The number of minutes after noon, Eastern Standard Time, that the sun sets in Boston for specific days of the year is approximated in the following table.

(a) Plot the data. Is it reasonable to assume that the times of sunset are periodic?
(b) Use a calculator with trigonometric regression to find a trigonometric function of the form s(t) = a sin(bt + c) + d that models these data when t is the day of the year and s(t) is the number of minutes past noon, Eastern Standard Time, that the sun sets.
(c) Estimate the time of sunset for days 60, 120, 240. Round answers to the nearest minute.

(d) Use part (b) to estimate the days of the year that the sun sets at 6:00 _P.M. In reality, the days are close to 82 and 290.

Transcribed Image Text:

Day of the Year 21 52 81 112 142 173 203 234 265 295 326 356 Sunset (minutes after noon) 283 323 358 393 425 445 434 396 343 292 257 255