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| Preface | |
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| Supplements Guide | |
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| Trigonometric Functions | |
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| Angles | |
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| Basic Terminology | |
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| Degree Measure | |
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| Standard Position | |
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| Coterminal Angles | |
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| Angle Relationships and Similar Triangles | |
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| Geometric Properties | |
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| Triangles | |
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| Trigonometric Functions | |
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| Trigonometric Functions | |
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| Quadrantal Angles | |
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| Using the Definitions of the Trigonometric Functions | |
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| Reciprocal Identities | |
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| Signs and Ranges of Function Values | |
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| Pythagorean Identities | |
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| Quotient Identities | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Acute Angles and Right Triangles | |
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| Trigonometric Functions of Acute Angles | |
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| Right-Triangle-Based Definitions of the Trigonometric Functions | |
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| Cofunctions | |
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| Trigonometric Function Values of Special Angles | |
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| Trigonometric Functions of Non-Acute Angles | |
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| Reference Angles | |
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| Special Angles as Reference Angles | |
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| Finding Angle Measures with Special Angles | |
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| Finding Trigonometric Function Values Using a Calculator | |
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| Finding Function Values Using a Calculator | |
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| Finding Angle Measures Using a Calculator | |
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| Solving Right Triangles | |
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| Significant Digits | |
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| Solving Triangles | |
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| Angles of Elevation or Depression | |
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| Further Applications of Right Triangles | |
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| Bearing | |
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| Further Applications | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Radian Measure and Circular Functions | |
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| Radian Measure | |
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| Radian Measure | |
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| Converting Between Degrees and Radians | |
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| Finding Function Values for Angles in Radians | |
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| Applications of Radian Measure | |
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| Arc Length on a Circle | |
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| Area of a Sector of a Circle | |
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| The Unit Circle and Circular Functions | |
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| Circular Functions | |
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| Finding Values of Circular Functions | |
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| Determining a Number with a Given Circular Function Value | |
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| Applying Circular Functions | |
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| Linear and Angular Speed | |
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| Linear Speed | |
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| Angular Speed | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Graphs of the Circular Functions | |
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| Graphs of the Sine and Cosine Functions | |
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| Periodic Functions | |
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| Graph of the Sine Function | |
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| Graph of the Cosine Function | |
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| Graphing Techniques, Amplitude, and Period | |
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| Using a Trigonometric Model | |
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| Translations of the Graphs of the Sine and Cosine Functions | |
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| Horizontal Translations | |
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| Vertical Translations | |
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| Combinations of Translations | |
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| Determining a Trigonometric Model Using Curve Fitting | |
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| Graphs of the Other Circular Functions | |
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| Graphs of the Cosecant and Secant Functions | |
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| Graphs of the Tangent and Cotangent Functions | |
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| Addition of Ordinates | |
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| Summary Exercises on Graphing Circular Functions | |
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| Harmonic Motion | |
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| Simple Harmonic Motion | |
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| Damped Oscillatory Motion | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Trigonometric Identities | |
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| Fundamental Identities | |
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| Negative-Angle Identities | |
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| Fundamental Identities | |
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| Using the Fundamental Identities | |
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| Verifying Trigonometric Identities | |
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| Verifying Identities by Working with One Side | |
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| Verifying Identities by Working with Both Sides | |
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| Sum and Difference Identities for Cosine | |
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| Difference Identity for Cosine | |
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| Sum Identity for Cosine | |
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| Cofunction Identities | |
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| Applying the Sum and Difference Identities | |
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| Sum and Difference Identities for Sine and Tangent | |
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| Sum and Difference Identities for Sine | |
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| Sum and Difference Identities for Tangent | |
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| Applying the Sum and Difference Identities | |
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| Double-Angle Identities | |
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| Double-Angle Identities | |
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| Product-to-Sum and Sum-to-Product Identities | |
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| Half-Angle Identities | |
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| Half-Angle Identities | |
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| Applying the Half-Angle Identities | |
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| Summary Exercises on Verifying Trigonometric Identities | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Inverse Circular Functions and Trigonometric Equations | |
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| Inverse Circular Functions | |
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| Inverse Functions | |
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| Inverse Sine Function | |
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| Inverse Cosine Function | |
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| Inverse Tangent Function | |
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| Remaining Inverse Circular Functions | |
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| Inverse Function Values | |
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| Trigonometric Equations I | |
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| Solving by Linear Methods | |
