Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 67 and 83 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 71 degrees?

Answer 1

Explanation:

given that outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 67 and 83 degrees during the day and the average daily temperature first occurs at 8 AM.

Max = 83 and min = 67

Hence amplitude = 8,

At 8 am, temp = average = 75

So we can take 8 a.m. as 0 time

Period = 24 hours

Equation would be

T(t) = 75+8sin pi t/12

So when t =0 at 8 am. we have average temperature = 75

When T(t) = 71

we have sin pit/12 = -4/8

Or pit/12 = 11pi/6

t=22

i.e. at 8+22 = 6 a.m. the temperature would be 71 degrees.