SOLUTION: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 94 degrees occurs at 6 PM and the average temperature for the day i
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Question 1176527: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 94 degrees occurs at 6 PM and the average temperature for the day is 75 degrees. Find the temperature, to the nearest degree, at 7 AM.
--- degrees Answer by greenestamps(13200) (Show Source):
A high temperature of 94 and an average temperature of 75 means the amplitude is 94-75=19 and the midline is 75.
The basic cosine function is at its maximum value at t=0; since we are given that the maximum temperature is at 6pm, we can model the temperature with a cosine function in which t=0 at 6pm.
t is 0 at 6pm; the period of the cosine function is 2pi. A time of 7am is 13 hours after 6pm, so a time of 7am is represented by an angle of 13/24 time 2pi, or 13/12 times pi.
