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