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Convert each coordinate then graph on the given polar coordinate system. Label your point.
A.
(-2,-(pi)/(3))
B.
(5,-(4pi)/(3))

Convert each coordinate then graph on the given polar coordinate system. Label your point. $\newline$ A. $\left(-2,-\frac{\pi}{3}\right)$ $\newline$ B. $\left(5,-\frac{4 \pi}{3}\right)$

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Evaluate integers raised to rational exponents

Full solution

Q. Convert each coordinate then graph on the given polar coordinate system. Label your point.

\newline

A.

\left(-2,-\frac{\pi}{3}\right)

\newline

B.

\left(5,-\frac{4 \pi}{3}\right)

Convert to Cartesian coordinates: Convert the polar coordinate $(-2, -\frac{\pi}{3})$ to Cartesian coordinates. $\newline$ To convert from polar to Cartesian coordinates, use the formulas $x = r \cdot \cos(\theta)$ and $y = r \cdot \sin(\theta)$ . $\newline$ For point $A$ , $r = -2$ and $\theta = -\frac{\pi}{3}$ . $\newline$ Calculate the x-coordinate: $x = -2 \cdot \cos(-\frac{\pi}{3})$ .
Calculate $x$ -coordinate: Calculate the $y$ -coordinate: $y = -2 \times \sin(-\frac{\pi}{3})$ .
Plot point $A$ : Plot the point $A$ on the polar coordinate system and label it.
Convert to Cartesian coordinates: Convert the polar coordinate $(5, -\frac{4\pi}{3})$ to Cartesian coordinates. $\newline$ For point B, $r = 5$ and $\theta = -\frac{4\pi}{3}$ . $\newline$ Calculate the x-coordinate: $x = 5 \cdot \cos(-\frac{4\pi}{3})$ .
Calculate y-coordinate: Calculate the y-coordinate: $y = 5 \times \sin\left(-\frac{4\pi}{3}\right)$ .
Plot point $B$ : Plot the point $B$ on the polar coordinate system and label it.

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