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| Solving by Factoring | |
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| Solving by Quadratic Methods | |
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| Solving by Using Trigonometric Identities | |
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| Trigonometric Equations II | |
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| Equations with Half-Angles | |
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| Equations with Multiple Angles | |
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| Equations Involving Inverse Trigonometric Functions | |
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| Solving for x in Terms of y Using Inverse Functions | |
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| Solving Inverse Trigonometric Equations | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Applications of Trigonometry and Vectors | |
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| Oblique Triangles and the Law of Sines | |
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| Congruency and Oblique Triangles | |
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| Derivation of the Law of Sines | |
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| Solving SAA and ASA Triangles (Case 1) | |
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| Area of a Triangle | |
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| The Ambiguous Case of the Law of Sines | |
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| Description of the Ambiguous Case | |
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| Solving SSA Triangles (Case 2) | |
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| Analyzing Data for Possible Number of Triangles | |
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| The Law of Cosines | |
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| Derivation of the Law of Cosines | |
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| Solving SAS and SSS Triangles (Cases 3 and 4) | |
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| Heron's Formula for the Area of a Triangle | |
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| Vectors, Operations, and the Dot Product | |
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| Basic Terminology | |
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| Algebraic Interpretation of Vectors | |
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| Operations with Vectors | |
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| Dot Product and the Angle Between Vectors | |
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| Applications of Vectors | |
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| The Equilibrant | |
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| Incline Applications | |
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| Navigation Applications | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Complex Numbers, Polar Equations, and Parametric Equations | |
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| Complex Numbers | |
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| Basic Concepts of Complex Numbers | |
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| Complex Solutions of Equations | |
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| Operations on Complex Numbers | |
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| Trigonometric (Polar) Form of Complex Numbers | |
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| The Complex Plane and Vector Representation | |
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| Trigonometric (Polar) Form | |
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| Converting Between Trigonometric and Polar Forms | |
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| An Application of Complex Numbers to Fractals | |
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| The Product and Quotient Theorems | |
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| Products of Complex Numbers in Trigonometric Form | |
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| Quotients of Complex Numbers in Trigonometric Form | |
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| De Moivre's Theorem; Powers and Roots of Complex Numbers | |
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| Powers of Complex Numbers (De Moivre's Theorem) | |
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| Roots of Complex Numbers | |
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| Polar Equations and Graphs | |
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| Polar Coordinate System | |
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| Graphs of Polar Equations | |
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| Converting from Polar to Rectangular Equations | |
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| Classifying Polar Equations | |
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| Parametric Equations, Graphs, and Applications | |
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| Basic Concepts | |
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| Parametric Graphs and Their Rectangular Equivalents | |
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| The Cycloid | |
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| Applications of Parametric Equations | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions | |
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| Exponents and Properties | |
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| Exponential Functions | |
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| Exponential Equations | |
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| Compound Interest | |
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| The Number e and Continuous Compounding | |
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| Exponential Models and Curve Fitting | |
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| Logarithmic Functions | |
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| Logarithms | |
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| Logarithmic Equations | |
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| Logarithmic Functions | |
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| Properties of Logarithms | |
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| Evaluating Logarithms; Equations and Applications | |
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| Common Logarithms | |
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| Natural Logarithms | |
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| Logarithms to Other Bases | |
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| Exponential and Logarithmic Equations | |
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| Summary | |
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| Review Exercises | |
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| Test | |
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| Quantitative Reasoning | |
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| Equations and Inequalities | |
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| Equations | |
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| Solving Linear Equations | |
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| Solving Quadratic Equations | |
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| Inequalities | |
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| Solving Linear Inequalities | |
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| Interval Notation | |
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| Three-Part Inequalities | |
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| Graphs of Equations | |
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| The Rectangular Coordinate System | |
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| The Pythagorean Theorem and the Distance Formula | |
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| The Midpoint Formula | |
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| Graphing Equations | |
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| Circles | |
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| Functions | |
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| Relations and Functions | |
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| Domain and Range | |
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| Determining Whether a Relation Is a Function | |
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| Function Notation | |
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| Increasing, Decreasing, and Constant Functions | |
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| Graphing Techniques | |
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| Stretching and Shrinking | |
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| Reflecting | |
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| Symmetry | |
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| Translations | |
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| Glossary | |
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| Solutions to Selected Exercises | |
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| Answers to Selected Exercises | |
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| Index of Applications | |
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| Index | |