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

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 $\ln r+\ln \cos \theta=\ln (r \cos \theta)$ Therefore, our Cartesian equation is $y=\ln x$ This shows a natural logarithmic function.