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

Question

$\text { Find the polar coordinates, } 0 \leq \theta < 2 \pi \text { and } r \geq 0 \text {, of the point given in Cartesian coordinates. }$
-(3, 3) 
A) $\left( 3 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$
B) $\left( 3 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
C) $\left( 3 , \frac { \pi } { 2 } \right)$
D) $\left( 3 , \frac { \pi } { 4 } \right)$

Quizplus · Accepted Answer

The polar coordinates $r$ and $\theta$ can be found using the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For the point (3, 3), $r = \sqrt{3^2 + 3^2} = 3\sqrt{2}$ and $\theta = \tan^{-1}\left(\frac{3}{3}\right) = \frac{\pi}{4}$.