To nitpick, if you look at the graph of f(x) = sin x where x is in radians then the "movement of y" never exceeds the "movement of x". In other words, the slope of a sine wave never exceeds 1. It only reaches 1 (or -1) at the crossings of the x axis.[...]as the sine waves nears the X axis the movement/fluctuation in the Y direction was greater than in the X. And since X represented the speed of light, the Y-component movement/fluctuation would have thus been exceeding c -- which prompted my question.
On the other hand, if you are allowed to increase the amplitude of a sine wave of a fixed frequency, its slope can become arbitrarily large. That could lead to the same difficulty [were it not for the fact that the slope does not amount to a velocity].