A thing to consider is that a modified servo (for continuous rotation) has very poor 'linearity' over it's then resulting control range, which I think will pay havoc with any attempt to have it follow a sine wave movement.
If a standard servo is said to be linear (over at least) it's 1 msec to 2 msec control range, I think you will find that the modified servo will have reached it's maximum speed in either direction at +/- 20% or less of it's control range from it's 1.5msec mid point stopped state.
I haven't mapped this out as I don't own any modified servos, just normal ones, but have read the reports of others that have mapped out actual speed vs pulse width commands. So it would be prudent for anyone contemplating something like the OP is trying here, to actually run some characterising tests to actual find out the actual speed control range Vs pulse width commands to see where on is starting out at before trying to nail down a algorithm or math functions best to use to meet the control objective.
Lefty