Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 617: 6

a) $\left(2,\frac{\pi}{2}\right)$

We are given the rectangular coordinates: $(x,y)=(0,-2)$ We determine the polar coordinates $(r,\theta)$: $r=\sqrt{x^2+y^2}=\sqrt{0^2+(-2)^2}=2$ $\tan\theta=\frac{y}{x}$ As $x=0$, we have $\theta=\frac{\pi}{2}$ The correct answer is a) $\left(2,\frac{\pi}{2}\right)$