Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 60 degrees at midnight and the high and low temperature during the day are 73 and 47 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Question

D(t)=

Answer 1

since the period is 24 hours, k = 2π/24 = π/12
the amplitude is (73-47)/2 = 13
the center line is (73+47)/2 = 60
Note that since 60 is right on the center line, that means we have just a sine wave since sin(0) = 0
D(t) = 60 + 13 sin(π/12 t)