The fraction of the moon illuminated at midnight Eastern Standard Time on dayt

of June, 2009 is given in the table below.

Day of June,t 3 6 9 12 15 18 21 24 27 30

Fraction Illuminated,F 0.81 0.97 0.98 0.83 0.57 0.27 0.04 0.03 0.26 0.58

a.

Fit a sinusoid to the given data.

b.

Using a graphing utility, graph your model along with the data set and explain the reasonableness of the fit.

c.

Use the model you found in part a. to predict the fraction of the moon illuminated on June 1, 2009.