Student Solutions Manual for Trigonometry

Description

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge’s intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor’s and Master’s degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John’s personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John’s other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.

Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks where she earned a bachelor’s degree in Secondary Mathematics Education. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding. She is able to pursue these interests as a contributor on the Lial Developmental Math series, and a co-author on the Precalculus series.

Table of Contents

• Preface
• Resources for Success

1. Algebra Review
   • R.1 Basic Concepts from Algebra
   • R.2 Real Number Operations and Properties
   • R.3 Exponents, Polynomials, and Factoring
   • R.4 Rational Expressions
   • R.5 Radical Expressions
   • R.6 Equations and Inequalities
   • R.7 Rectangular Coordinates and Graphs
   • R.8 Functions
   • R.9 Graphing Techniques
2. Trigonometric Functions
   • 1-1 Angles
   • 1-2 Angle Relationships and Similar Triangles
   • 1-3 Trigonometric Functions
   • 1-4 Using the Definitions of the Trigonometric Functions
   • Test Prep
   • Review Exercises
   • Test
3. Acute Angles and Right Triangles
   • 2-1 Trigonometric Functions of Acute Angles
   • 2-2 Trigonometric Functions of Non-Acute Angles
   • 2-3 Approximations of Trigonometric Function Values
   • 2-4 Solutions and Applications of Right Triangles
   • 2-5 Further Applications of Right Triangles
   • Test Prep
   • Review Exercises
   • Test
4. Radian Measure and the Unit Circle
   • 3-1 Radian Measure
   • 3-2 Applications of Radian Measure
   • 3-3 The Unit Circle and Circular Functions
   • 3-4 Linear and Angular Speed
   • Test Prep
   • Review Exercises
   • Test
5. Graphs of the Circular Functions
   • 4-1 Graphs of the Sine and Cosine Functions
   • 4-2 Translations of the Graphs of Sine and Cosine Functions
   • 4-3 Graphs of the Tangent and Cotangent Functions
   • 4-4 Graphs of the Secant and Cosecant Functions
   • 4-5 Harmonic Motion
   • Test Prep
   • Review Exercises
   • Test
6. Trigonometric Identities
   • 5-1 Fundamental Identities
   • 5-2 Verifying Trigonometric Identities
   • 5-3 Sum and Difference Identities for Cosine
   • 5-4 Sum and Difference Identities for Sine and Tangent
   • 5-5 Double-Angle Identities
   • 5-6 Half-Angle Identities
   • Test Prep
   • Review Exercises
   • Test
7. Inverse Circular Functions and Trigonometric Equations
   • 6-1 Inverse Circular Functions
   • 6-2 Trigonometric Equations I
   • 6-3 Trigonometric Equations II
   • 6-4 Equations Involving Inverse Trigonometric Functions
   • Test Prep
   • Review Exercises
   • Test
8. Applications of Trigonometry and Vectors
   • 7-1 Oblique Triangles and the Law of Sines
   • 7-2 The Ambiguous Case of the Law of Sines
   • 7-3 The Law of Cosines
   • 7-4 Geometrically Defined Vectors and Applications
   • 7-5 Algebraically Defined Vectors and the Dot Product
   • Test Prep
   • Review Exercises
   • Test
9. Complex Numbers, Polar Equations, and Parametric Equations
   • 8-1 Complex Numbers
   • 8-2 Trigonometric (Polar) Form of Complex Numbers
   • 8-3 The Product and Quotient Theorems
   • 8-4 De Moivre’s Theorem
   • 8-5 Polar Equations and Graphs
   • 8-6 Parametric Equations, Graphs, and Applications
   • Test Prep
   • Review Exercises
   • Test

Answers to Selected Exercises

Photo Credits

Index

Content changes

Also available with MyLab Math 

• Integrated Review is available for every title in the Lial Series. MyLab™ Math with Integrated Review courses 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.
• Personal Inventory Assessments are a collection of online exercises designed to promote self-reflection and engagement in students. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment.
• Enhanced Sample Assignments: Author Callie Daniels makes course set-up easier by giving instructors a starting point for each section. Following Callie’s best practices in the classroom, Enhanced Sample Assignments maximize students’ performance.
• Prep Assignments include Example Videos with assessment questions. This assignment pairs with MyNotes.  Students actively participate while taking notes from the Example Video and then work the related exercises.  
• Section Homework includes author-selected problems and increases in difficulty.
• Cumulative Review Quizzes draw from section homework questions covered to that point in the course–helping students feel prepared for a final exam at any point.

• The video program helps students study anytime, anywhere.
• Quick reviews cover Key definitions through the detailed solution process for every example in the textbook.
• Example Solutions walk students through the detailed solution process for every example in the textbook.
• The new Essential College Algebra Video Series covers the essential topics your students need to master to be successful in the course. Interactive questions are embedded throughout to allow students to stop and think about the next step, and worksheets are available to guide students through the material. 

Support for all classroom types and students

A complete suite of materials includes updates to MyLab™ Math.

NEW – Integrated Review is now included within MyLab Math courses for every Lial title, including Precalculus, College Algebra & Trigonometry, and College Algebra. Integrated review can be used in corequisite courses or simply to help students who enter without a full understanding of prerequisite skills. Each student receives the help that he or she needs – no more, no less.

• Integrated Review provides videos on review topics with corresponding worksheets, along with premade, assignable skills-check quizzes and personalized review homework assignments

UPDATED – The Video Program helps students study anytime, anywhere.

