Posted by **Doug** on Monday, September 28, 2009 at 11:07pm.

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**, Monday, September 28, 2009 at 11:20pm
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**, Monday, September 28, 2009 at 11:22pm
The formula I gave is correct, but the vernal equinox (from which t is measured) is March 21.

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