Answer
$(-5, \frac{5\pi}{6})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(5, \frac{11\pi}{6})$
$(-5, -\frac{7\pi}{6})$
(c) $(x,y) = (\frac{5\sqrt{3}}{2}, -\frac{5}{2})$
Work Step by Step
$(-5, \frac{5\pi}{6})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(5, \frac{11\pi}{6})$
$(-5, -\frac{7\pi}{6})$
(c) We can find the rectangular coordinates:
$r = 5$ and $\theta = \frac{11\pi}{6}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (5~cos~\frac{11\pi}{6}, 5~sin~\frac{11\pi}{6})$
$(x,y) = (\frac{5\sqrt{3}}{2}, -\frac{5}{2})$
