Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Question

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 55 degrees and the low temperature of 35 degrees occurs at 5 AM.

Answer 1

D(t) = Asin(Bt + C) + E;

A = (55 - 35)/2 = 10°, E = (55 + 35)/2 = 45°; B = 2π/24 = π/12.

Now we have: D(t) = 10sin(πt/12 + C) + 45.

At 5 AM t = 5 and D(5) = 10sin(5π/12 + C) + 45 = 35; sin(5π/12 + C) = - 1; 5π/12 + C = 3π/2; C = 13π/12;

D(t)= 10sin(πt/12 + 13π/12) + 45 degrees