Find the Cartesian coordinates of the given point.
-$( - 7,5 \pi / 6 )$
A) $\left( \frac { - 7 } { 2 } , \frac { - 7 } { 2 } \right)$
B) $\left( \frac { 7 \sqrt { 3 } } { 2 } , \frac { - 7 } { 2 } \right)$
C) $\left( \frac { - 7 } { 2 } , \frac { 7 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 7 \sqrt { 3 } } { 2 } , \frac { 7 } { 2 } \right)$

Question

Quizplus · Accepted Answer

To convert polar coordinates $(r, \theta)$ to Cartesian coordinates $(x, y)$, we use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For the point $(-7, 5\pi/6)$, $r = -7$ and $\theta = 5\pi/6$. Thus, $x = -7 \cos(5\pi/6) = -7(-\sqrt{3}/2) = 7\sqrt{3}/2$ and $y = -7 \sin(5\pi/6) = -7(1/2) = -7/2$, making the Cartesian coordinates $\left( \frac{7\sqrt{3}}{2}, \frac{-7}{2} \right)$.

Find the Cartesian Coordinates of the Given Point (−7,5π/6)( - 7,5 \pi / 6 )(−7,5π/6)

Find the Cartesian Coordinates of the Given Point $( - 7,5 \pi / 6 )$