Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 100 degrees occurs at 4 PM and the average temperature for the day is 80 degrees. Find the temperature, to the nearest degree, at 7 AM.
Max is 100, average is 80.
so the variation of this sine function is 20 degrees in either direction from the mean=80.
So fitting this data onto the interval [pi/2, 3*pi/2]. max heat of the day at 4 pm where sine is 1
sunrise at 7 am where temperature begins to rise where sine is -1.
The sinusoidal wave can be represented by the
where, A is the amplitude; ω=2π/period, ω=2π/period; α=α= phase shift on the Y-axis; and C = midline.
Given C=80, A=20, period =24, a=10, x=7
On solving,the temperature, to the nearest degree, at 7 AM is 79.72
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