Answer
An exponential function with base $e$.
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) $y=r \sin \theta$
On multiplying with $\sin \theta$ on both sides of the equation, we get $r \sin \theta=e^{r \cos \theta}$
Therefore, our Cartesian equation is $y=e^x$
This shows an exponential function with base $e$.
