The following data represent the average monthly temperatures for Washington, D.C.

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

(b) Find a sinusoidal function of the form y = Asin(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.

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

January, 1 …………………………………………………………….. 34.6

February, 2 ……………………………………………………………. 37.5

March, 3 ………………………………………………………………. 47.2

April, 4 ………………………………………………………………… 56.5

May, 5 ………………………………………………………………….. 66.4

June, 6 ………………………………………………………………….. 75.6

July, 7  ………………………………………………………………….. 80.0

August, 8 ………………………………………………………………. 78.5

September, 9 …………………………………………………………… 71.3

October, 10 …………………………………………………………….. 59.7

November, 11 …………………………………………………………… 49.8

December, 12  …………………………………………………………… 39.4