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Need Help with some Trig for a model (graph)

I attached a crude drawing of the function I'm trying to graph. I'm doing a problem with the model $\displaystyle \frac{dT}{dt}=k(T-T_m)$, where $\displaystyle T_m$ is a function shown in the graph, but I need help with the trigonometry here. Note that the graph I drew is sloppy, but you should be able to get the idea. It's just a transformed sine function.

$\displaystyle T_m(t)=asin(bt+c)+d$

The amplitude is a=30, and it's been moved up 80 units, so d=80. Since I know that b divides the normal period $\displaystyle 2\pi$ so that $\displaystyle \frac{2\pi}{b}=period$. The period appears to be 24, so I think the $\displaystyle b=\frac{\pi}{12}$. I'm kind of confused about what the phase shift should be though.