Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature for the day is 57 degrees and the low temperature of 43 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer 1

Assume y = m + Asin(k(t-h))
center line at (57+43)/2 = 50
y = 50+sin(k(t-h))

amplitude is (57-43)/2 = 7
y = 50+7sin(k(t-h))

minimum is at t=3, so
y = 50 - 7cos(k(t-3))

period is 24 hours, so 2π/k = 24
y = 50 - 7cos(π/12 (t-3))