Monthly Temperature The following data represent the average monthly temperatures for Phoenix, Arizona.

(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 fits 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 the scatter diagram.

Month, m ……………………………………..  Average Monthly Temperature, T

January, 1 ………………………………………………………..  51

February, 2………………………………………………………. 55

March, 3……………………………………………………….… 63

April, 4 ………………………………………………………….. 67

May, 5 …………………………………………………………... 77

June, 6 …………………………………………………………... 86

July, 7 ………………………………………………………….... 90

August, 8 ………………………………………………………... 90

September, 9 ……………………………………………………. 84

October, 10 ……………………………………………………... 71

November, 11 ………………………………………………….... 59

December, 12 …………………………………………………..... 52