Question 1176031: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 96 degrees occurs at 4 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 7 AM.
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
Outside temperature over a day can be modeled as a sinusoidal function.
Suppose you know the high temperature of 96 degrees occurs at 4 PM and
the average temperature for the day is 85 degrees.
Find the temperature, to the nearest degree, at 7 AM.
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Our 24-hour cycle of the daily temperature change starts at 4 pm, when the temperature is maximal.
So, our sinusoidal function is, actually, the cosine function, if to start counting time from 4 pm = 16:00, or
T(t) =  + 
where "t" is the local astronomic time in the 24-hours "military" time scale in your watch.
At 7 am next day, we have  of the full cycle elapsed.
It corresponds to  on the unit circle, and  = -  .
So, the temperature at 7 am next day will be
 =  = 85° - 0.707*11° = 77.2°.
ANSWER. We can expect 77.2°, or 77° rounded at 7 am next day.
Solved.
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