College Trigonometry, 2011a

More documents

Recommendations

Info

1076 Index perpendicular, 167 point-slope form, 155 slope of, 151 slope-intercept form, 155 vertical, 23 linear equation n variables, 554 two variables, 549 linear function, 156 local maximum formal definition of, 102 intuitive definition of, 101 local minimum formal definition of, 102 intuitive definition of, 101 logarithm algebraic properties of, 438 change of base formula, 442 common, 422 general, “base b”, 422 graphical properties of, 423 inverse properties of, 437 natural, 422 one-to-one properties of, 437 solving equations with, 459 logarithmic scales, 431 logistic growth, 475 LORAN, 538 lower triangular matrix, 593 main diagonal, 585 major axis of an ellipse, 516 Markov Chain, 592 mathematical model, 60 matrix addition associative property, 579 commutative property, 579 definition of, 578 properties of, 579 additive identity, 579 additive inverse, 579 adjoint, 622 augmented, 568 characteristic polynomial, 626 cofactor, 616 definition, 567 determinant definition of, 614 properties of, 616 dimension, 567 entry, 567 equality, 578 invertible, 602 leading entry, 569 lower triangular, 593 main diagonal, 585 matrix multiplication associative property of, 585 definition of, 584 distributive property, 585 identity for, 585 properties of, 585 minor, 616 multiplicative inverse, 602 product of row and column, 584 reduced row echelon form, 570 rotation, 986 row echelon form, 569 row operations, 568 scalar multiplication associative property of, 581 definition of, 580 distributive properties, 581 identity for, 581 properties of, 581 zero product property, 581 size, 567 square matrix, 586 sum, 578 upper triangular, 593 maximum formal definition of, 102 intuitive definition of, 101 measure of an angle, 693
Index 1077 midpoint definition of, 12 midpoint formula, 13 minimum formal definition of, 102 intuitive definition of, 101 minor, 616 minor axis of an ellipse, 516 model mathematical, 60 modulus of a complex number definition of, 991 properties of, 993 multiplicity effect on the graph of a polynomial, 245, 249 of a zero, 244 natural base, 420 natural logarithm, 422 natural number definition of, 2 set of, 2 negative angle, 698 Newton’s Law of Cooling, 421, 474 Newton’s Law of Universal Gravitation, 351 oblique asymptote, 311 obtuse angle, 694 odd function, 95 Ohm’s Law, 350, 605 one-to-one function, 381 ordered pair, 6 ordinary frequency, 708 ordinate, 6 orientation, 1048 oriented angle, 697 oriented arc, 704 origin, 7 orthogonal projection, 1038 orthogonal vectors, 1037 overdetermined system, 554 parabola axis of symmetry, 191 definition of, 505 directrix, 505 focal diameter, 507 focal length, 506 focus, 505 from slicing a cone, 496 graph of a quadratic function, 188 latus rectum, 507 reflective property, 510 standard equation horizontal, 508 vertical, 506 vertex, 188, 505 vertex formulas, 194 paraboloid, 510 parallel vectors, 1030 parameter, 1048 parametric equations, 1048 parametric solution, 552 parametrization, 1048 partial fractions, 628 Pascal’s Triangle, 688 password strength, 477 period circular motion, 708 of a function, 790 of a sinusoid, 881 periodic function, 790 pH, 432 phase, 795, 881 phase shift, 795, 881 pi, π, 700 piecewise-defined function, 62 point of diminishing returns, 477 point-slope form of a line, 155 polar coordinates conversion into rectangular, 924 definition of, 919 equivalent representations of, 923 polar axis, 919 pole, 919
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:
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 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 373 and 374: 11.10 Parametric Equations 1057 Our
Page 377 and 378: 11.10 Parametric Equations 1061 Sup
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: Index 1075 matrix, multiplicative,
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?