • Finding nth roots with 1/n notation.
     • Solving cubic equations.
     • Finding sine and cosine of large angles.

• Numerous explanations, examples, and exercises have been rewritten in response to comments from users of the fourth edition.
• Many new nonstandard exercises ranging from easy to challenging – see exercise 33, page 274 on the Law of Sines.
• Section 2.5, Combining Functions, has been rewritten to put more emphasis on producing the graphs with a graphing calculator versus drawing by hand.
• Section 3.2, Verifying Identities, has been rewritten to provide six examples corresponding to the six-point strategy for verifying identities.
• Multiplying trigonometric binomials and factoring trigonometric expressions have been moved from Section 3.2 to Section 3.1. Section 3.2 now focuses solely on verifying identities using the six-point strategy.
• All graphing calculator screenshots have been redone using the TI-84 Plus CE.
• A new section 6.6, Fun with Polar and Parametric Equations, experiments with polar and parametric equations, producing interesting graphs on a calculator that would be impossible to draw by hand. This section contains only one exercise, and the author will award a $100 prize to the first student who submits a correct solution.

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math

• New – Integrated Review Notebook is a printed guide that aligns to the Integrated Review topics and gives students a structured place to take notes as they work through the prerequisite objectives. Definitions, unique examples, and important concepts are highlighted. The notebook is also available in MyLab Math for download.
• New – Worked Example Videos engage and support students outside the classroom, covering all Integrated Review prerequisite topics and key examples from the book, hand-picked by the author. Lightboard technology creates a personal experience and simulates an in-class environment. Accompanying assessment questions in MyLab Math make these brand new videos assignable.

• New – Guided Visualizations bring mathematical concepts to life, helping students visualize appropriate Integrated Review topics and key concepts from the main text through directed explorations and purposeful manipulation. Guided Visualizations and accompanying assessment exercises can be assigned in MyLab Math to encourage active learning, critical thinking, and conceptual understanding.

The Integrated Review Notebook is a printed guide that aligns with the Integrated Review topics and gives students a structured place to take notes as they work through the foundational objectives. Definitions, unique examples, and important concepts are highlighted.  Each topic has a mini-exercise set for extra practice. The notebook is also available in MyLab Math for download.

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, giving students guidance right where 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 A.
• Summaries of important concepts are included to help students clarify ideas that have multiple parts.
• 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. 
• New – All graphing calculator screenshots have been redone using the TI-84 Plus CE.

Milestones Along the Way

• Updated – Data used in examples, exercises, and chapter openers has been updated to make this text relevant for today’s students. Exercises are arranged by difficulty, from easy to challenging. Exercises that require a graphing calculator are marked with an icon and may be skipped.
• For Thought exercises are 10 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. Answers are given in the Annotated Instructor’s Edition and complete solutions can be found in the Instructor’s Solutions Manual.
• 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. Answers are given in the Annotated Instructor’s Edition, and full solutions can be found in the Instructor’s Solutions Manual.

Tying It All Together

Chapter review material contains all of the following features to help students review and synthesize 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 students’ readiness for a typical one-hour classroom test. Instructors may also use them as a model for their own end-of-chapter tests.

Check out the preface for a complete list of features and what’s new in this edition.

Also available with MyLab Math 

MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

• New – The Integrated Review MyLab Math course can be used in corequisite courses or simply to help students who enter Trigonometry without a full understanding of foundational skills and concepts. Here’s how it works:
• Students begin each chapter by completing a Skills Check assignment to pinpoint which prerequisite topics, if any, they need to review.
• Students who demonstrate mastery of the foundational topics will move straight into the Trigonometry content.
• Those who require additional review proceed to a personalized review homework assignment that allows them to remediate on the specific prerequisite topics where they need help. Students can also review the relevant prerequisite concepts using new worked example videos, Guided Visualizations, and the Integrated Review Notebook.

• New – The Integrated Review Notebook is a printed guide that aligns with the Integrated Review topics and gives students a structured place to take notes as they work through the foundational objectives. Definitions, unique examples, and important concepts are highlighted.  Each topic has a mini-exercise set for extra practice. The notebook is also available in MyLab Math for download.
• New – Worked Example Video Series engages and supports students outside the classroom, covering all Integrated Review prerequisite topics as well as key examples from the main book, hand-picked by the author. Lightboard technology creates a personal experience and simulates an in-class environment. Accompanying assessment questions in MyLab Math make these brand new videos assignable.

• New – Guided Visualizations bring mathematical concepts to life, helping students visualize Integrated Review topics as well as key concepts from the main text through directed explorations and purposeful manipulation. Guided Visualizations and accompanying assessment exercises can be assigned in MyLab Math to encourage active learning, critical thinking, and conceptual understanding.

• Mindset videos and assignable, open-ended exercises foster a growth mindset in students. This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities — so often a hurdle for math students.
• Setup & Solve exercises require students to first describe how they will set up and approach the problem. This reinforces conceptual understanding of the process applied in approaching the problem, promotes long term retention of the skill and mirrors what students will be expected to do on a test.

• Enhanced Sample Assignments: Newly redesigned, these assignments put a powerful combination of author expertise and dynamic MyLab content at your fingertips. Comprising author-selected exercises and our newest question types, including video assessment and interactive figures with assessment, these prebuilt assignments give you the best of the best for each section in a snap.

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