## University Calculus: Early Transcendentals (3rd Edition)

An exponential function with base $e$.
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 $e$.