ISBN13: 978-0534380274

ISBN10: 0534380271

Cover type:

Edition/Copyright: 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

ISBN10: 0534380271

Cover type:

Edition/Copyright: 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

James Stewart, the author of the best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. This trigonometry text has been designed specifically to help students learn to think mathematically and to develop true problem-solving skills. Patient, clear, and accurate, this text consistently illustrates how useful and applicable trigonometry is to real life.

**Features**

- The text is structured so professors can begin with either the unit circle approach or the right triangle approach. This option is unique in this market.
- Each approach to trigonometry is accompanied by the applications appropriate for that approach, clarifying the reasons for different approaches to trigonometry.
- The authors make use of the graphing calculator whenever appropriate. Subsections, examples, and exercises that deal with graphing devices are labeled with an icon so that those who prefer not to use the graphing calculator can easily skip this material.
- Each chapter ends with a FOCUS ON MODELING section that illustrates modeling techniques as well as how trigonometry can be applied to model real-life situations. These sections, as well as others, are devoted to teaching students how to create their own mathematical models, rather than using prefabricated formulas.
- Real-World Applications from engineering, physics, chemistry, business, biology, environmental studies, and other fields demonstrate how trigonometry is used to model real-life situations.
- MATHEMATICS IN THE MODERN WORLD vignettes show that mathematics is a living science crucial to the scientific and technological progress of recent times, as well as to the social, behavioral, and life sciences.
- Each exercise set ends with Discovery - Discussion problems that encourage students to first experiment with the concepts developed in the section and then to write about what they have learned, rather than simply look for an answer.
- Special projects in each chapter are designed to engage students and make them active learners by having them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed.
- Review Sections and Chapter Tests are found at the end of each chapter. These are designed to help students gauge their progress. Brief answers to the odd-numbered exercises in each section, and to all questions in the Chapter Tests, are given at the back of the book.

Author Bio

**Stewart, James : McMaster University**

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford. Stewart is currently a Professor of Mathematics at McMaster University. His research field is harmonic analysis. James Stewart is the author of a best-selling calculus textbook series published by Brooks/Cole, including CALCULUS, 5th Edition, CALCULUS: EARLY TRANSCENDENTALS, 5th Edition, and CALCULUS: CONCEPTS AND CONTEXTS, 2nd Edition, as well as a series of precalculus texts.

**Redlin, Lothar : The Pennsylvania State University**

Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington College. His research field is topology.

**Watson, Saleem : McMaster University**

Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.

1. FUNCTIONS AND GRAPHS.

The Coordinate Plane. Lines in the Coordinate Plane. Functions and Their Graphs. Transformations of Functions. One-to-One Functions and Their Inverses. Focus on Modeling: Fitting Lines to Data.

2. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.

The Unit Circle Trigonometric Functions of Real Numbers Trigonometric Graphs. Mo re Trigonometric Graphs. Harmonic Motion. Focus on Modeling: Sinusoidal Curve Fi tting.

3. TRIGONOMETRIC FUNCTIONS OF ANGLES.

Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angle s. The Law of Sines. The Law of Cosines. Focus on Modeling: Mapping the Earth.

4. ANALYTIC TRIGONOMETRY.

Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half- Angle, and Sum-Product Identities. Inverse Trigonometric Functions. Trigonometri c Equations. Vectors. Focus on Modeling.

5. POLAR COORDINATES; COMPLEX NUMBERS.

Polar Coordinates. Graphs of Polar Equations Complex Numbers. Polar Form of Comp lex Numbers. DeMoivre's Theorem. Focus on Modeling.

6. TOPICS IN ANALYTIC GEOMETRY.

Parabolas. Ellipses. Hyperbolas. Shifted Conics Rotation of Axes. Polar Equation s of Conics. Parametric Equations. Focus on Modeling: The Path of a Projectile.

7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions. Logarithmic Functions. Laws of Logarithms Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Foc us on Modeling: Exponential, Power, and Polynomial Curve Fitting.

