Preface | p. viii |

Supplements Guide | p. xii |

Trigonometric Functions | p. 1 |

Angles | p. 2 |

Basic Terminology | |

Degree Measure | |

Standard Position | |

Coterminal Angles | |

Angle Relationships and Similar Triangles | p. 9 |

Geometric Properties | |

Triangles | |

Trigonometric Functions | p. 20 |

Trigonometric Functions | |

Quadrantal Angles | |

Using the Definitions of the Trigonometric Functions | p. 27 |

Reciprocal Identities | |

Signs and Ranges of Function Values | |

Pythagorean Identities | |

Quotient Identities | |

Summary | p. 37 |

Review Exercises | p. 39 |

Test | p. 42 |

Quantitative Reasoning | p. 44 |

Acute Angles and Right Triangles | p. 45 |

Trigonometric Functions of Acute Angles | p. 46 |

Right-Triangle-Based Definitions of the Trigonometric Functions | |

Cofunctions | |

Trigonometric Function Values of Special Angles | |

Trigonometric Functions of Non-Acute Angles | p. 55 |

Reference Angles | |

Special Angles as Reference Angles | |

Finding Angle Measures with Special Angles | |

Finding Trigonometric Function Values Using a Calculator | p. 62 |

Finding Function Values Using a Calculator | |

Finding Angle Measures Using a Calculator | |

Solving Right Triangles | p. 68 |

Significant Digits | |

Solving Triangles | |

Angles of Elevation or Depression | |

Further Applications of Right Triangles | p. 77 |

Bearing | |

Further Applications | |

Summary | p. 86 |

Review Exercises | p. 88 |

Test | p. 91 |

Quantitative Reasoning | p. 92 |

Radian Measure and Circular Functions | p. 93 |

Radian Measure | p. 94 |

Radian Measure | |

Converting Between Degrees and Radians | |

Finding Function Values for Angles in Radians | |

Applications of Radian Measure | p. 99 |

Arc Length on a Circle | |

Area of a Sector of a Circle | |

The Unit Circle and Circular Functions | p. 108 |

Circular Functions | |

Finding Values of Circular Functions | |

Determining a Number with a Given Circular Function Value | |

Applying Circular Functions | |

Linear and Angular Speed | p. 116 |

Linear Speed | |

Angular Speed | |

Summary | p. 122 |

Review Exercises | p. 124 |

Test | p. 128 |

Quantitative Reasoning | p. 129 |

Graphs of the Circular Functions | p. 131 |

Graphs of the Sine and Cosine Functions | p. 132 |

Periodic Functions | |

Graph of the Sine Function | |

Graph of the Cosine Function | |

Graphing Techniques, Amplitude, and Period | |

Using a Trigonometric Model | |

Translations of the Graphs of the Sine and Cosine Functions | p. 146 |

Horizontal Translations | |

Vertical Translations | |

Combinations of Translations | |

Determining a Trigonometric Model Using Curve Fitting | |

Graphs of the Other Circular Functions | p. 155 |

Graphs of the Cosecant and Secant Functions | |

Graphs of the Tangent and Cotangent Functions | |

Addition of Ordinates | |

Summary Exercises on Graphing Circular Functions | p. 168 |

Harmonic Motion | p. 168 |

Simple Harmonic Motion | |

Damped Oscillatory Motion | |

Summary | p. 173 |

Review Exercises | p. 175 |

Test | p. 178 |

Quantitative Reasoning | p. 779 |

Trigonometric Identities | p. 181 |

Fundamental Identities | p. 182 |

Negative-Angle Identities | |

Fundamental Identities | |

Using the Fundamental Identities | |

Verifying Trigonometric Identities | p. 188 |

Verifying Identities by Working with One Side | |

Verifying Identities by Working with Both Sides | |

Sum and Difference Identities for Cosine | p. 197 |

Difference Identity for Cosine | |

Sum Identity for Cosine | |

Cofunction Identities | |

Applying the Sum and Difference Identities | |

Sum and Difference Identities for Sine and Tangent | p. 205 |

Sum and Difference Identities for Sine | |

Sum and Difference Identities for Tangent | |

Applying the Sum and Difference Identities | |

Double-Angle Identities | p. 212 |

Double-Angle Identities | |

Product-to-Sum and Sum-to-Product Identities | |

Half-Angle Identities | p. 221 |

Half-Angle Identities | |

Applying the Half-Angle Identities | |

Summary Exercises on Verifying Trigonometric Identities | p. 227 |

Summary | p. 229 |

Review Exercises | p. 231 |

Test | p. 233 |

Quantitative Reasoning | p. 234 |

Inverse Circular Functions and Trigonometric Equations | p. 235 |

Inverse Circular Functions | p. 236 |

Inverse Functions | |

Inverse Sine Function | |

Inverse Cosine Function | |

Inverse Tangent Function | |

Remaining Inverse Circular Functions | |

