>On the other hand, it does occur to me that any sinusoidal function (or cosines for that matter) would inherently suffer from discontinuities at a radial center. If you take any cross-section of the curve through the radius, it's obvious that, except when the phase is other than +/-PI/2 (?), there is going to be a sharp peak or trough at the origin with the cross section reflected on both sides.

But look: Math_Functions_9 is directly connected to
the displacement. M_F_9 is smooth, the preview and the
final render are not.

M_F_11 (not shown here) can change the phase of the sin.
But this tip remains always, no matter which value I enter
there.

Ernst