Intersections betweens sinusoids

[mnb96]

I'm facing the following problem which sounded simple but apparently it is not (at least for me):

I have two sinusoids: different amplitude, different frequency, different phase difference and I want to find the intersection points, which is equivalent to solving the following equation in \theta:

A_{1}sin(f_{1}\theta+\phi_{1}) = A_{2}sin(f_{2}\theta+\phi_{2})

I was not able either to solve the problem in the general case, nor to find a solution around the net.

 

[jostpuur]

I don't believe that a solution formula exists at all, although I cannot prove this claim. I'm afraid you'll have to approximate. For example write the sines as second order Taylor series close to some zero, and solve an approximation there. Or then some kind of perturbation series.

What one should do of course depends on what one wants.