Answer
The rectangular coordinates $(x,y) = (\frac{3~\sqrt{2}}{2},-\frac{3~\sqrt{2}}{2})$
Work Step by Step
We can find the x-coordinate:
$x = r~cos~\theta$
$x = (3)~cos~315^{\circ}$
$x = (3)~cos~(-45^{\circ})$
$x = (3)~cos~(45^{\circ})$
$x = (3)~(\frac{\sqrt{2}}{2})$
$x = \frac{3~\sqrt{2}}{2}$
We can find the y-coordinate:
$y = r~sin~\theta$
$y = (3)~sin~315^{\circ}$
$y = (3)~sin~(-45^{\circ})$
$y = (3)~(-sin~45^{\circ})$
$y = (3)~(-\frac{\sqrt{2}}{2})$
$y = -\frac{3~\sqrt{2}}{2}$
The rectangular coordinates $(x,y) = (\frac{3~\sqrt{2}}{2},-\frac{3~\sqrt{2}}{2})$
