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

Question

$\text { Find the polar coordinates, } 0 \leq \theta < 2 \pi \text { and } r \geq 0 \text {, of the point given in Cartesian coordinates. }$
-$( 0 , \sqrt { 6 } )$
A) $\left( 6 , \frac { 3 \pi } { 2 } \right)$
B) $\left( 6 , \frac { \pi } { 2 } \right)$
C) $\left( \sqrt { 6 } , \frac { \pi } { 2 } \right)$
D) $\left( \sqrt { 6 } , \frac { 3 \pi } { 2 } \right)$

Quizplus · Accepted Answer

The polar coordinates are found using $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point $(0, \sqrt{6})$, $r = \sqrt{0^2 + (\sqrt{6})^2} = \sqrt{6}$ and $\theta = \frac{\pi}{2}$ because the point is directly above the origin on the y-axis.