Posted by Doug on .
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.

Math 
drwls,
The sum of the length of the longest day and the shortest day should be 24 hours. The mean has to be 12.
Assuming instead that the numbers are 7 and 18, as your problem states, the formula would be
D (daylight hours) =
12.5 + 5.5 sin (2 pi t/365)
where t is measured in days from the vernal equinox (June 21 in the northern hemisphere)
If you want to measure t from January 1, you will have to do a transformation and include a cosine term 
Math (correction) 
drwls,
The formula I gave is correct, but the vernal equinox (from which t is measured) is March 21.