If wave shape is not a problem, try the bottom function for another shape so that the fly leg elements all have the same velocity. It's still not quite right as shown because in a cast, gravity will be acting on the fly leg, and in a cast, the triangle would not be any where near as "equilateral" as this shows.

The pure sine function can never approximate how we move the rod tip in a cast. If someone presented to me with that sine wave loop shape, I'd tell them they need to stop later and keep accelerating their rod tip for as long as possible. The sine wave begins decelerating as soon as "midnight" is reached. We go later than that.
Cheers,
Graeme