Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 54 and 36 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answer 1

D = 9sin(2π(t + a)/24) + 45

Explanation:

Let's find the average temperature;

(54 + 36)/2 = 45°

Amplitude = 54 - 45 = 9

From the wave equation, we can write the temperature as;

D = 9sin(2π(t + a)/24) + 45

Where;

D is the temperature

t is the time in hours after midnight

a is a "phase" that is used to set the time at which temperature(D) occurs