Hours of daylight Refer to Exercise 61. The maximum number of daylight hours at 40°N i...

Hours of daylight

Refer to Exercise 61. The maximum number of daylight hours at 40°N is 15.02 hours and occurs on June 21. The minimum number of daylight hours is 9.32 hours and occurs on December 22.

(a) Determine a function D(t) = a sin (bt + c) + d that models the number of daylight hours, where t is in months t = 1 and corresponds to January 1.

(b) Graph the function D using the viewing rectangle by [0.5, 24.5, 4] by [0, 20, 4].

(c) Predict the number of daylight hours on February 1 and September 1. Compare your answers to the true values of 10.17 and 13.08 hours, respectively.

Reference of Exercise 61:

Hours of daylight

The number of daylight hours D at a particular location varies with both the month and the latitude. The table lists the number of daylight hours on the first day of each month at 60°N latitude.

(a) Let t be time in months, with t = 1 corresponding to January, t = 2 to February, . . . , t = 12 to December, t = 13 to January, and so on. Plot the data for a two year period.

(b) Find a function D(t) = a sin (bt + c) + d that approximates the number of daylight hours. Graph the function D with the data.