Each circle corresponds to a different value of r (the first coordinate, on the left).
And each line segment emanating from the center corresponds to a different value of θ (second coordinate, on the right).
Also, we need to know that a negative value of θ corresponds to the angle 2π - θ.
Furthermore, if r is negative, we need to plot the point opposite by the center to the point (-r, θ).
So, let's begin by plotting the point
[tex](-5,-\frac{7\pi}{6})[/tex]
Since the second entry is negative, it corresponds to the angle:
[tex]2\pi-\frac{7\pi}{6}=\frac{12\pi-7\pi}{6}=\frac{5\pi}{6}[/tex]
Also, since the first entry is negative, we need to plot the point on the circle corresponding to r = 5, but in the opposite direction of the ray corresponding to the angle 5π/6:
Now, the second point is
[tex](3,\frac{3\pi}{4})[/tex]
For this point, both coordinates are positive. So, we need to plot it (red point below) on the circle corresponding to r = 3, and on the ray corresponding to θ = 3π/4:
