Answer
Please see the figure attached.
Work Step by Step
We have $r = \sin \theta $.
Since $r = \sqrt {{x^2} + {y^2}} $ and $y = r\sin \theta $, converting to rectangular coordinates we get
$\sqrt {{x^2} + {y^2}} = \frac{y}{{\sqrt {{x^2} + {y^2}} }}$
${x^2} + {y^2} = y$, ${\ \ \ }$ ${x^2} + {y^2} - y = 0$
${x^2} + {\left( {y - \frac{1}{2}} \right)^2} - \frac{1}{4} = 0$
${x^2} + {\left( {y - \frac{1}{2}} \right)^2} = \frac{1}{4}$
Notice that the last equation is a circle of radius $\frac{1}{2}$ centered at $\left( {0,\frac{1}{2}} \right)$. Since there is no constraint on $z$, the equation $r = \sin \theta $ represents a cylinder of radius $\frac{1}{2}$.
