Answer
The point in rectangular coordinates is $(1,-1)$
Work Step by Step
$(\sqrt{2},-\pi/4)$
The point has $r=\sqrt{2}$ and $\theta=-\dfrac{\pi}{4}$. The formulas for converting polar to rectangular coordinates are $x=r\cos\theta$ and $y=r\sin\theta$
Substitute the known values into the formulas to obtain $x$ and $y$:
$x=r\cos\theta$
$x=(\sqrt{2})\cos\Big(-\dfrac{\pi}{4}\Big)=(\sqrt{2})\Big(\dfrac{\sqrt{2}}{2}\Big)=\dfrac{(\sqrt{2})^{2}}{2}=\dfrac{2}{2}=1$
$y=r\sin\theta$
$y=(\sqrt{2})\sin\Big(-\dfrac{\pi}{4}\Big)=(\sqrt{2})\Big(-\dfrac{\sqrt{2}}{2}\Big)=-\dfrac{(\sqrt{2})^{2}}{2}=-\dfrac{2}{2}=-1$
The point in rectangular coordinates is $(1,-1)$
