Chapter 6.6, Problem 38AE

Hours of Daylight According to the Old Fanner's Alumnae, in Honolulu, Hawaii, the number of hours of sunlight on the summer solstice of 2015 was $13.42$, and the number of hours of sunlight on the winter solstice was $10.83$.

(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 Fanner's Almanac, and compare the actual hours of daylight to the results found in part $\left(b\right)$.