The times S of sunset (Greenwich Mean Time) at 40° north latitude on the 15th of each month starting with January are: 16:59, 17:35, 18:06, 18:38, 19:08, 19:30, 19:28, 18:57, 18:10, 17:21, 16:44, and 16:36. A model (in which minutes have been converted to the decimal parts of an hour) for the data is
S (t) = 18.10 - 1.41 sin (πt / 6 + 1.55)
Where t represents the months, with t = 1 corresponding to January.
(a) Use a graphing utility to graph the data and the model in the same viewing window.
(b) What is the period of the model? Is it what you expected? Explain.
(c) What is the amplitude of the model? What does it represent in the context of the problem?