Instead a regularly repeating sine wave, consider a flat line which has a single full sine wave every 3 wavelengths. Does this have a simple expression that can be graphed without specifying domains?
EDIT: Clarification for comments below. I am looking for a fully differentiable function that has a flat line with a full sine wave every 3 wavelengths. Modulo functions as well as composite functions are not what I am looking for. Rather, I am thinking about a fourier series which sums to the desired function but I do not know how to derive it.