https://answers.yahoo.com/question/index?qid=20140409164816AA8AFq8
1) The normal mean air temperatures for Fairbanks Alaska is given by the function
f(x)= 37sin [2pi/365 (x-101)] + 25 "f' is temp in degrees
Fahrenheit and x is the number of the day counting from the beginning of the year.
a) Determine the mean temperature for June 30.
b) Determine the date(s) that the mean temperature is 40 degrees F.
June 30 is the 181st day of the year.
For part A, insert that into the formula.
For part B, solve for the sin first: 40=37 sin +25
15=37 sin
sin=15/35
Now take the arcsin of 15/35 (make sure you're using radians)
That lovely expression = 0.4429
Multiply by 365/2pi
x-101=25.7
x=126.7 call it 127 which is May 7 but there will be one more day (It's going up to the peak and there should be one on the way back down)
That lovely expression will also equal pi-0.4429=2.6987 (remember your reference angles?)
Multiply by 365/2pi
x-101=157
x=258 which is Sept. 15