Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 67 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer 1

the amplitude is 67-60, so start with
D(t) = 60 + 7 sin(t)
Since the period is 24 hours,
D(t) = 60 + 7 sin(π/12 t)
Since the high occurs at t=17, use cosine, instead of sine.
D(t) = 60 + 7 cos(π/12 (t-17))