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by Margaret Lial, John Hornsby and John Hornsby

Edition: 8TH 05Copyright: 2005

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

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Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features**

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new applied examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems 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.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of some chapters, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

**1. The Trigonometric Functions. **

Angles.

Angle Relationships and Similar Triangles.

Using the Definitions of the Trigonometric Functions.

**2. Acute Angles and Right Triangles. **

Trigonometric Functions of Acute Angles.

Trigonometric Functions of Non-Acute Angles.

Finding Trigonometric Function Values Using a Calculator.

Solving Right Triangles.

Further Applications of Right Triangles.

**3. Radian Measure and the Circular Functions. **

Radian Measure.

Applications of Radian Measure.

The Unit Circle and Circular Functions.

Linear and Angular Velocity.

**4. Graphs of the Circular Functions. **

Graphs of the Sine and Cosine Functions.

Translations of the Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**5. Trigonometric Identities. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities for Cosine.

Sum and Difference Identities for Sine and Tangent.

Double-Angle Identities.

Half-Angle Identities.

**6. Inverse Trigonometric Functions and Trigonometric Equations. **

Inverse Trigonometric Functions.

Trigonometric Equations I.

Trigonometric Equations II.

Equations Involving Inverse Trigonometric Functions.

**7. Applications of Trigonometry and Vectors. **

Oblique Triangles and the Law of Sines.

The Ambiguous Case of the Law of Sines.

The Law of Cosines.

Vectors and the Dot Product.

Applications of Vectors.

**8. Complex Numbers, Polar Equations, and Parametric Equations. **

Complex Numbers.

Trigonometric (Polar) Form of Complex Numbers.

The Product and Quotient Theorems.

Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Exponential and Logarithmic Functions. **

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms; Equations and Applications.

Appendix A: Equations and Inequalities.

Appendix B: Graphs of Equations.

Appendix C: Functions.

Appendix D: Graphing Techniques.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.

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Summary

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features**

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new applied examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems 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.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of some chapters, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

Table of Contents

**1. The Trigonometric Functions. **

Angles.

Angle Relationships and Similar Triangles.

Using the Definitions of the Trigonometric Functions.

**2. Acute Angles and Right Triangles. **

Trigonometric Functions of Acute Angles.

Trigonometric Functions of Non-Acute Angles.

Finding Trigonometric Function Values Using a Calculator.

Solving Right Triangles.

Further Applications of Right Triangles.

**3. Radian Measure and the Circular Functions. **

Radian Measure.

Applications of Radian Measure.

The Unit Circle and Circular Functions.

Linear and Angular Velocity.

**4. Graphs of the Circular Functions. **

Graphs of the Sine and Cosine Functions.

Translations of the Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**5. Trigonometric Identities. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities for Cosine.

Sum and Difference Identities for Sine and Tangent.

Double-Angle Identities.

Half-Angle Identities.

**6. Inverse Trigonometric Functions and Trigonometric Equations. **

Inverse Trigonometric Functions.

Trigonometric Equations I.

Trigonometric Equations II.

Equations Involving Inverse Trigonometric Functions.

**7. Applications of Trigonometry and Vectors. **

Oblique Triangles and the Law of Sines.

The Ambiguous Case of the Law of Sines.

The Law of Cosines.

Vectors and the Dot Product.

Applications of Vectors.

**8. Complex Numbers, Polar Equations, and Parametric Equations. **

Complex Numbers.

Trigonometric (Polar) Form of Complex Numbers.

The Product and Quotient Theorems.

Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Exponential and Logarithmic Functions. **

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms; Equations and Applications.

Appendix A: Equations and Inequalities.

Appendix B: Graphs of Equations.

Appendix C: Functions.

Appendix D: Graphing Techniques.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Published: 2005

International: No

Focusing on helping students to develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, we present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. We have tried to address the diverse needs of today's students through a more open design, updated figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Students will benefit from the text's student-oriented approach. We believe instructors will particularly welcome the new Annotated Instructor's Edition, which provides answers in the margin to almost all exercises, plus helpful Teaching Tips.

**Features**

- Real-Life Applications We are always on the lookout for interesting data to use in real-life applications. As a result, we have updated or incorporated many new applied examples and exercises from fields such as business, pop culture, sports, life sciences, and environmental studies that show the relevance of algebra to daily life. Applications that feature mathematical modeling are labeled with a Modeling head. All applications are titled, and a comprehensive Index of Applications is included at the back of the text.
- Use of Technology As in the previous edition, we have integrated the use of graphing calculators where appropriate, although graphing technology is not a central feature of this text. We continue to stress that graphing calculators are an aid to understanding and that students must master the underlying mathematical concepts first. We have included graphing calculator solutions for selected examples and continue to mark all graphing calculator notes and exercises that use graphing calculators with an icon for easy identification and added flexibility. This graphing calculator material is optional and can be omitted without loss of continuity.
- Cautions and Notes We often give students warnings of common errors and emphasize important ideas in Caution and Note comments that appear throughout the exposition.
- Looking Ahead to Calculus These margin notes offer glimpses of how the algebraic topics currently being studied are used in calculus.
- Connections This boxed feature provides connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing, class discussion, or group work.
- Relating Concepts Exercises Appearing in selected exercise sets, these sets of problems 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.

