Trigonometry

591 Pages·2012·24.8 MB·English

by  Charles P. McKeague

T
7
RIGONOMETRY
E
Charles P. McKeague
Cuesta College
Mark D. Turner
Cuesta College
Australia •Brazil •Japan •Korea •Mexico •Singapore •Spain •United Kingdom •United States
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Trigonometry,Seventh Edition © 2013, 2008Brooks/Cole, Cengage Learning
Charles P. McKeague, Mark D. Turner
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BRIEF CONTENTS
1
CHAPTER The Six Trigonometric Functions 1
2
CHAPTER Right Triangle Trigonometry 54
3
CHAPTER Radian Measure 114
4
CHAPTER Graphing and Inverse Functions 178
5
CHAPTER Identities and Formulas 270
6
CHAPTER Equations 318
7
CHAPTER Triangles 360
8
CHAPTER Complex Numbers and Polar Coordinates 418
Appendix A Review of Functions 478
Answers to Selected Exercises A-1
Index I-1
iii
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CCOONNTTEENNTTSS
Preface ix
A Special Note to the Student xv
1
The Six Trigonometric Functions 1
CHAPTER
1.1 Angles,Degrees,and Special Triangles 2
1.2 The Rectangular Coordinate System 15
1.3 Definition I:Trigonometric Functions 27
1.4 Introduction to Identities 34
1.5 More on Identities 42
SUMMARY 48
TEST 50
PROJECTS 52
2
Right Triangle Trigonometry 54
CHAPTER
2.1 Definition II:Right Triangle Trigonometry 55
2.2 Calculators and Trigonometric Functions ofanAcuteAngle 64
2.3 Solving Right Triangles 74
2.4 Applications 85
2.5 Vectors:A Geometric Approach 98
SUMMARY 109
TEST 111
PROJECTS 113
3
Radian Measure 114
CHAPTER
3.1 Reference Angle 115
3.2 Radians and Degrees 123
3.3 Definition III:Circular Functions 135
3.4 Arc Length and Area of a Sector 147
3.5 Velocities 158
SUMMARY 170
TEST 172
PROJECTS 174
CUMULATIVE TEST 176
v
(cid:2)
vi CONTENTS
4
Graphing and Inverse Functions 178
CHAPTER
4.1 Basic Graphs 179
4.2 Amplitude,Reflection,and Period 194
4.3 Vertical and Horizontal Translations 208
4.4 The Other Trigonometric Functions 220
4.5 Finding an Equation from Its Graph 231
4.6 Graphing Combinations of Functions 245
4.7 Inverse Trigonometric Functions 251
SUMMARY 264
TEST 267
PROJECTS 268
5
Identities and Formulas 270
CHAPTER
5.1 Proving Identities 271
5.2 Sum and Difference Formulas 281
5.3 Double-Angle Formulas 291
5.4 Half-Angle Formulas 299
5.5 Additional Identities 306
SUMMARY 313
TEST 315
PROJECTS 316
6
Equations 318
CHAPTER
6.1 Solving Trigonometric Equations 319
6.2 More on Trigonometric Equations 328
6.3 Trigonometric Equations Involving Multiple Angles 334
6.4 Parametric Equations and Further Graphing 343
SUMMARY 354
TEST 355
PROJECTS 356
CUMULATIVE TEST 358
(cid:2)
CONTENTS vii
7
Triangles 360
CHAPTER
7.1 The Law of Sines 361
7.2 The Law of Cosines 372
7.3 The Ambiguous Case 382
7.4 The Area of a Triangle 391
7.5 Vectors:An Algebraic Approach 397
7.6 Vectors:The Dot Product 407
SUMMARY 413
TEST 415
PROJECTS 416
8
Complex Numbers and Polar Coordinates 418
CHAPTER
8.1 Complex Numbers 419
8.2 Trigonometric Form for Complex Numbers 427
8.3 Products and Quotients in Trigonometric Form 434
8.4 Roots of a Complex Number 441
8.5 Polar Coordinates 449
8.6 Equations in Polar Coordinates and Their Graphs 459
SUMMARY 471
TEST 474
PROJECTS 475
CUMULATIVE TEST 477
A Review of Functions 478
APPENDIX
A.1 Introduction to Functions 478
A.2 The Inverse of a Function 489
Answers to Selected Exercises A-1
Index I-1
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