College Trigonometry, 2011a

More documents

Recommendations

Info

828 Foundations of <strong>Trigonometry</strong> Theorem 10.28. Properties of the Arcsecant and Arccosecant Functions a ˆ Properties of F (x) = arcsec(x) – Domain: {x : |x| ≥1} =(−∞, −1] ∪ [1, ∞) – Range: [ 0, π ) ( 2 ∪ π 2 ,π] – as x →−∞, arcsec(x) → π + 2 ;asx →∞, arcsec(x) → π − 2 – arcsec(x) =t ifandonlyif0≤ t< π 2 or π 2
10.6 The Inverse Trigonometric Functions 829 Solution. 1. (a) Using Theorem 10.28, we have arcsec(2) = arccos ( ) 1 2 = π 3 . (b) Once again, Theorem 10.28 comes to our aid giving arccsc(−2) = arcsin ( − 1 2) = − π 6 . (c) Since 5π 4 doesn’t fall between 0 and π 2 or π 2 and π, we cannot use the inverse property stated in Theorem 10.28. We can, nevertheless, begin by working ‘inside out’ which yields arcsec ( sec ( )) √ ( √ ) 5π 4 = arcsec(− 2) = arccos − 2 2 = 3π 4 . (d) One way to begin to simplify cot (arccsc (−3)) is to let t = arccsc(−3). Then, csc(t) =−3 and, since this is negative, we have that t lies in the interval [ − π 2 , 0) . We are after cot (arccsc (−3)) = cot(t), so we use the Pythagorean Identity 1 + cot 2 (t) = csc 2 (t). Substituting, we have 1 + cot 2 (t) =(−3) 2 , or cot(t) =± √ 8=±2 √ 2. Since − π 2 ≤ t
Page 1 and 2:
College Trigonometry Version ⌊π
Page 3 and 4:
Table of Contents vii 10 Foundation
Page 5 and 6:
Preface Thank you for your interest
Page 7 and 8:
xi text and we have gone to great l
Page 9 and 10:
Chapter 10 Foundations of Trigonome
Page 11 and 12:
10.1 Angles and their Measure 695 k
Page 13 and 14:
10.1 Angles and their Measure 697 2
Page 15 and 16:
Page 17 and 18:
10.1 Angles and their Measure 701 T
Page 19 and 20:
10.1 Angles and their Measure 703 y
Page 21 and 22:
10.1 Angles and their Measure 705 y
Page 23 and 24:
10.1 Angles and their Measure 707 h
Page 25 and 26:
Page 27 and 28:
10.1 Angles and their Measure 711 I
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
10.2 The Unit Circle: Cosine and Si
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
30 ◦ 1 10.2 The Unit Circle: Cosi
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
10.3 The Six Circular Functions and
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
10.4 Trigonometric Identities 771 f
Page 89 and 90:
10.4 Trigonometric Identities 773 2
Page 91 and 92:
10.4 Trigonometric Identities 775 3
Page 93 and 94: 10.4 Trigonometric Identities 777 2
Page 95 and 96: 10.4 Trigonometric Identities 779 T
Page 97 and 98: 10.4 Trigonometric Identities 781 R
Page 101 and 102: 10.4 Trigonometric Identities 785 I
Page 107 and 108: 10.5 Graphs of the Trigonometric Fu
Page 135 and 136: 10.6 The Inverse Trigonometric Func
Page 143: 10.6 The Inverse Trigonometric Func
Page 173 and 174: 10.7 Trigonometric Equations and In
Page 195 and 196:
10.7 Trigonometric Equations and In
Page 197 and 198:
Chapter 11 Applications of Trigonom
Page 199 and 200:
11.1 Applications of Sinusoids 883
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
11.2 The Law of Sines 897 minimizes
Page 215 and 216:
11.2 The Law of Sines 899 a angle-s
Page 217 and 218:
11.2 The Law of Sines 901 determine
Page 219 and 220:
