Answer
cylinder with radius $1$ and center $(0,1,0)$
Work Step by Step
We are given that $r=2 \sin \theta$
In the cylindrical coordinate system, we have $x=r \cos \theta \\ y=r \sin \theta \\z=z$
Conversion of rectangular to cylindrical coordinate system, we have $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
Thus, we have
$x^2+y^2=2y$
or, $x^2+y^2-2y=0$
or, $x^2+(y^2-2y+1)=1 $
or, $x^2+(y-1)^2=1^2$
Hence, we get an equation of a cylinder with radius $1$ and center $(0,1,0)$ .