James Stewart, Lothar Redlin and Saleem Watson

ISBN13: 978-0534380274ISBN10: 0534380271

Cover type:

Edition/Copyright: 03

Publisher: Brooks/Cole Publishing Co.

Published: 2003

International: No

James Stewart, the author of the best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. This trigonometry text has been designed specifically to help students learn to think mathematically and to develop true problem-solving skills. Patient, clear, and accurate, this text consistently illustrates how useful and applicable trigonometry is to real life.

**Features**

- The text is structured so professors can begin with either the unit circle approach or the right triangle approach. This option is unique in this market.
- Each approach to trigonometry is accompanied by the applications appropriate for that approach, clarifying the reasons for different approaches to trigonometry.
- The authors make use of the graphing calculator whenever appropriate. Subsections, examples, and exercises that deal with graphing devices are labeled with an icon so that those who prefer not to use the graphing calculator can easily skip this material.
- Each chapter ends with a FOCUS ON MODELING section that illustrates modeling techniques as well as how trigonometry can be applied to model real-life situations. These sections, as well as others, are devoted to teaching students how to create their own mathematical models, rather than using prefabricated formulas.
- Real-World Applications from engineering, physics, chemistry, business, biology, environmental studies, and other fields demonstrate how trigonometry is used to model real-life situations.
- MATHEMATICS IN THE MODERN WORLD vignettes show that mathematics is a living science crucial to the scientific and technological progress of recent times, as well as to the social, behavioral, and life sciences.
- Each exercise set ends with Discovery - Discussion problems that encourage students to first experiment with the concepts developed in the section and then to write about what they have learned, rather than simply look for an answer.
- Special projects in each chapter are designed to engage students and make them active learners by having them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed.
- Review Sections and Chapter Tests are found at the end of each chapter. These are designed to help students gauge their progress. Brief answers to the odd-numbered exercises in each section, and to all questions in the Chapter Tests, are given at the back of the book.

Author Bio

**Stewart, James : McMaster University**

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford. Stewart is currently a Professor of Mathematics at McMaster University. His research field is harmonic analysis. James Stewart is the author of a best-selling calculus textbook series published by Brooks/Cole, including CALCULUS, 5th Edition, CALCULUS: EARLY TRANSCENDENTALS, 5th Edition, and CALCULUS: CONCEPTS AND CONTEXTS, 2nd Edition, as well as a series of precalculus texts.

**Redlin, Lothar : The Pennsylvania State University**

Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington College. His research field is topology.

**Watson, Saleem : McMaster University**

Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.

Table of Contents

1. FUNCTIONS AND GRAPHS.

The Coordinate Plane. Lines in the Coordinate Plane. Functions and Their Graphs. Transformations of Functions. One-to-One Functions and Their Inverses. Focus on Modeling: Fitting Lines to Data.

2. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.

The Unit Circle Trigonometric Functions of Real Numbers Trigonometric Graphs. Mo re Trigonometric Graphs. Harmonic Motion. Focus on Modeling: Sinusoidal Curve Fi tting.

3. TRIGONOMETRIC FUNCTIONS OF ANGLES.

Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angle s. The Law of Sines. The Law of Cosines. Focus on Modeling: Mapping the Earth.

4. ANALYTIC TRIGONOMETRY.

Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half- Angle, and Sum-Product Identities. Inverse Trigonometric Functions. Trigonometri c Equations. Vectors. Focus on Modeling.

5. POLAR COORDINATES; COMPLEX NUMBERS.

Polar Coordinates. Graphs of Polar Equations Complex Numbers. Polar Form of Comp lex Numbers. DeMoivre's Theorem. Focus on Modeling.

6. TOPICS IN ANALYTIC GEOMETRY.

Parabolas. Ellipses. Hyperbolas. Shifted Conics Rotation of Axes. Polar Equation s of Conics. Parametric Equations. Focus on Modeling: The Path of a Projectile.

7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions. Logarithmic Functions. Laws of Logarithms Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Foc us on Modeling: Exponential, Power, and Polynomial Curve Fitting.

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