Question

Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 75 degrees at midnight and the high and low temperature during the day are 87 and 63 degrees, respectively. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.

Answer 1

We presume the temperature is decreasing at midnight, so reaches a low at 6 a.m.. The amplitude of the variation is (87-63)/2 = 12 degrees. We want the period to be 24 hours, so the argument of the sine function will be 2π(t/24) = πt/12. Then we can write

... d = 75-12sin(π·t/12)