The monthly average temperatures for a city are given in the following table:

Month 1 2 3 4 5 6 7 8 9 10 11 12

Temperature (F) 29 38 50 64 73 75 72 63 51 39 28 26

(a) Find a function of the form y = A sin(Bx C) + D that roughly fits this data. Note that the given data is not perfectly sinusoidal and so you will have to make some assumptions or approximations in order to find your function, just be sure to clearly explain each step in your process for how you can find A, B, C, and D.

(b) On the same set of axes, draw the function that you found in part a and also plot the 12 given points in the table above to make sure that your function approximately matches your data.