Convert a Point from Rectangular to Polar Coordinates
-$( 5 \sqrt { 3 } , 5 )$
A) $\left( 10 , \frac { \pi } { 6 } \right)$
B) $\left( 5 , \frac { \pi } { 6 } \right)$
C) $\left( 10 , \frac { \pi } { 3 } \right)$
D) $\left( 5 , \frac { \pi } { 3 } \right)$

Question

Quizplus · Accepted Answer

The polar coordinates $(r, \theta)$ can be found using $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}\left(\frac{y}{x}\right)$. For $(5\sqrt{3}, 5)$, $r = \sqrt{(5\sqrt{3})^2 + 5^2} = 10$ and $\theta = \tan^{-1}\left(\frac{5}{5\sqrt{3}}\right) = \frac{\pi}{6}$.

Convert a Point from Rectangular to Polar Coordinates - (53,5)( 5 \sqrt { 3 } , 5 )(53​,5)

Convert a Point from Rectangular to Polar Coordinates
- $( 5 \sqrt { 3 } , 5 )$