BRIEF CONTENTS 1 Ch 1, THE SIX TRIGONOMETRIC FUNCTIONS 51 Ch 2, RIGHT ANGLE Trigonometry 106 Ch 3, RADIAN MEASURE 162 Ch 4, GRAPHING AND INVERSE FUNCTIONS 236 Ch 5, IDENTITIES AND FORMULAS 279 Ch 6, EQUATIONS 316 Ch 7, TRIANGLES 368 Ch 8, COMPLEX NUMBERS AND POLAR COORDINATES 422 APPENDIX A - REVIEW OF FUNCTIONS 447 APPENDIX B - EXPONENTIAL AND LOGARITHMIC FUNCTIONS COMPLETE CONTENTS Chapter 1 THE SIX TRIGONOMETRIC FUNCTIONS Page 1 2 1.1 ANGLES, DEGREES, AND SPECIAL TRIANGLES 14 1.2 THE RECTANGULAR COORDINATE SYSTEM 26 1.3 DEFINITION I: TRIGONOMETRIC FUNCTIONS 32 1.4 INTRODUCTION TO IDENTITIES 40 1.5 MORE ON IDENTITIES 45 SUMMARY 47 TEST 49 PROJECTS Chapter 2 RIGHT TRIANGLE TRIGONOMETRY Page 51 52 2.1 DEFINITION II: RIGHT TRIANGLE TRIGONOMETRY 61 2.2 CALCULATORS AND TRIGONOMETRIC FUNCTIONS OF AN ACUTE ANGLE 69 2.3 SOLVING RIGHT TRIANGLES 78 2.4 APPLICATIONS 91 2.5 VECTORS: A GEOMETRIC APPROACH 100 SUMMARY 103 TEST 104 PROJECTS Chapter 3 RADIAN MEASURE Page 106 107 3.1. REFERENCE ANGLE 114 3.2 RADIANS AND DEGREES 124 3.3 DEFINITION III: CIRCULAR FUNCTIONS 133 3.4 ARC LENGTH AND AREA OF A SECTOR 144 3.5 VELOCITIES 155 SUMMARY 157 TEST 159 PROJECTS Chapter 4 GRAPHING AND INVERSE FUNCTIONS Page 162 163 4.1 BASIC GRAPHS AND AMPLITUDE 177 4.2 PERIOD, REFLECTION, AND VERTICAL TRANSLATION 189 4.3 PHASE SHIFT O 200 4.4 FINDING AN EQUATION FROM ITS GRAPH 211 4.5 GRAPHING COMBINATIONS OF FUNCTIONS 217 4.6 INVERSE TRIGONOMETRIC FUNCTIONS 229 SUMMARY 232 TEST 234 PROJECTS Chapter 5 IDENTITIES AND FORMULAS Page 236 237 5.1. PROVING IDENTITIES 255 5.2 SUM AND DIFFERENCE FORMULAS 245 5.3 DOUBLE-ANGLE FORMULAS 262 5.4 HALF-ANGLE FORMULAS 267 5.5 ADDITIONAL IDENTITIES 276 SUMMARY 274 TEST 277 PROJECTS Chapter 6 EQUATIONS Page 279 280 6.1 SOLVING TRIGONOMETRIC EQUATIONSvi 289 6.2 MORE ON TRIGONOMETRIC EQUATIONS 294 6.3 TRIGONOMETRIC EQUATIONS INVOLVING MULTIPLE ANGLES 302 6.4. PARAMETRIC EQUATIONS AND FURTHER GRAPHING 311 SUMMARY 312 TEST 313 PROJECTS Chapter 7 TRIANGLES Page 316 317 7.1 THE LAW OF SINESO 328 7.2 THE AMBIGUOUS CASE 336 7.3 THE LAW OF COSINES 343 7.4 THE AREA OF A TRIANGLE 348 7.5 VECTORS: AN ALGEBRAIC APPROACH APPROACH 348 357 7.6 VECTORS: THE DOT PRODUCT 362 SUMMARY 364 TEST 366 PROJECTS Chapter 8 COMPLEX NUMBERS AND POLAR COORDINATES Page 368 369 8.1 COMPLEX NUMBERS 377 8.2 TRIGONOMETRIC FORM FOR COMPLEX NUMBERS 383 8.3 PRODUCTS AND QUOTIENTS IN TRIGONOMETRIC FORM 396 8.4 ROOTS OF A COMPLEX NUMBER 389 8.5 POLAR COORDINATES 406 8.6 EQUATIONS IN POLAR COORDINATES AND THEIR GRAPHS 416 SUMMARY 419 TEST 420 PROJECTS APPENDIX A 422 APPENDIX A REVIEW OF FUNCTIONS 423 A.1 INTRODUCTION TO FUNCTIONS 435 A.2 THE INVERSE OF A FUNCTION APPENDIX B 447 APPENDIX B EXPONENTIAL AND LOGARITHMIC FUNCTIONS 448 B.1 EXPONENTIAL FUNCTIONS 457 B.2 LOGARITHMS ARE EXPONENTS 465 B.3 PROPERTIES OF LOGARITHMS 470 B.4 COMMON LOGARITHMS AND NATURAL LOGARITHMS 478 B.5 EXPONENTIAL EQUATIONS AND CHANGE OF BASE ANSWERS TO EXERCISES AND CHAPTER TESTS A-1 INDEX I-1