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