College Algebra & Trigonometry, 2018a

More documents

Recommendations

Info

9.1. TRIGONOMETRIC FUNCTIONS OF NON-ACUTE ANGLES 391 Reference Angles for Negative Angles Negatively measured angles rotate in a clockwise direction. θ + 180 ◦ θ 1 (cos θ, sin θ) There are a variety of methods for finding the reference angle for a negatively valued angle. You can find a positive angle that is co-terminal with the negative angle and then find the reference angle for the positive angle. You can also drop a perpendicular to the x-axis to find the reference angle for the negative angle directly. For example, the angle −120 ◦ terminates in Quadrant III and is co-terminal with the positive angle 240 ◦ . Either way, when you drop a perpendicular to the x-axis, you find that the reference angle is 60 ◦ . If you are given the value of one of the trigonometric functions of an angle θ, and know which quadrant θ is located in, you can find the other trigonometric functions for that angle. Example Given θ in Quadrant IV with cos θ = 1 5 , find sin θ and tan θ. If cos θ = 1 5 , then the adjacent side and the hypotenuse must be in a ratio of 1:5.
392 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS We can label these sides as 1 and 5 and then find the length of the third side in the triangle. This will allow us to find sin θ and tan θ. θ 1 360 ◦ −θ 5 √ 24 Using the Pythagorean Theorem: 5 2 =1 2 + s 2 25 − 1=s 2 √ 24 = s we find that the side opposite the reference angle for θ is √ 24 or 2 √ 6. We can now find sin θ and tan θ: √ sin θ = 24 5 and tan θ = √ 24 1 = √ 24
Page 1 and 2:
College Algebra & Trigonometry
Page 3 and 4:
c○2018 Richard W. Beveridge This
Page 5 and 6:
2
Page 7 and 8:
4 CONTENTS 2.4 Solution of Rational
Page 9 and 10:
6 CONTENTS 8.2 The Trigonometric Ra
Page 11 and 12:
8 CONTENTS
Page 13 and 14:
10 CHAPTER 1. ALGEBRA REVIEW Exampl
Page 15 and 16:
12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
Page 17 and 18:
14 CHAPTER 1. ALGEBRA REVIEW 1.2 Fa
Page 19 and 20:
16 CHAPTER 1. ALGEBRA REVIEW Trinom
Page 21 and 22:
18 CHAPTER 1. ALGEBRA REVIEW Here,
Page 23 and 24:
20 CHAPTER 1. ALGEBRA REVIEW (3x ?)
Page 25 and 26:
22 CHAPTER 1. ALGEBRA REVIEW which
Page 27 and 28:
24 CHAPTER 1. ALGEBRA REVIEW Differ
Page 29 and 30:
26 CHAPTER 1. ALGEBRA REVIEW If we
Page 31 and 32:
28 CHAPTER 1. ALGEBRA REVIEW 25) 8y
Page 33 and 34:
30 CHAPTER 1. ALGEBRA REVIEW Then,
Page 35 and 36:
32 CHAPTER 1. ALGEBRA REVIEW We can
Page 37 and 38:
34 CHAPTER 1. ALGEBRA REVIEW PROGRA
Page 39 and 40:
36 CHAPTER 1. ALGEBRA REVIEW In mov
Page 41 and 42:
38 CHAPTER 1. ALGEBRA REVIEW 1.4 Co
Page 43 and 44:
40 CHAPTER 1. ALGEBRA REVIEW devise
Page 45 and 46:
42 CHAPTER 1. ALGEBRA REVIEW −7i(
Page 47 and 48:
44 CHAPTER 1. ALGEBRA REVIEW Exerci
Page 49 and 50:
46 CHAPTER 1. ALGEBRA REVIEW 43) (3
Page 51 and 52:
48 CHAPTER 1. ALGEBRA REVIEW When w
Page 53 and 54:
50 CHAPTER 1. ALGEBRA REVIEW If we
Page 55 and 56:
52 CHAPTER 1. ALGEBRA REVIEW The fa
Page 57 and 58:
54 CHAPTER 1. ALGEBRA REVIEW 1.6 Mu
Page 59 and 60:
56 CHAPTER 1. ALGEBRA REVIEW the 4
Page 61 and 62:
58 CHAPTER 1. ALGEBRA REVIEW The sa
Page 63 and 64:
Page 65 and 66:
62 CHAPTER 1. ALGEBRA REVIEW 1.7 Ad
Page 67 and 68:
64 CHAPTER 1. ALGEBRA REVIEW 7 x 2
Page 69 and 70:
Page 71 and 72:
68 CHAPTER 1. ALGEBRA REVIEW 1.8 Co
Page 73 and 74:
Page 75 and 76:
72 CHAPTER 1. ALGEBRA REVIEW If a p
Page 77 and 78:
74 CHAPTER 1. ALGEBRA REVIEW Exampl
Page 79 and 80:
76 CHAPTER 1. ALGEBRA REVIEW As is
Page 81 and 82:
78 CHAPTER 1. ALGEBRA REVIEW 17) 5
Page 83 and 84:
80 CHAPTER 1. ALGEBRA REVIEW Addend
Page 85 and 86:
82 CHAPTER 1. ALGEBRA REVIEW 12) At
Page 87 and 88:
84 CHAPTER 1. ALGEBRA REVIEW 26) On
Page 89 and 90:
86 CHAPTER 1. ALGEBRA REVIEW 40) A
Page 91 and 92:
88 CHAPTER 2. POLYNOMIAL AND RATION
