Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 55 degrees at midnight and the high and low temperature during the day are 62 and 48 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer 1

the period is 24 hours, so if the minimum occurs at time h hours after 12:00, so start with something like
D = -cos(π/12 (t-h))
the amplitude is (62-48)/2 = 7
the central axis is (62+48)/2 = 55
aha! we see that D(0) is the minimum, so h=0.
we can revise our function to
D = 55 - 7cos(π/12 t)
there is no horizontal shift