Suppose I'm given a function
f(x) = sin(Ax + B) + sin(Cx + D)
is there a simple (or, perhaps, not-so-simple) way to compute the range of this function? My goal is ultimately to construct a function g(x, S, T) that maps f to the range [S, T].
My strategy is to first compute the range of f, then scale it to the range [0,1], then scale that to the range [S, T].
Ideally I would like to be able to do this for an arbitrary number of waves, although to keep things simple I'm willing to be satisfied with 2 if it's the easiest route.
Numerical methods welcome, although an explicit solution would be preferable.