The way you're thinking about it currently-yes. Sinusoidal deformations occur in 3D rather than 2D, and the resulting effects on reflections do not resemble sine waves (due to their shapes being determined by the angles of incidence and therefore being only indirectly influenced by the wave motion), so it doesn't make much sense to draw them as such.

If you want to understand water in a mathematical way, then you'd need to work in 3D, as 2D necessarily obscures some important information. If you want to learn how to draw good-looking 2D water, then you shouldn't worry too much about the mathematics and focus on observing the effects, spend time looking at water (ideally, in real life so you can change your viewing angle, mess with the water surface, etc, but videos can be helpful too). Try animating some non-looping water from reference, at various angles and with various kinds of waves. You can always make it loop later once you have a better feel for how it works. Just as with walk cycles, billowing clothing, etc, IRL there aren't perfect loops for most natural things, but we animators always find a way to make it work by fudging the details :]