Answer
a) $(\frac{3\sqrt 3}{2},\frac{3}{2})$
b) $(-3\sqrt 2, 3\sqrt 2)$
c) $(0,0)$
d) $(0, -5)$
Work Step by Step
Recall: The $x$ and $y$ coordinates in a rectangular coordinate system are given by
$x= r\cos\theta$ and $y= r\sin\theta$.
Thus, we have:
a) $x= 3\cos\frac{\pi}{6}=\frac{3\sqrt 3}{2}$
$y= 3\sin\frac{\pi}{6}=3\times\frac{1}{2}=\frac{3}{2}$
$(x,y)=(\frac{3\sqrt 3}{2},\frac{3}{2})$
b) $x=6\cos\frac{3\pi}{4}=6\times-\frac{1}{\sqrt 2}=-3\sqrt 2$
$y=6\sin\frac{3\pi}{4}=6\times\frac{1}{\sqrt 2}=3\sqrt 2$
$(x,y)=(-3\sqrt 2, 3\sqrt 2)$
c) $x= 0\cos\frac{\pi}{5}=0$
$y=0\sin\frac{\pi}{5}=0$
$(x,y)=(0,0)$
d) $x= 5\cos(-\frac{\pi}{2})=5\times0=0$
$y=5\sin(-\frac{\pi}{2})=5\times(-1)=-5$
$(x,y)=(0, -5)$
