Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 85 degrees occurs at 6 PM and the average temperature for the day is 65 degrees. Find the temperature, to the nearest degree, at 9 AM.

Answer 1

(max + min)/2 = avg
(85+min)/2 = 65
min = 45
amplitude = 20
period is 24 hours,
24 = 2π/k, k = π/12

start with t = 0 representing midnight, and the temp would logically
start to decrease from there.
temp = -20sin (π/12 t) + 65 would be a good start

For this equation the max happens when t = 18 ,(6 pm)
which is what we want

so at 9:00 am, t = 9
temp = -20sin(π/12(9)) + 65
= 50.9°