> I was attempting to work out what the result of
> 
>   A sin t + B cos t
> 
> is. I was convinced there was a standard identity for this, but I can't 
> find it. In the end I came up with
> 
>   Sqrt(A^2 + B^2) sin (t + atan(B/A))
> 
> but I don't even know if that's correct. And I still have to apply it to 
> my original formula to figure out the result.

I think...

a*sin(t) + b*cos(t) = sqrt(a^2+b^2)*cos(t-atan(a/b))

notice that yours was reciprocal and positive.

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