Answer
$(-2, \frac{\pi}{3})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(2, \frac{4\pi}{3})$
$(-2, -\frac{5\pi}{3})$
(c) $(x,y) = (-1, -\sqrt{3})$
Work Step by Step
$(-2, \frac{\pi}{3})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(2, \frac{4\pi}{3})$
$(-2, -\frac{5\pi}{3})$
(c) We can find the rectangular coordinates:
$r = 2$ and $\theta = \frac{4\pi}{3}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (2~cos~\frac{4\pi}{3}, 2~sin~\frac{4\pi}{3})$
$(x,y) = (-1, -\sqrt{3})$
