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Trigonometry
ISBN: 9780673995537 | 0673995534
Edition: 6thFormat: Hardcover
Publisher: Pearson College Div
Pub. Date: 10/1/1996
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Student's Solution Manual Complete, worked-out solutions are given for odd-numbered exercises and chapter review exercises and all chapter test exercises in a volume available for purchase by students. In addition, a practice chapter test and cumulative review exercises are provided for each chapter.
| 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 | ... MOREp. 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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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