Question

Find Parametric equations for Cardioids x=a(1+cosθ)​

Answer 1

The relationship between Cartesian coordinates and Polar coordinates is

xy=rcos(θ)=rsin(θ)rθ=x2+y2−−−−−−√=arctan(yx)+π(12−x2|x|)

Using the left equations, and the relationship for your curve, leaves you with

xy=(1−cos(θ))cos(θ)=(1−cos(θ))sin(θ)

So you have the parametrization you describe.

Hope it helps you ❤️