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It is a sinusoid:
Is it a sinusoid or this curve has any other name?
I will not sleep until I get an answer!
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.
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.