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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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