Chapter 5.6, Problem 43AYU

Hours of Daylight According to the Old Farmer’s Almanac, in Anchorage, Alaska, the number of hours of sunlight on the summer solstice of $2018$ was $19.37$, and the number of hours of sunlight on the winter solstice was $5.45$.

Find a sinusoidal function of the form

$y=A\sin \left(\omega \chi -\varphi \right)+B$

that models the data

Use the function found in part (a) to predict the number of hours of sunlight on April $1$ the $91\text{st}$ day of the year.

Draw a graph of the function bound in pan (a).

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 (b).