Answer
$(-4, 30^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(4, 210^{\circ})$
$(-4, -330^{\circ})$
(c) $(x,y) = (-2\sqrt{3},-2)$
Work Step by Step
$(-4, 30^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(4, 210^{\circ})$
$(-4, -330^{\circ})$
(c) We can find the rectangular coordinates:
$r = 4$ and $\theta = 210^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (4~cos~210^{\circ}, 4~sin~210^{\circ})$
$(x,y) = (-2\sqrt{3},-2)$
