Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 64 and 26 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.\

Answer 1

Answer:

$D = 45+19*sin(\frac{\pi}{12}*t)$

Step-by-step explanation:

The amplitude (A) and the mean (M) temperature are given by:

$A=\frac{64-26}{2}\\ A= 19\\M=\frac{64+26}{2}\\ M= 45$

The mean temperature, 45 degrees. occurs at midnight (t=0) and the frequency is f=24h. Therefore, the temperature D, in degrees, as a function of t, in hours, is:

$D = M+A*sin(\frac{2\pi}{24}*t)\\D = 45+19*sin(\frac{\pi}{12}*t)$