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
100 CHAPTER 2. POLYNOMIAL AND RATIO
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
140 CHAPTER 3. EXPONENTS AND LOGARI
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
190 CHAPTER 4. FUNCTIONS by substit
Page 195 and 196:
192 CHAPTER 4. FUNCTIONS 4.2 Domain
Page 197 and 198:
194 CHAPTER 4. FUNCTIONS Exercises
Page 199 and 200:
196 CHAPTER 4. FUNCTIONS 8) 12 10 8
Page 201 and 202:
198 CHAPTER 4. FUNCTIONS We can use
Page 203 and 204:
200 CHAPTER 4. FUNCTIONS 3) 20 16 1
Page 205 and 206:
202 CHAPTER 4. FUNCTIONS Vertical S
Page 207 and 208:
204 CHAPTER 4. FUNCTIONS Now, if, i
Page 209 and 210:
206 CHAPTER 4. FUNCTIONS So the gra
Page 211 and 212:
208 CHAPTER 4. FUNCTIONS Stretching
Page 213 and 214:
210 CHAPTER 4. FUNCTIONS Multiplyin
Page 215 and 216:
Page 217 and 218:
214 CHAPTER 4. FUNCTIONS 3) Match e
Page 219 and 220:
216 CHAPTER 4. FUNCTIONS 6) f(x) 7)
Page 221 and 222:
218 CHAPTER 4. FUNCTIONS Being fami
Page 223 and 224:
Page 225 and 226:
222 CHAPTER 4. FUNCTIONS 4.6 Piecew
Page 227 and 228:
Page 229 and 230:
226 CHAPTER 4. FUNCTIONS 4.7 Compos
Page 231 and 232:
228 CHAPTER 4. FUNCTIONS 17) h(x) =
Page 233 and 234:
230 CHAPTER 4. FUNCTIONS Original f
Page 235 and 236:
232 CHAPTER 4. FUNCTIONS Then we sw
Page 237 and 238:
234 CHAPTER 4. FUNCTIONS 19) f(x) =
Page 239 and 240:
236 CHAPTER 4. FUNCTIONS 4.9 Optimi
Page 241 and 242:
238 CHAPTER 4. FUNCTIONS 2) The gra
Page 243 and 244:
Page 245 and 246:
242 CHAPTER 4. FUNCTIONS 8) A recta
Page 247 and 248:
244 CHAPTER 4. FUNCTIONS So, our fi
Page 249 and 250:
Page 251 and 252:
248 CHAPTER 4. FUNCTIONS Distance O
Page 253 and 254:
250 CHAPTER 4. FUNCTIONS The graph
Page 255 and 256:
252 CHAPTER 4. FUNCTIONS Distance/T
Page 257 and 258:
254 CHAPTER 4. FUNCTIONS The graph
Page 259 and 260:
256 CHAPTER 4. FUNCTIONS 3) A power
Page 261 and 262:
258 CHAPTER 5. CONIC SECTIONS - CIR
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
288 CHAPTER 6. SEQUENCES AND SERIES
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
Page 309 and 310:
306 CHAPTER 7. COMBINATORICS differ
Page 311 and 312:
308 CHAPTER 7. COMBINATORICS Exampl
Page 313 and 314:
310 CHAPTER 7. COMBINATORICS 4) A c
Page 315 and 316:
312 CHAPTER 7. COMBINATORICS 7.2 Fa
Page 317 and 318:
314 CHAPTER 7. COMBINATORICS EXERCI
Page 319 and 320:
316 CHAPTER 7. COMBINATORICS 7.3 Pe
Page 321 and 322:
318 CHAPTER 7. COMBINATORICS EXERCI
Page 323 and 324:
320 CHAPTER 7. COMBINATORICS 7.4 Ge
Page 325 and 326:
322 CHAPTER 7. COMBINATORICS SET II
Page 327 and 328:
324 CHAPTER 7. COMBINATORICS 22) A
Page 329 and 330:
326 CHAPTER 7. COMBINATORICS 28) A
Page 331 and 332:
328 CHAPTER 7. COMBINATORICS Anothe
Page 333 and 334:
330 CHAPTER 7. COMBINATORICS Exerci
Page 335 and 336:
332 CHAPTER 7. COMBINATORICS The pr
Page 337 and 338:
334 CHAPTER 7. COMBINATORICS Exampl
Page 339 and 340:
336 CHAPTER 7. COMBINATORICS 4) Whe
Page 341 and 342:
338 CHAPTER 7. COMBINATORICS 14) Fo
Page 343 and 344: 340 CHAPTER 7. COMBINATORICS 34) A
Page 345 and 346: 342 CHAPTER 7. COMBINATORICS
Page 347 and 348: 344 CHAPTER 8. RIGHT TRIANGLE TRIGO
Page 387 and 388: 384 CHAPTER 9. GRAPHING THE TRIGONO
Page 393: 390 CHAPTER 9. GRAPHING THE TRIGONO
Page 441 and 442: 438 CHAPTER 10. TRIGONOMETRIC IDENT
Page 443 and 444: 440 CHAPTER 10. TRIGONOMETRIC IDENT
Page 445 and 446:
442 CHAPTER 10. TRIGONOMETRIC IDENT
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
472 CHAPTER 11. THE LAW OF SINES TH
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
Page 541 and 542:
Page 543 and 544:
Page 545 and 546:
Page 547 and 548:
Page 549 and 550:
Page 551 and 552:
Page 553 and 554:
Page 555 and 556:
Page 557 and 558:
show all

College Algebra & Trigonometry, 2018a

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?