Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature of 60 degrees occurs at 3 PM and the average temperature for the day is 45 degrees. 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 (60+45)/2 = 52.5
y = 52.5+sin(k(t-h))

amplitude is (60-45)/2 = 7.5
y = 52.5+7.5sin(k(t-h))

minimum is at t=15 which is 3PM, so
y = 52.5 - 7.5cos(k(t-15))

period is 24 hours, so 2π/k = 24
y = 52.5 - 7.5cos(π/12 (t-15))