help me and explain clear its due in a hour

Question

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the temperature varies between 46 and 74 degrees during the day and the average daily temperature first occurs at 9 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

 = 

Answer 1

David is nearly correct. You need to add 60 (the average) to his expression because we need D to be 60 when t=9.

Also the cycle repeats every 24 hours, so 24 hours is the period. The coefficient of (t-9) is always (2 pi / period).

Answer 2

It usually helps to draw a picture.

The temperature ranges from 46 to 74 degrees with an average of 60 degrees, which occurs at 9am.

The time starts at midnight, and goes through one cycle in the next 24 hrs. So, subtract 9 from t, then make it a fraction that goes from 0 to 2Π.

D = sin ( ( (t-9)/24)*2*3.14 ) + 60

or

D = sin ( (t-9) * 0.26 ) + 60