Find the answer in degrees.

Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 68 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 8 AM.

Answer 1

The amplitude is 68-60 = 8 and the vertical offset is +60. We want the maximum of the sine function to occur at 5pm = 17:00 hours, which is 1/4 of a day (6 hours) after time zero when the function = 0, so the fraction of a day elapsed after 11:00 is frac = (t - 11)/24. This gives us T(t) = 8 sin(2π•frac) + 60. Put calculator in RADIANS mode!! T(8) = 8 sin(2π•(-0.125)) + 60 = 54 degrees.