$\text { Find the polar coordinates, } 0 \leq \theta

Question

$\text { Find the polar coordinates, } 0 \leq \theta < 2 \pi \text { and } r \geq 0 \text {, of the point given in Cartesian coordinates. }$
-(0, -2) 
A) $\left( 2 , \frac { \pi } { 2 } \right)$
B) $\left( 2 , \frac { 3 \pi } { 2 } \right)$
C) $( 2 , \pi )$
D) $( 2,0 )$

Quizplus · Accepted Answer

The polar coordinates of a point given in Cartesian coordinates (x, y) can be found using $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$, with adjustments based on the quadrant. For the point (0, -2), $r = \sqrt{0^2 + (-2)^2} = 2$ and the angle $\theta$ points directly downward, which corresponds to $\frac{3\pi}{2}$ radians.