Find all the polar coordinates of the point.
-$( - 6 , \pi / 3 )$
A) $( 6,4 \pi / 3 + 2 \mathrm { n } \pi ) , ( - 6 , \pi / 3 + 2 \mathrm { n } \pi )$
B) $( 6 , \pi / 3 + 2 \mathrm { n } \pi ) , ( 6,4 \pi / 3 + 2 \mathrm { n } \pi )$
C) $( 6,4 \pi / 3 + 2 n \pi ) , ( - 6 , - \pi / 3 + 2 n \pi )$
D) $( 6,4 \pi / 3 + 2 n \pi ) , ( - 6,2 \pi / 3 + 2 n \pi )$

Question

Quizplus · Accepted Answer

The polar coordinates of a point can be represented in two forms: $(r, \theta)$ and $( - r, \theta + \pi)$, where $r$ is the radius and $\theta$ is the angle. For the point $(-6, \pi/3)$, the correct transformations are $(6, 4\pi/3 + 2n\pi)$ for the positive radius representation and $(-6, \pi/3 + 2n\pi)$ for the negative radius representation, accounting for the periodic nature of polar coordinates.

Find All the Polar Coordinates of the Point (−6,π/3)( - 6 , \pi / 3 )(−6,π/3)

Find All the Polar Coordinates of the Point $( - 6 , \pi / 3 )$