Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 95 degrees occurs at 3 PM and the average temperature for the day is 80 degrees. Find the temperature, to the nearest degree, at 8 AM

Answer 1

amplitude is (95-80)=15
center line is 80, so start with the assumption that the minimum occurs at midnight (0 hours):

y = -15cos(kx)+80

The function has a period of 24 hours, so 2?/k = 24, making k=?/12

y = -15cos(?/12 x) + 80

Now we know that the max occurs at x=15, not x=12, so we need to shift by 3:

y = -15cos(?/12 (x-3)) + 80

See the graph at

http://www.wolframalpha.com/input/?i=plot+-15cos(%CF%80%2F12+(x-3))+%2B+80++for+0%3C%3Dx%3C%3D24