Sinusoid or not sinusoid

[ValeryOchkov]

It is a sinusoid:

Is it a sinusoid or this curve has any other name?

I will not sleep until I get an answer!

[Werner_E]

Its a Cardioide! Try sin(x)-1 instead of sin(x) and use a regular polar plot (with zero in the centre).

You may see it every morning on the surface of your cup of coffee because the caustic of a circle is a Cardoide.

https://en.wikipedia.org/wiki/File:Caustique.jpg

[ValeryOchkov]

My method to animate the cardiod

[Werner_E]

What your pic shows is an Epicycloid (or Hypercycloid).

Most of them don't have special names.
Only if r1=r2 its called a Cardioid and if r1=2*r2 its called a Nephroid.

If a circle rolls INSIDE another, the path is called a Hypocycloid.

And if you watch for the path of a point not on the perimeter of the circle, its called a trochoide.