Help with sinusoidal function rule

Tthis is a sinusoidal function and the following information is given, the lenght of a day was 12 hours on may 1st

The length of a day kept going up until it reached its max at 15 hours and 30 mins. It then continued going down until its minimum at 8 hours and 30mins. It finally went back up to 12 hours on may 1st. What is the function rule?

Thanks

Re: Help with sinusoidal function rule

Let May 1 correspond with $\displaystyle x = 0$ and $\displaystyle x = 365$. The "amplitude" is 3.5 hours. Hence our equation could look something like

$\displaystyle f(x) = 12 + 3.5 \sin {\frac{x}{365}}$