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You could try to use the following method. $$y=a\sin \left[\dfrac{\pi}{12}x-b\right]+ c$$ $$=a\left[\sin \dfrac{\pi}{12}x \cos b - \sin b \cos \dfrac{\pi}{12}x \right] +c$$ $$=a\sin \dfrac{\pi}{12}x \cos b - a \sin b \cos \dfrac{\pi}{12}x +c$$ The last equation indicates that we can switch to new parameters $w_1 = a\cos b$, $w_2=-a\sin b$, and $w_0=c$. ...