Choose the one alternative that best completes the statement or answers the question.
The polar coordinates of a point are given. Find the rectangular coordinates of the point.
-$\left( 7 , \frac { 2 \pi } { 3 } \right)$
A) $\left( - \frac { 7 } { 2 } , \frac { 7 \sqrt { 3 } } { 2 } \right)$
B) $\left( \frac { 7 } { 2 } , \frac { - 7 \sqrt { 3 } } { 2 } \right)$
C) $\left( - \frac { 7 } { 2 } , \frac { - 7 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 7 } { 2 } , \frac { 7 \sqrt { 3 } } { 2 } \right)$

Question

Quizplus · Accepted Answer

To convert from polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$, we use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For $\left( 7 , \frac { 2 \pi } { 3 } \right)$, we have $x = 7 \cos\left(\frac{2\pi}{3}\right) = 7 \left(-\frac{1}{2}\right) = -\frac{7}{2}$ and $y = 7 \sin\left(\frac{2\pi}{3}\right) = 7 \left(\frac{\sqrt{3}}{2}\right) = \frac{7\sqrt{3}}{2}$, which matches choice A.

Choose the One Alternative That Best Completes the Statement or Answers