Question

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.

Answer 1

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 equation:y=A∗sin[ω(x−α)]+Cy=A∗sin[ω(x−α)]+C
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

y=20∗sin[2π/24(7−10)]+80

On solving,the temperature, to the nearest degree, at 7 AM is 79.72