To understand the function better, let's convert it from polar coordinates to cartesian coordinates. The relation between those coordinates are
[tex]\begin{cases}x=r\cos \theta \\ y=r\sin \theta\end{cases}[/tex]Our function is
[tex]r=2\cos \theta[/tex]If we multiply both sides by r, we have
[tex]r^2=2r\cos \theta[/tex]The square of the radius is equal to the sum of the squares of the cartesian coordinates
[tex]x^2+y^2=r^2[/tex]Using this identity, we can rewrite our function as
[tex]x^2+y^2=2x[/tex]Completing the square, we can rewrite our function as
[tex]\begin{gathered} x^2+y^2=2x \\ x^2+y^2-2x=0 \\ x^2-2x+y^2=0 \\ x^2-2x+1-1+y^2=0 \\ (x-1)^2-1+y^2=0 \\ (x-1)^2+y^2=1 \end{gathered}[/tex]This is a equation of a circle.
