Answer
$r= \csc \theta$
Work Step by Step
Conversion of polar coordinates and Cartesian coordinates are as follows:
a) $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
c) $x=r \cos \theta$
d) $y=r \sin \theta$
Here, we have $r \sin \theta=1$
Thus, we have $r=1(\dfrac{1}{\sin \theta})$
Hence, $r= \csc \theta$
