Posted by **Doug** on Monday, September 28, 2009 at 10:51pm.

The number of daylight hours in a day is harmonic. Suppose that in a particular location, the shortest day of the year has 7 hours of daylight and the longest day of the year has 18 hours. Then, we can model its motion with the function N=Asin(Bt) + C where t is expressed in days and A, B > 0. Find A and B, using 365 days for one year.

I need to find what A, B, and C equal. Thanks.

- Trigonometry -
**MathMate**, Tuesday, September 29, 2009 at 8:09am
In the equation:

N=Asin(Bt) + C

A represents half of the difference between the maximum and minimum, sometimes called amplitude.

B is a multiplitive factor to ensure that the cycle of sine (2π) fits into the physical cycle, in this problem, 365 days.

Since the amplitude of daylight hours is (18-7)/2=5.5, we obtain A=5.5.

We need a value of B such that when t=0 and t=365, Bt becomes 0 and 2π.

So 365B = 2π, or B=2π/365.

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