11.2 The Law of Sines 903 Let x den
Page 221 and 222:
11.2 The Law of Sines 905 24. Along
Page 223 and 224:
11.2 The Law of Sines 907 33. The a
Page 225 and 226:
11.2 The Law of Sines 909 25. (a)
Page 227 and 228:
11.3 The Law of Cosines 911 of B ar
Page 229 and 230:
11.3 The Law of Cosines 913 the pre
Page 231 and 232:
11.3 The Law of Cosines 915 A 2 = =
Page 233 and 234:
11.3 The Law of Cosines 917 22. A n
Page 235 and 236:
11.4 Polar Coordinates 919 11.4 Pol
Page 237 and 238:
11.4 Polar Coordinates 921 The poin
Page 239 and 240:
11.4 Polar Coordinates 923 4. We mo
Page 241 and 242:
11.4 Polar Coordinates 925 Solution
Page 243 and 244:
11.4 Polar Coordinates 927 Solution
Page 245 and 246:
11.4 Polar Coordinates 929 algebrai
Page 247 and 248:
11.4 Polar Coordinates 931 45. ( )
Page 249 and 250:
11.4 Polar Coordinates 933 5. ( 12,
Page 251 and 252:
11.4 Polar Coordinates 935 13. (
Page 253 and 254:
11.4 Polar Coordinates 937 73. r =7
Page 255 and 256:
11.5 Graphs of Polar Equations 939
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
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:
11.6 Hooked on Conics Again 973 11.
Page 291 and 292:
11.6 Hooked on Conics Again 975 Exa
Page 293 and 294:
11.6 Hooked on Conics Again 977 The
Page 295 and 296:
11.6 Hooked on Conics Again 979 We
Page 297 and 298:
Page 299 and 300:
11.6 Hooked on Conics Again 983 The
Page 301 and 302:
11.6 Hooked on Conics Again 985 In
Page 303 and 304:
Page 305 and 306:
11.6 Hooked on Conics Again 989 2 9
Page 307 and 308:
11.7 Polar Form of Complex Numbers
Page 309 and 310:
Page 311 and 312:
Page 313 and 314:
Page 315 and 316:
Page 317 and 318:
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
11.8 Vectors 1013 Q ′ (1, 7) up 4
Page 331 and 332:
11.8 Vectors 1015 ⃗v + ⃗w = 〈
Page 333 and 334:
11.8 Vectors 1017 ⃗v − ⃗w =
Page 335 and 336:
11.8 Vectors 1019 The remaining pro
Page 337 and 338:
11.8 Vectors 1021 ‖k⃗v‖ = ‖
Page 339 and 340:
11.8 Vectors 1023 at the origin, th
Page 341 and 342:
11.8 Vectors 1025 Geometrically, th
Page 343 and 344:
11.8 Vectors 1027 11.8.1 Exercises
Page 345 and 346:
11.8 Vectors 1029 44. ⃗v = 〈−
Page 347 and 348:
11.8 Vectors 1031 11.8.2 Answers 1.
Page 349 and 350:
11.8 Vectors 1033 47. ‖⃗v‖ =2
Page 351 and 352:
11.9 The Dot Product and Projection
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
11.10 Parametric Equations 1049 obj
Page 367 and 368:
11.10 Parametric Equations 1051 2.
Page 369 and 370:
11.10 Parametric Equations 1053 Now
Page 371 and 372:
Page 373 and 374:
11.10 Parametric Equations 1057 Our
Page 375 and 376:
Page 377 and 378:
11.10 Parametric Equations 1061 Sup
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Index n th root of a complex number
Page 387 and 388:
Index 1071 central angle, 701 chang
Page 389 and 390:
Index 1073 reflective property, 523
Page 391 and 392:
Index 1075 matrix, multiplicative,
Page 393 and 394:
Index 1077 midpoint definition of,
Page 395 and 396:
Index 1079 instantaneous, 161, 472
Page 397 and 398:
Index 1081 inconsistent, 553 indepe
show all

College Trigonometry, 2011a

Create successful ePaper yourself

Delete template?

Save as template?