Change the point $\left(5, \frac{2 \pi}{3}\right)$ in the polar coordinate system to the equivalent point in the rectangular coordinate system.
A) $(-2.5,-4.33)$
B) $(-2.5,4.33)$
C) $(4.33,-2.5)$
D) $(-4.33,2.5)$

Question

Quizplus · Accepted Answer

The conversion from polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$ is given by:$$x = r \cos \theta$$$$y = r \sin \theta$$Substituting the given values, we get:$$x = 5 \cos \frac{2 \pi}{3} = 5 \left(-\frac{1}{2}\right) = -2.5$$$$y = 5 \sin \frac{2 \pi}{3} = 5 \left(\frac{\sqrt{3}}{2}\right) = 4.33$$Therefore, the equivalent point in the rectangular coordinate system is $(-2.5, 4.33)$.

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