# Chapter 8 - Test - Page 412: 10a

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 $(x,y) = (\frac{3~\sqrt{2}}{2},-\frac{3~\sqrt{2}}{2})$

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