Function-generated sketches?

Basically I want to use trigonometric functions to generate continuous, smooth transitions (smoother than splines) between straight edges over a finite distance, which could then be extruded to form a supremely smooth surface. Unfortunately, I have no idea how to efficiently create trig curves in the app, so if anyone has pointers (assuming it’s possible), that would be greatly appreciated.

I’ve created a Desmos widget if anyone wants to play around with it to see what I mean:

smooth angle widget

and a screenshot for the lazy:
desmos-graph