Find the Cartesian coordinates of the given point.
-$( - 9,2 \pi / 3 )$
A) $\left( \frac { - 9 \sqrt { 3 } } { 2 } , \frac { 9 } { 2 } \right)$
B) $\left( \frac { - 9 } { 2 } , \frac { 9 } { 2 } \right)$
C) $\left( \frac { 9 } { 2 } , \frac { - 9 } { 2 } \right)$
D) $\left( \frac { 9 } { 2 } , \frac { - 9 \sqrt { 3 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

Using the formulas $x=r\cos	heta$ and $y=r\sin	heta$, we have
$$x=-9\cos\frac{2\pi}{3}=-9\left(-\frac12ight)=\frac92,$$
$$y=-9\sin\frac{2\pi}{3}=-9\cdot\frac{\sqrt3}{2}=-\frac92\sqrt3.$$
Therefore, the Cartesian coordinates of the point are $\left(\frac92,-\frac92\sqrt3ight)$, which matches answer choice D.

Find the Cartesian Coordinates of the Given Point (−9,2π/3)( - 9,2 \pi / 3 )(−9,2π/3)

Find the Cartesian Coordinates of the Given Point $( - 9,2 \pi / 3 )$