**New To This Edition **

- Examples We have added even more examples in this edition. Step-by-step solutions to examples are now easily identified using a Solution head. We have carefully polished all solutions and incorporated more side comments and explanations, including helpful section references to previously-covered material. Selected examples continue to provide graphing calculator solutions alongside traditional algebraic solutions. The graphing calculator solutions can be easily omitted if desired.
- Now try Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. In this way, students are able to immediately apply and reinforce the concepts and skills presented in the examples.
- Exercise Sets We have taken special care to respond to the suggestions of users and reviewers and have added many new exercises to this edition based on their feedback. As a result, the text includes more problems than ever to provide students with ample opportunities to practice, apply, connect, and extend concepts and skills. We have included writing exercises and optional graphing calculator problems as well as multiple-choice, matching, true/false, and completion problems. Concept Check problems, which focus on mathematical thinking and conceptual understanding, were well received in the previous edition and have been expanded in this edition.
- Solutions to Selected Exercises Exercise numbers enclosed in a blue circle indicate that a complete solution for the problem is included at the back of the text. These new solutions are given for selected exercises that extend the skills and concepts presented in the section examples. There are approximately 3 to 5 per section.
- Summary Exercises These new sets of in-chapter exercises in most chapters provide students with the all-important mixed review problems they need to synthesize concepts and select appropriate solution methods.
- Function Boxes Beginning in Chapter 2, functions are a unifying theme throughout the remainder of the text. To that end, special function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
- Chapter Reviews Each Chapter ends with an expanded Summary, featuring a section-by-section list of Key Terms, New Symbols, and a Quick Review of important Concepts, presented alongside corresponding all-new Examples. A comprehensive set of Review Excercises and a Chapter Test are also provided.
- Quantitative Reasoning Now appearing at the end of some chapters, these problems enable students to apply algebraic concepts to real-life situations, such as financial planning for retirement or determining the value of a college education. A photo highlights each problem.
- Glossary As an additional student study aid, a comprehensive glossary of key terms from throughout the text is provided at the back of the book.
- New Annotated Instructor's Edition This special edition of the text provides answers to almost all text exercises in color on the page that the exercise appears. This provides the instructor with immediate access to answers without searching the back of the book.

**1. The Trigonometric Functions. **

Angles.

Angle Relationships and Similar Triangles.

Using the Definitions of the Trigonometric Functions.

**2. Acute Angles and Right Triangles. **

Trigonometric Functions of Acute Angles.

Trigonometric Functions of Non-Acute Angles.

Finding Trigonometric Function Values Using a Calculator.

Solving Right Triangles.

Further Applications of Right Triangles.

**3. Radian Measure and the Circular Functions. **

Radian Measure.

Applications of Radian Measure.

The Unit Circle and Circular Functions.

Linear and Angular Velocity.

**4. Graphs of the Circular Functions. **

Graphs of the Sine and Cosine Functions.

Translations of the Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

**5. Trigonometric Identities. **

Fundamental Identities.

Verifying Trigonometric Identities.

Sum and Difference Identities for Cosine.

Sum and Difference Identities for Sine and Tangent.

Double-Angle Identities.

Half-Angle Identities.

**6. Inverse Trigonometric Functions and Trigonometric Equations. **

Inverse Trigonometric Functions.

Trigonometric Equations I.

Trigonometric Equations II.

Equations Involving Inverse Trigonometric Functions.

**7. Applications of Trigonometry and Vectors. **

Oblique Triangles and the Law of Sines.

The Ambiguous Case of the Law of Sines.

The Law of Cosines.

Vectors and the Dot Product.

Applications of Vectors.

**8. Complex Numbers, Polar Equations, and Parametric Equations. **

Complex Numbers.

Trigonometric (Polar) Form of Complex Numbers.

The Product and Quotient Theorems.

Powers and Roots of Complex Numbers.

Polar Equations and Graphs.

Parametric Equations, Graphs, and Applications.

**9. Exponential and Logarithmic Functions. **

Exponential Functions.

Logarithmic Functions.

Evaluating Logarithms; Equations and Applications.

Appendix A: Equations and Inequalities.

Appendix B: Graphs of Equations.

Appendix C: Functions.

Appendix D: Graphing Techniques.

Glossary.

Solutions to Selected Exercises.

Answers to Selected Exercises.

Index of Applications.

Index.