Answer
IV
Work Step by Step
To plot the point $(r, \theta )=(2, \frac{5\pi }{3})$, begin with the $\frac{5\pi }{3}$ angle. Because $\frac{5\pi }{3}$ is a positive angle, draw $\theta = \frac{5\pi }{3}$ counterclockwise from the polar axis. Now consider $r=2$. Because $r \gt 0$, plot the point by going out two units on the terminal side of $\theta$.
So, looking at the graph, we see that the point lies in the quadrant IV.
