Yahoo Answers 4-29-14

Trig - The average temperature monthly (in F) in Phoenix, Arizona is shown on the table. https://s.yimg.com/hd/answers/i/720b4171558747ecb9c43243bfc46c0b_A.png?a=answers&mr=0&x=1398816521&s=110d0b705c665f6489b7641e3ec5533a a. Predict the average yearly temperature. b. Plot the average monthly temperature over a two year period, letting x = 1 correspond to January of the first year. c. Determine a function of the forms f(x) = aCOS(b(x-d)) + c, where a, b, c, and d are constants, that models the data. d. Graph f together with the data on the data on the same coordinate axes. How well does f model the data? e. Use the sine regression capability of a graphing calculator to find the equation of a sine curve that fits these data (two years). a. The average will be 1/2 between the high and the low. (or 73.5) b. See chart c. aCOS(b(x-d))+c The average is what we need to add to the overall Cos function to shift it up (+c) the difference between high and low is 40 degrees (approx) so we need to multiply the whole function by 20 to account for the range (a) b affects the period, as b gets smaller the period gets longer. The distance from low point to low point (1 cycle) is 12 months. A normal period is 2*pi (call it 6). So we need to double the period. b=1/2 d moves the curve left or right. It needs to move a little more than half way to the left. Call it 5pi/4. f=20COS(1/2(x-5pi/2))+73.5 d and e See chart