Answer
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(1, -315^{\circ})$
$(-1, 225^{\circ})$
(c) $(x,y) = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$
Work Step by Step
(a) We can see the point plotted on the graph below.
(b) $(1, 45^{\circ})$
We can write two other pairs of polar coordinates for this point:
$(1, -315^{\circ})$
$(-1, 225^{\circ})$
(c) We can find the rectangular coordinates:
$r = 1$ and $\theta = 45^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (1~cos~45^{\circ}, 1~sin~45^{\circ})$
$(x,y) = (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$
