Answer
(a) We can see the point $(2,\frac{3\pi}{2})$ on the graph.
The Cartesian coordinates are $(0,-2)$
(b) We can see the point $(\sqrt{2},\frac{\pi}{4})$ on the graph.
The Cartesian coordinates are $(1,1)$
(c) We can see the point $(-1,-\frac{\pi}{6})$ on the graph.
The Cartesian coordinates are $(-\frac{\sqrt{3}}{2},\frac{1}{2})$
Work Step by Step
(a) We can see the point $(2,\frac{3\pi}{2})$ on the graph.
We can find the Cartesian coordinates:
$x = 2~cos~\frac{3\pi}{2} = 0$
$y = 2~sin~\frac{3\pi}{2} = -2$
The Cartesian coordinates are $(0,-2)$
(b) We can see the point $(\sqrt{2},\frac{\pi}{4})$ on the graph.
We can find the Cartesian coordinates:
$x = \sqrt{2}~cos~\frac{\pi}{4} = 1$
$y = \sqrt{2}~sin~\frac{\pi}{4} = 1$
The Cartesian coordinates are $(1,1)$
(c) We can see the point $(-1,-\frac{\pi}{6})$ on the graph.
We can find the Cartesian coordinates:
$x = -1~cos~\frac{-\pi}{6} = -\frac{\sqrt{3}}{2}$
$y = -1~sin~\frac{-\pi}{6} = \frac{1}{2}$
The Cartesian coordinates are $(-\frac{\sqrt{3}}{2},\frac{1}{2})$
