Question

What is the polar graph of r=1-cosx?

Answer 1

See the graph and the explanation.

Explanation:

graph{x^2+y^2=sqrt(x^2+y^2)-x2 [-5, 5, -2.5, 2.5]}

Using usual polar `theta`, instead of x,

`r = 1-cos theta>=0 and <=2`,

represents the curve that is befittingly named cardioid.

It has a dimple, at the pole r = 0.

For the Cartesian frame, the equation is

`x^2+y^2= r^2=rxxr=r(1-costheta)=r-rcostheta=sqrt(x^2+y^2)-x`,

giving

`x^2+y^2=sqrt(x^2+y^2)-x`, This is used for the readily available

Socratic utility.

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