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

Question

$\text { Find the polar coordinates, } 0 \leq \theta < 2 \pi \text { and } r \geq 0 \text {, of the point given in Cartesian coordinates. }$
-$( \sqrt { 2 } , - \sqrt { 2 } )$
A) $\left( 2 , \frac { 7 \pi } { 4 } \right)$
B) $\left( 2 , \frac { 5 \pi } { 4 } \right)$
C) $\left( \sqrt { 2 } , \frac { 7 \pi } { 4 } \right)$
D) $\left( 4 , \frac { 5 \pi } { 4 } \right)$

Quizplus · Accepted Answer

The polar coordinates $r$ and $\theta$ can be found using $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point $(\sqrt{2}, -\sqrt{2})$, $r = \sqrt{(\sqrt{2})^2 + (-\sqrt{2})^2} = \sqrt{2 + 2} = \sqrt{4} = 2$. The angle $\theta$ in the fourth quadrant (since $x > 0$ and $y < 0$) is $\frac{7\pi}{4}$.