Answer
$a.\quad(3,0)$
$b.\quad(-3,0)$
$c.\quad(-1,\sqrt{3})$
$d.\quad(1,\sqrt{3})$
$e.\quad(3,0)$
$f.\quad(1,\sqrt{3})$
$g.\quad(-3,0)$
$h.\quad(-1,\sqrt{3})$
Work Step by Step
$ a.\quad$
Polar: $(r,\theta)=(3,0)$
Cartesian: $(r\cos\theta,r\sin\theta)=(3\cdot 1,3\cdot 0)=(3,0)$
$ b.\quad$
Polar: $(r,\theta)=(-3,0)$
Cartesian: $(r\cos\theta,r\sin\theta)=(-3\cdot 1,-3\cdot 0)=(-3,0)$
$ c.\quad$
Polar: $(r,\theta)=(2,2\pi/3)$
Cartesian: $(r\displaystyle \cos\theta,r\sin\theta)=(2\cdot(-\frac{1}{2}),2\cdot\frac{\sqrt{3}}{2})=(-1,\sqrt{3})$
$ d.\quad$
Polar: $(r,\theta)=(2,7\pi/3)$
Cartesian: $(r\displaystyle \cos\theta,r\sin\theta)=(2\cdot(\frac{1}{2}),2\cdot\frac{\sqrt{3}}{2})=(1,\sqrt{3})$
$ e.\quad$
Polar: $(r,\theta)=(-3,\pi)$
Cartesian: $(r\cos\theta,r\sin\theta)=(-3\cdot(-1),-3\cdot 0)=(3,0)$
$ f.\quad$
Polar: $(r,\theta)=(2,\pi/3)$
Cartesian: $(r\displaystyle \cos\theta,r\sin\theta)=(2\cdot(\frac{1}{2}),2\cdot\frac{\sqrt{3}}{2})=(1,\sqrt{3})$
$ g.\quad$
Polar: $(r,\theta)=(3,2\pi)$
Cartesian: $(r\cos\theta,r\sin\theta)=(-3\cdot 1,3\cdot 0)=(-3,0)$
$ h.\quad$
Polar: $(r,\theta)=(-2,-\pi/3)$
Cartesian: $(r\displaystyle \cos\theta,r\sin\theta)=(-2\cdot(\frac{1}{2}),-2\cdot(-\frac{\sqrt{3}}{2}))=(-1,\sqrt{3})$
