The following data represent the average monthly temperatures for Indianapolis, Indiana.

Month, x …………………………….. Average Monthly Temperature, ˚F

January, 1 …………………………………………………………….. 25.5

February, 2 ……………………………………………………………. 29.6

March, 3 ………………………………………………………………. 41.4

April, 4 ………………………………………………………………… 52.4

May, 5 ………………………………………………………………….. 62.8

June, 6 ………………………………………………………………….. 71.9

July, 7  ………………………………………………………………….. 75.4

August, 8 ………………………………………………………………. 73.2

September, 9 …………………………………………………………… 66.6

October, 10 …………………………………………………………….. 54.7

November, 11 …………………………………………………………… 43.0

December, 12  …………………………………………………………… 30.9

(a) Draw a scatter diagram of the data for one period.

(b) Find a sinusoidal function of the form y = A sin(ωx – ϕ) + B that models the data.

(c) Draw the sinusoidal function found in part (b) on the scatter diagram.

(d) Use a graphing utility to find the sinusoidal function of best fit.

(e) Graph the sinusoidal function of best fit on a scatter diagram of the data.