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Using data from Time and Date AS, a Norwegian company, create a sinusoidal function f(t) = a sin(btc) + d to describe the mysterious variable in the data set. Show your work and (symbolic) formulas that you used making your calculations. Round your final calculations to two decimal places (like the data). You may decide to average some results, which is fine. TYPE YOUR RESULTS. Equilibrium Value/Vertical Shift 1. What is the maximum value of the variable? 15.99 On what day(s) of the year does the maximum occur? 170-173 2. What is the minimum value of the variable? 8.42 On what day(s) of the year does the minimum occur? 355-356 value of function 3. How is the equilibrium value related to the maximum and minimum values? 4. What is the equilibrium value of the variable? On what day(s) of the year does the equilibrium value occur? What is the equilibrium value of the untransformed sine function? What is the cal shift of the function? Amplitude 1. How is the amplitude related to the maximum, minimum, and equilibrium values? 2. What is the ampliitude of the function? Period 1. How is the period related to maximum values? How is the period related to minimum values? How is the period related to equilibrium values? In summary: how is the period related to the spacing between maximum, minimum, or equilibrium values? 2. What is the period of the function? Page 1 of 2
Horizontal shift 1. If this were an unshifted sine function, f(t) would start (t = 0) at... When does the first equilibrium value of the mysterious function occur? 2. If this were an unshifted sine function, the first max would occur at... When does the first max occur? 3. If this were an unshifted sine function, the second equilibrium value would occur at When does the second equilibrium value occur? 4. There is more than one possible calculation to determine the horizontal shift - equilibrium, maximum, or minimum values can be involved. What is the horizontal shift? 5. Use the horizontal shift and the period to calculate c. Putting it All Together Write f(t)= a sin(btc)+d with the values you founnd above.
Day of year 1 2 Variable 8.51 8.53 8.55 8.57 8.59 6:59 8.61 8.64 5.04 8.66 8.66 8.69 8.71 8.74 8.74 877 8.77 9 90 8.80 884 8.84 9.97 8.87 0.00 8.90 8.04 8.94 0.07 8.97 9.01 DIVA 9.05 3:09 9.09 9.13 9.17 9.21 9.25 0.20 9.30 DOL 9.34 0:30 9.39 9.43 9.48 31 9.53 25 32 9.57 3:37 33 9.62 P 34 9.67 630 35 9.72 077 36 9.77 *** 27 37 9.82 38 9.87 39 9.92 10 0.07 40 9.97 10.02 41 10.02 42 10.08 10.08 43 10 13 10.13 44 10.18 10.18 45 10.24 46 10.29 47 10.34 48 10.40 49 10.45 50 10.51 51 10.56 52 10.62 53 10.67 54 10.73 10.78 55 56 10.84 3 4 5 6 7 8 9 10 20 11 12 13 13 14 14 15 16 17 18 19 20 21 22 23 24 25 26 27 20 28 2 29 20 30 20 Values of a Mysterious Variable for Each Day of the Year in Seattle, WA Day of Variable Variable year Day of year 113 Day of year Day of Variable Day of year Variable Variable Day of 57 10.90 14.07 year 169 15.98 225 58 11.28 10.95 114 14.38 14.33 14.12 170 15.99 226 11.23 59 11.01 115 14.17 171 15.99 14.28 year 281 282 283 284 285 11.17 60 11.07 116 227 228 14.23 172 15.99 20 14.23 *** 11.11 61 117 11.12 117 * 14.28 173 15.99 229 14.18 **** 11.06 62 11.18 11.18 110 118 14.33 174 15.98 286 *100 63 11.00 110 11.24 230 231 14.12 14.07 119 14.38 **** 175 15.98 49:30 287 10.95 64 11.29 120 04 11.29 120 14.43 176 15.98 232 14.02 300 49:30 14.02 288 10.89 11 25 11.35 65 121 121 14.48 177 15.97 233 299 10.05 13.97 289 10.83 11.41 123 66 140 11.41 122 14.53 178 15.96 234 13.91 200 