Here is an updated version, which requires that a center point be picked.

CircularSineWave3 is deleted.

CircularSineWave4 uses a picked center point.
For orienting the sine wave, prior setup of a cplane is very helpful. Then use 3d view to avoid stacked points.

Otherwise, the orientation is based upon the view used to select the point.
If two points are stacked in the Top/Bottom, Front/Back, or Right/Left view, the selected point is the point closer to the observer.

- Brian