The following data represent the average monthly temperatures for Baltimore, Maryland.

(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.

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

January, 1 …………………………………………………………….. 31.8

February, 2 ……………………………………………………………. 34.8

March, 3 ………………………………………………………………. 44.1

April, 4 ………………………………………………………………… 53.4

May, 5 ………………………………………………………………….. 63.4

June, 6 ………………………………………………………………….. 72.5

July, 7  ………………………………………………………………….. 77.0

August, 8 ………………………………………………………………. 75.6

September, 9 …………………………………………………………… 68.5

October, 10 …………………………………………………………….. 56.6

November, 11 …………………………………………………………… 46.8

December, 12  …………………………………………………………… 36.7