10.78 *** 290 11.47 10.78 12 *** 67 11.47 123 14.58 179 15.95 235 13.86 201 wwwww 10.72 291 *** 10.72 19.00 59 200 11.52 20 68 11.52 124 14.63 180 15.94 236 13.81 202 ** 10.67 292 400 10.67 19.01 N 11.58 2010 69 69 11.58 125 14.68 181 15.93 237 202 44:00 13.75 10.61 293 **** 19:15 10.61 11.63 70 11.64 126 14.73 182 15.92 238 204 13.70 15.70 10.56 10.56 *** 11.30 ATV 294 71 11.70 127 14.78 183 15.90 239 13.64 295 10 51 200 15.04 295 10.51 72 11.75 128 14.82 184 15.89 240 13.59 296 10.45 10.45 AP 2 www 240 73 11.81 129 14.87 185 15.87 241 13.53 297 10.40 200 20:07 15.55 10.40 297 74 11.87 130 14.91 186 15.85 242 13.48 298 BATO 10.34 298 242 100 75 11.93 131 14.96 187 15.83 243 299 13.43 299 10.29 CO 15.00 76 11.98 132 15.00 188 244 13.37 13.37 300 10.24 15.81 189 15.79 189 201 77 12.04 133 15.05 13.31 301 10.19 245 246 202 10 12 78 12.10 15.09 190 15.76 13.26 302 10.13 14:40 134 135 79 12.16 15.13 191 15.74 247 13.20 10.08 303 10.08 10.02 80 12.22 136 15.18 192 15.71 248 13.15 304 10.03 81 12.27 137 15.22 193 15.69 249 13.09 305 9.98 82 12.33 138 15.26 194 15.66 15.00 250 13.04 20:0 306 2:30 9.93 83 12.39 139 15.30 195 15.63 251 12.98 307 9.88 15:50 5000 *** 234 14:30 84 12.45 140 15.33 19:39 196 15.60 252 12.92 308 9.83 200 20:00 254 3:09 85 12.50 141 15.37 197 15.57 253 12.87 309 9.78 14:30 AMA 19:37 P ** 9.78 200 **Cor 86 12.56 12:30 142 15.41 198 15.54 254 12.81 12:01 402 310 310 9.73 P 87 12.62 143 15.44 199 15.50 255 12.76 19:30 24:02 311 *** 49 9.68 20 12.10 511 88 12.68 144 15.48 200 15.47 256 12.70 312 9.63 24,00 20 AO 400 20091 230 12.10 89 12.73 145 15.51 201 15.44 257 12.64 14:19 313 20 20:02 257 200 4300 9.58 12.64 90 12.79 146 15.55 202 15.40 258 12.59 314 14:15 AND 20:30 50€ 43:40 256 12.59 314 9.54 91 12.85 147 15.58 203 15.36 259 49:30 44:09 12.53 200 13:30 315 200 12.53 9.49 92 12.90 148 15.61 15.33 204 260 44:30 12.47 20:04 19:35 5 20 20% 260 316 12.47 9.44 93 12.96 149 15.64 15.29 205 261 12:30 12.42 20:09 200 15.29 261 2 12.42 317 9.40 94 13.02 A 150 15.67 19.02 206 15.25 0.35 20:07 262 12.36 M * 15.25 318 200 9.35 95 13.08 151 15.70 207 15.21 20:00 0.21 19.70 263 12.30 15.21 10 319 of 2 9.31 96 13.13 152 15.72 208 15.17 12.25 264 037 320 ***** 12.25 07 40 9.27 97 13.19 2 153 15.75 1940 209 19:15 15.13 265 Do A 321 12.19 9.22 *** 98 13.25 20:40 154 15.77 210 266 1233 15.08 49:77 S 240 266 12.13 322 9.18 200 00 99 100 155 15.80 211 257 15.04 49.00 12.08 211 267 12.08 323 9.14 200 13.30 13.36 100 13.36 12.41 101 13.41 156 15.82 3:34 212 268 13.03 20:04 15.00 *** 268 12.02 324 9.10 157 15.84 213 14.95 269 3:40 19.04 11.06 *** 269 14.99 11.96 325 9.06 102 13.47 158 15.86 214 49.60 14.91 11.00 270 ** 11.90 326 9.02 13.53 159 15.87 215 14.86 221 11.0 2:06 271 * 24:00 11.85 327 8.99 103 104 105 13.58 160 15.89 216 9:39 14.82 272 11.70 272 11.79 328 13.64 15.01 8.95 161 15.91 217 14.77 11.72 273 11.73 329 8.91 106 13.69 162 15.92 218 14.72 274 11.68 330 8.88 13.75 15.93 219 14.68 275 11.62 331 13.80 8.85 15.95 220 14.63 276 11.56 332 107 108 109 110 111 8.81 163 164 165 15.96 166 15.96 167 221 14.58 277 11.51 13.85 13.91 13.96 333 8.78 222 14.53 278 11.45 334 15.97 8.75 223 14.48 279 11.39 112 14.02 335 168 15.98 8.72 224 14.43 280 11.34 336 8.70 337 338 339 340 341 342 343 344 COM 345 CNC 346 M 347 20 348 * 349 are 350 ar 351 353 352 ara 353 274 354 arr 355 356 356 257 357 350 358 250 359 360 361 362 363 364 365 Variable 8.67 8.64 8.62 8.60 8.58 8.56 8.54 8.52 8.50 8.49 8.48 8.46 8.45 8.45 8.44 8.43 640 8.43 210 8.43 8.42 24 8.42 2.43 8.43 20 8.43 8.43 8.44 8.45 0.49 8.46 8.47 8.48 8.49