Chapter 5.4, Problem 36E

Let S (t) be the number of daylight hours on the t th day of the year 2012 in Rome, Italy. We are given the following data for S(t):

We wish to fit a trigonometric function of the form
$f\left(t\right)=a+b\sin \left(\frac{2\pi }{366}t\right)+c\cos \left(\frac{2\pi }{366}t\right)$
to these data. Find the best approximation of this form, using least squares.How many daylight hours does your model predict for the longest day of the year 2012? (The actualvalue is 15 hours, 13 minutes, 39 seconds.)