Equation of sine

it should be, in cartesian coordinates

x = (R + a · sin(n·θ)) · cos(θ) + xc

y = (R + a · sin(n·θ)) · sin(θ) + yc

where

R is circle's radius

a is sinusoid amplitude

θ is the parameter (angle), from 0 to 2π

xc,yc is circle's center point

n is number of sinusoids on circle

you can also get a pure cartesian equation (non-parametric) on x/y, but just for half circle, solving second for sin(θ) and replacing it on first one.

Do it first for the circle centered at the origin in polar coordinates.

Then switch do Cartesian coordinates, then shift to the actual center of the circle.