College Trigonometry, 2011a

More documents

Recommendations

Info

viii Table of Contents 11.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916 11.3.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918 11.4 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 11.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 930 11.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932 11.5 Graphs of Polar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938 11.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958 11.5.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963 11.6 Hooked on Conics Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973 11.6.1 Rotation of Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973 11.6.2 The Polar Form of Conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 981 11.6.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986 11.6.4 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987 11.7 Polar Form of Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 991 11.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004 11.7.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007 11.8 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 11.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027 11.8.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1031 11.9 The Dot Product and Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034 11.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043 11.9.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045 11.10 Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048 11.10.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 11.10.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063 Index 1069
Preface Thank you for your interest in our book, but more importantly, thank you for taking the time to read the Preface. I always read the Prefaces of the textbooks which I use in my classes because I believe it is in the Preface where I begin to understand the authors - who they are, what their motivation for writing the book was, and what they hope the reader will get out of reading the text. Pedagogical issues such as content organization and how professors and students should best use a book can usually be gleaned out of its Table of Contents, but the reasons behind the choices authors make should be shared in the Preface. Also, I feel that the Preface of a textbook should demonstrate the authors’ love of their discipline and passion for teaching, so that I come away believing that they really want to help students and not just make money. Thus, I thank my fellow Preface-readers again for giving me the opportunity to share with you the need and vision which guided the creation of this book and passion which both Carl and I hold for Mathematics and the teaching of it. Carl and I are natives of Northeast Ohio. We met in graduate school at Kent State University in 1997. I finished my Ph.D in Pure Mathematics in August 1998 and started teaching at Lorain County Community College in Elyria, Ohio just two days after graduation. Carl earned his Ph.D in Pure Mathematics in August 2000 and started teaching at Lakeland Community College in Kirtland, Ohio that same month. Our schools are fairly similar in size and mission and each serves a similar population of students. The students range in age from about 16 (Ohio has a Post-Secondary Enrollment Option program which allows high school students to take college courses for free while still in high school.) to over 65. Many of the “non-traditional” students are returning to school in order to change careers. A majority of the students at both schools receive some sort of financial aid, be it scholarships from the schools’ foundations, state-funded grants or federal financial aid like student loans, and many of them have lives busied by family and job demands. Some will be taking their Associate degrees and entering (or re-entering) the workforce while others will be continuing on to a four-year college or university. Despite their many differences, our students share one common attribute: they do not want to spend $200 on a College Algebra book. The challenge of reducing the cost of textbooks is one that many states, including Ohio, are taking quite seriously. Indeed, state-level leaders have started to work with faculty from several of the colleges and universities in Ohio and with the major publishers as well. That process will take considerable time so Carl and I came up with a plan of our own. We decided that the best way to help our students right now was to write our own College Algebra book and give it away electronically for free. We were granted sabbaticals from our respective institutions for the Spring
Page 1 and 2: College Trigonometry Version ⌊π
Page 3: Table of Contents vii 10 Foundation
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 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 27 and 28: 10.1 Angles and their Measure 711 I
Page 33 and 34: 10.2 The Unit Circle: Cosine and Si
Page 53 and 54: 30 ◦ 1 10.2 The Unit Circle: Cosi
Page 55 and 56:
10.2 The Unit Circle: Cosine and Si
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:
Page 93 and 94:
Page 95 and 96:
10.4 Trigonometric Identities 779 T
Page 97 and 98:
10.4 Trigonometric Identities 781 R
Page 99 and 100:
Page 101 and 102:
10.4 Trigonometric Identities 785 I
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
10.5 Graphs of the Trigonometric Fu
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:
10.6 The Inverse Trigonometric Func
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
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:
10.7 Trigonometric Equations and In
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:
Page 195 and 196:
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?