SOLUTION: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day i

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Question 1156302: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day is 75 degrees. Find the temperature, to the nearest degree, at 9 AM.
Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.

The amplitude is 80-75 = 5 degrees.


The period is 24 hours.


We want represent the function as the sine function.

So, we will start the period at  (1/4)  of 24 hours before 5 pm.

Hence, the start for the period is 11 am.


Now the general formula is


    T(t) = 5*sin(2*pi*((t-11)/24)) + 75,


where t is the time (in hours) on the clock during the day in 24-hours military notation.



In particular, at t = 9 am the temperature is  


    T(9 am) = 5%2Asin%282%2Api%2A%28%289-11%29%2F24%29%29+%2B+75 = 5%2Asin%282%2Api%2A%28-2%2F24%29%29+%2B+75 = 5%2Asin%28pi%2A%28-4%2F24%29%29+%2B+75%29 = 5%2Asin%28-pi%2F6%29+%2B+75 =  


            = -5%2Asin%28pi%2F6%29+%2B+75 = -5%2A%281%2F2%29+%2B+75 = 75 - 2.5 = 72.5   degrees.       ANSWER

Solved.