The following data represent the average monthly temperatures for Juneau, Alaska.

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

January, 1 …………………………………………………………….. 24.2

February, 2 ……………………………………………………………. 28.4

March, 3 ………………………………………………………………. 32.7

April, 4 ………………………………………………………………… 39.7

May, 5 ………………………………………………………………….. 47.0

June, 6 ………………………………………………………………….. 53.0

July, 7  ………………………………………………………………….. 56.0

August, 8 ………………………………………………………………. 55.0

September, 9 …………………………………………………………… 49.4

October, 10 …………………………………………………………….. 42.2

November, 11 …………………………………………………………… 32.0

December, 12  …………………………………………………………… 27.1

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