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

$\dfrac{\pi}{4} \leq \theta \leq \dfrac{3\pi}{4}$ and $0\leq r\leq \csc \theta$
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) $y=r \sin \theta$ As $y=r \cos \theta =1\implies r=\csc \theta$ Therefore, the region described in polar coordinates is: $\dfrac{\pi}{4} \leq \theta \leq \dfrac{3\pi}{4}$ and $0\leq r\leq \csc \theta$