Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 70 degrees at midnight and the high and low temperature during the day are 83 and 57 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
well 70 is halfway between 57 and 83,
so we are talking 70 + or - 13
if it is zero at 0 , midnight, it better drop to 57 in a quarter of a day, 6 hours
so try
D = 70 - 13 sin (2 pi t /24)