Answer
$r=\frac{3}{\cos \theta-\sin \theta}$
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\frac{y}{x} \implies \theta =\tan^{-1} \frac{y}{x}$
3. $x=r \cos \theta$ and
4. $y=r \sin \theta$
Given: $x=r \cos \theta$ and $y=r \sin \theta$
Now, we have the polar equation such as:
$r \cos \theta-r \sin \theta=3$
$r(\cos \theta - \sin \theta) = 3$
$r=\frac{3}{\cos \theta-\sin \theta}$