• Quick Reviews cover Key definitions through the detailed solution process for every example in the textbook.
• Example Solutions walk students through the detailed solution process for every example in the textbook.
• NEW – The Essential College Algebra Video Series covers the essential topics your students need to master to be successful in the course. Interactive questions are embedded throughout to allow students to stop and think about the next step, and online worksheets are available to guide students through the material. 

UPDATED – The note-taking guides organize students in the classroom and while working independently.

• MyNotes, from co-author Callie Daniels, provide structure for students working independently to use while they read the textbook or watch the MyLab Math videos.
• MyClassroom Examples offer structure for notes taken during lecture, and align with the Classroom Examples found in the Annotated Instructor’s Edition.
• Both MyNotes and MyClassroomExamples are available in MyLab Math and can be customized by the instructor.

NEW – Enhanced Sample Assignments in MyLab Math follow the best practices of co-author Callie Daniels in her own classroom and maximize students’ performance.

• Prep Assignments include Example Videos with assessment questions. This assignment pairs with MyNotes.  Students actively participate while taking notes from the Example Video and then work the related exercises.  
• Section Homework includes author-selected problems and increases in difficulty.
• Cumulative Review Quizzes draw from section homework questions covered to that point in the course–helping students feel prepared for a final exam at any point.

Support for learning concepts

A systematic approach is used to present each topic and is designed to actively engage students in the learning process. As a result, students develop both the conceptual understanding and the analytical skills necessary for success.

• The variety of exercise types promotes conceptual understanding and reduces rote memorization.
• Concept Preview Exercises begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are assignable in MyLab Math and available in Learning Catalytics.
• Concept Check exercises focus on mathematical thinking and conceptual understanding.
• Relating Concepts Exercises help students tie together topics and develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students and are available in selected exercise sets. These are also assignable in MyLab Math.
• Pointers in the examples provide on-the-spot reminders and warnings about common pitfalls. Examples offer additional side comments where appropriate in the step-by-step solutions, and there are more section references to previously covered material.
• Now Try exercises conclude every example with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. Students are able to immediately apply and reinforce the concepts and skills presented in the examples.

Support for review and test preparation

Ample opportunities for review are interspersed within chapters and also found at the end of chapters.

• NEW – Chapter R provides a thorough review of the basic algebraic concepts that trigonometry students need in order to succeed. 
• Topics include real number operations and properties, rules for exponents, operations on polynomials and factoring, rational and radical expressions, solving equations and inequalities, circles, functions, domain, range, and graphing techniques. 
• Instructors can choose to cover review topics from Chapter R at the beginning of their course or insert these topics as needed. Students who are under-prepared for the demands of trigonometry, as well as those who need a quick review, will benefit from the material. 
• A comprehensive end-of-chapter Test Prep is also included

• Quizzes appear periodically throughout the chapter for students to check their progress. Answers are located in the student answer section at the back of the text. 
• Summary Exercises offer mixed review, requiring students to decide which methods covered in the chapter should apply to a particular problem.
• Cumulative Review assignments, drawn from best practices of author Callie Daniels for her students, are available to assign in MyLab Math for each chapter.
• Chapter Reviews and Test Prep conclude every chapter with the following features:
• An extensive Summary, featuring a section-by-section list of Key Terms and New Symbols.
• A Quick Review of important concepts, presented alongside corresponding Examples. Also presented in video format and assignable in MyLab Math.
• A comprehensive set of Review Exercises.
• A Chapter Test covering all skills and concepts from the chapter.

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.

Reach every student with MyLab

• Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.
• NEW – Enhanced Sample Assignments: Author Callie Daniels makes MyLab Math course set-up easier by giving instructors a starting point for each section. Following Callie’s best practices in the classroom, Enhanced Sample Assignments maximize students’ performance.
• Prep Assignments include Example Videos with assessment questions. This assignment pairs with MyNotes. Students actively participate while taking notes from the Example Video and then work the related exercises.  
• Section Homework includes author-selected problems and increases in difficulty.
• Cumulative Review Quizzes draw from section homework questions covered to that point in the course–helping students feel prepared for a final exam at any point.

• Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need – when and where they need it – to be successful.
• NEW – Integrated Review is available for every title in the Lial Series. MyLab Math with Integrated Review courses 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 – Personal Inventory Assessments are a collection of online exercises designed to promote self-reflection and engagement in students. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment.
• NEW – MyNotes with Integrated Review Worksheets: MyNotes offer structure for students as they watch videos or read the text. Available as printed supplement and in MyLab Math.
• Includes textbook examples along with ample space for students to write solutions and notes.
• Includes key concepts along with prompts for students to read, write, and reflect on what they have just learned.
• It’s customizable; instructors can add their own examples or remove examples that are not covered in their course.
• Integrated Review Worksheets prepare students for the College Algebra material. Includes key terms, guided examples with ample space for students to work and reference where in MyLab Math to get extra help.

• Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust – and that keep your students engaged. 
• Improve student results: When you teach with MyLab, student performance often improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students. 

Additional information

Dimensions	0.85 × 8.55 × 10.90 in
Imprint	Pearson
Format	gen
ISBN-13	09780135926048
ISBN-10	0135926041
Author	Callie J. Daniels, David I. Schneider, John Hornsby, Margaret L. Lial
Subjects	mathematics, higher education, trigonometry, Precalculus