pre calc help please

Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 72 degrees occurs at 3 PM and the average temperature for the day is 55 degrees. Find the temperature, to the nearest degree, at 11 AM.

Answer 1

°Lowest temperature is 2·55 - 72 = 38°. Then temperature T = 17°°sin(π/6t) + 55.

At 11AM time t = -1, because we count time from 12PM. SO, T = 17sin(-π/6) + 55 = - 8.5 + 55 = 46.5°