Chapter 6.6, Problem 36AE

Hours of Daylight According to the Old Farmer's Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice of 2015 was $15.27$, and the number of hours of sunlight on the winter solstice was $9.07$.

(a) Find a sinusoidal function of the form $y=A\sin (\omega x-\varphi )+B$ that models the data.

(b) Use the function found in part $\left(a\right)$ to predict the number of hours of sunlight on April 1, the 91st day of the year.

(c) Draw a graph of the function found in part $\left(a\right)$.

(d) Look up the number of hours of sunlight for April 1 in the Old Farmer’s Almanac, and compare the actual hours of daylight to the results found in part $\left(b\right)$.