Answer
$(2, -45^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(2, 315^{\circ})$
$(-2, 135^{\circ})$
(c) (x,y) = (\sqrt{2},-\sqrt{2})$
Work Step by Step
$(2, -45^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(2, 315^{\circ})$
$(-2, 135^{\circ})$
(c) We can find the rectangular coordinates:
$r = 2$ and $\theta = 315^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (2~cos~315^{\circ}, 2~sin~315^{\circ})$
$(x,y) = (\sqrt{2},-\sqrt{2})$