Inverse Function Values | |

Trigonometric Equations I | p. 249 |

Solving by Linear Methods | |

Solving by Factoring | |

Solving by Quadratic Methods | |

Solving by Using Trigonometric Identities | |

Trigonometric Equations II | p. 256 |

Equations with Half-Angles | |

Equations with Multiple Angles | |

Equations Involving Inverse Trigonometric Functions | p. 262 |

Solving for x in Terms of y Using Inverse Functions | |

Solving Inverse Trigonometric Equations | |

Summary | p. 269 |

Review Exercises | p. 271 |

Test | p. 273 |

Quantitative Reasoning | p. 274 |

Applications of Trigonometry and Vectors | p. 275 |

Oblique Triangles and the Law of Sines | p. 276 |

Congruency and Oblique Triangles | |

Derivation of the Law of Sines | |

Solving SAA and ASA Triangles (Case 1) | |

Area of a Triangle | |

The Ambiguous Case of the Law of Sines | p. 287 |

Description of the Ambiguous Case | |

Solving SSA Triangles (Case 2) | |

Analyzing Data for Possible Number of Triangles | |

The Law of Cosines | p. 293 |

Derivation of the Law of Cosines | |

Solving SAS and SSS Triangles (Cases 3 and 4) | |

Heron's Formula for the Area of a Triangle | |

Vectors, Operations, and the Dot Product | p. 305 |

Basic Terminology | |

Algebraic Interpretation of Vectors | |

Operations with Vectors | |

Dot Product and the Angle Between Vectors | |

Applications of Vectors | p. 315 |

The Equilibrant | |

Incline Applications | |

Navigation Applications | |

Summary | p. 322 |

Review Exercises | p. 325 |

Test | p. 329 |

Quantitative Reasoning | p. 330 |

Complex Numbers, Polar Equations, and Parametric Equations | p. 331 |

Complex Numbers | p. 332 |

Basic Concepts of Complex Numbers | |

Complex Solutions of Equations | |

Operations on Complex Numbers | |

Trigonometric (Polar) Form of Complex Numbers | p. 341 |

The Complex Plane and Vector Representation | |

Trigonometric (Polar) Form | |

Converting Between Trigonometric and Polar Forms | |

An Application of Complex Numbers to Fractals | |

The Product and Quotient Theorems | p. 347 |

Products of Complex Numbers in Trigonometric Form | |

Quotients of Complex Numbers in Trigonometric Form | |

De Moivre's Theorem; Powers and Roots of Complex Numbers | p. 352 |

Powers of Complex Numbers (De Moivre's Theorem) | |

Roots of Complex Numbers | |

Polar Equations and Graphs | p. 359 |

Polar Coordinate System | |

Graphs of Polar Equations | |

Converting from Polar to Rectangular Equations | |

Classifying Polar Equations | |

Parametric Equations, Graphs, and Applications | p. 371 |

Basic Concepts | |

Parametric Graphs and Their Rectangular Equivalents | |

The Cycloid | |

Applications of Parametric Equations | |

Summary | p. 379 |

Review Exercises | p. 382 |

Test | p. 385 |

Quantitative Reasoning | p. 386 |

Exponential and Logarithmic Functions | p. 387 |

Exponential Functions | p. 388 |

Exponents and Properties | |

Exponential Functions | |

Exponential Equations | |

Compound Interest | |

The Number e and Continuous Compounding | |

Exponential Models and Curve Fitting | |

Logarithmic Functions | p. 402 |

Logarithms | |

Logarithmic Equations | |

Logarithmic Functions | |

Properties of Logarithms | |

Evaluating Logarithms; Equations and Applications | p. 413 |

Common Logarithms | |

Natural Logarithms | |

Logarithms to Other Bases | |

Exponential and Logarithmic Equations | |

Summary | p. 426 |

Review Exercises | p. 428 |

Test | p. 431 |

Quantitative Reasoning | p. 432 |

Equations and Inequalities | p. 433 |

Equations | |

Solving Linear Equations | |

Solving Quadratic Equations | |

Inequalities | |

Solving Linear Inequalities | |

Interval Notation | |

Three-Part Inequalities | |

Graphs of Equations | p. 442 |

The Rectangular Coordinate System | |

The Pythagorean Theorem and the Distance Formula | |

The Midpoint Formula | |

Graphing Equations | |

Circles | |

Functions | p. 450 |

Relations and Functions | |

Domain and Range | |

Determining Whether a Relation Is a Function | |

Function Notation | |

Increasing, Decreasing, and Constant Functions | |

Graphing Techniques | p. 460 |

Stretching and Shrinking | |

Reflecting | |

Symmetry | |

Translations | |

Glossary | p. 469 |

Solutions to Selected Exercises | p. S-1 |

Answers to Selected Exercises | p. A-1 |

Index of Applications | p. I-1 |

Index | p. I-3 |

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