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The Fourth Edition of College Trigonometry continues to promote student success by engaging students in mathematics, thus helping them see the dynamic link between concepts and applications. The authors' hallmark approach, the Aufmann Interactive Method, encourages students to interact with math by presenting an annotated example, then guiding students with a Try Exercise, and finally presenting a worked-out solution for immediate reinforcement of the concept. A wealth of new features designed to enhance learning include more in-text guidance as well as special web-based resources, and an unparalleled Instructor's Annotated Edition facilitates teaching.
Note: Each chapter concludes with a Summary, True/False Exercises, Review Exercises, and a Chapter Test.
1. Functions and Graphs
1.1 Equations and Inequalities
1.2 A Two-Dimensional Coordinate System and Graphs
1.3 Introduction to Functions
1.4 Properties of Graphs
1.5 The Algebra of Functions
1.6 Inverse Functions
1.7 Modeling Data Using Regression
Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator
2. Trigonometric Functions
2.1 Angles and Arcs
2.2 Trigonometric Functions of Acute Angles
2.3 Trigonometric Functions of Any Angle
2.4 Trigonometric Functions of Real Numbers
2.5 Graphs of the Sine and Cosine Functions
2.6 Graphs of the Other Trigonometric Fuctions
2.7 Graphing Techniques
2.8 Harmonic Motion--An Application of the Sine and Cosine Functions
Exploring Concepts with Technology: Sinusoidal Families
3. Trigonometric Identities and Equations
3.1 Verification of Trigonometric Identities
3.2 Sum, Difference, and Cofunction Identities
3.3 Double- and Half-Angle Identities
3.4 Identities Involving the Sum of Trigonometric Functions
3.5 Inverse Trigonometric Functions
3.6 Trigonometric Equations
Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials
4. Applications of Trigonometry
4.1 The Law of Sines
4.2 The Law of Cosines and Area
4.3 Vectors
Exploring Concepts with Technology: Optimal Branching of Arteries
5. Complex Numbers
5.1 Complex Numbers
5.2 Trigonometric Form of Complex Numbers
5.3 De Moivre's Theorem
Exploring Concepts with Technology: The Mandelbrot Replacement Procedure
6. Topics in Analytic Geometry
6.1 Parabolas
6.2 Ellipses
6.3 Hyperbolas
6.4 Rotation of Axes
6.5 Introduction to Polar Coordinates
6.6 Polar Equations of the Conics
6.7 Parametric Equations
Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Root of z
7. Exponential and Logarithmic Functions
7.1 Exponential Functions and Their Graphs
7.2 Logarithmic Functions and Their Graphs
7.3 Properties of Logarithms
7.4 Exponential and Logarithmic Equations
7.5 Applications of Exponential and Logarithmic Functions
7.6 Modeling Data with Exponential and Logarithmic Functions
Exploring Concepts with Technology: Using a Semi-Log Graph to Model Exponential Decay
Solutions to Selected Exercises
Answers to Odd-Numbered Exercises
Glossary
Index
The Fourth Edition of College Trigonometry continues to promote student success by engaging students in mathematics, thus helping them see the dynamic link between concepts and applications. The authors' hallmark approach, the Aufmann Interactive Method, encourages students to interact with math by presenting an annotated example, then guiding students with a Try Exercise, and finally presenting a worked-out solution for immediate reinforcement of the concept. A wealth of new features designed to enhance learning include more in-text guidance as well as special web-based resources, and an unparalleled Instructor's Annotated Edition facilitates teaching.
Table of Contents
Note: Each chapter concludes with a Summary, True/False Exercises, Review Exercises, and a Chapter Test.
1. Functions and Graphs
1.1 Equations and Inequalities
1.2 A Two-Dimensional Coordinate System and Graphs
1.3 Introduction to Functions
1.4 Properties of Graphs
1.5 The Algebra of Functions
1.6 Inverse Functions
1.7 Modeling Data Using Regression
Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator
2. Trigonometric Functions
2.1 Angles and Arcs
2.2 Trigonometric Functions of Acute Angles
2.3 Trigonometric Functions of Any Angle
2.4 Trigonometric Functions of Real Numbers
2.5 Graphs of the Sine and Cosine Functions
2.6 Graphs of the Other Trigonometric Fuctions
2.7 Graphing Techniques
2.8 Harmonic Motion--An Application of the Sine and Cosine Functions
Exploring Concepts with Technology: Sinusoidal Families
3. Trigonometric Identities and Equations
3.1 Verification of Trigonometric Identities
3.2 Sum, Difference, and Cofunction Identities
3.3 Double- and Half-Angle Identities
3.4 Identities Involving the Sum of Trigonometric Functions
3.5 Inverse Trigonometric Functions
3.6 Trigonometric Equations
Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials
4. Applications of Trigonometry
4.1 The Law of Sines
4.2 The Law of Cosines and Area
4.3 Vectors
Exploring Concepts with Technology: Optimal Branching of Arteries
5. Complex Numbers
5.1 Complex Numbers
5.2 Trigonometric Form of Complex Numbers
5.3 De Moivre's Theorem
Exploring Concepts with Technology: The Mandelbrot Replacement Procedure
6. Topics in Analytic Geometry
6.1 Parabolas
6.2 Ellipses
6.3 Hyperbolas
6.4 Rotation of Axes
6.5 Introduction to Polar Coordinates
6.6 Polar Equations of the Conics
6.7 Parametric Equations
Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Root of z
7. Exponential and Logarithmic Functions
7.1 Exponential Functions and Their Graphs
7.2 Logarithmic Functions and Their Graphs
7.3 Properties of Logarithms
7.4 Exponential and Logarithmic Equations
7.5 Applications of Exponential and Logarithmic Functions
7.6 Modeling Data with Exponential and Logarithmic Functions
Exploring Concepts with Technology: Using a Semi-Log Graph to Model Exponential Decay
Solutions to Selected Exercises
Answers to Odd-Numbered Exercises
Glossary
Index