I am trying to find the solution to the following sine wave equation
wavt = 2Pi*a*Sin[2Pi*a*t]+2Pi*b*Sin[2Pi*b*t]+2Pi*c*Sin[2Pi*c*t]; Solve[wavt==0,t]
where a, b and c are all positive real numbers that do not necessarily share a common GCD. I've tried both Solve and Reduce but it gives the message "this system cannot be solved by the methods available to...". Using FindRoot only gives an answer for t = 0. Substituting real numbers does give solutions, which makes me suspect that this equation is transcendental. I've spent days here looking at workarounds for other transcendental equations but have been unable to modify them to this problem. They all seem to involve setting numerical limits on the symbolic variables but this is beyond my humble programming abilities. If I include conditions such as
then it does evaluate but without stopping. I only need to find a finite number of solutions from t = 0 so I'm pretty sure a solution can be found. Any help would be greatly appreciated.