Recall that:
The terminal ray of the angle θ drawn in standard position lie in:
1) Quadrant I if:
[tex]0<\theta<\frac{\pi}{2}\text{.}[/tex]
2) Quadrant II if:
[tex]\frac{\pi}{2}<\theta<\pi\text{.}[/tex]
3) Quadrant III if:
[tex]\pi<\theta<\frac{3\pi}{2}\text{.}[/tex]
4) Quadrant IV if:
[tex]\frac{3\pi}{2}<\theta<2\pi\text{.}[/tex]
Also, recall that θ and θ+2πn (with n an integer) are equivalent angles.
Now, notice that:
[tex]\begin{gathered} \frac{\pi}{2}<\frac{3\pi}{4}<\pi, \\ \frac{57\pi}{8}\rightarrow\frac{9}{8}\pi\text{ and }\frac{\pi}{2}<\frac{9\pi}{8}<\pi, \\ \frac{13}{6}\pi\rightarrow\frac{1}{6}\pi\text{ and }0<\frac{\pi}{6}<\frac{\pi}{2}, \\ -\frac{35\pi}{4}\rightarrow\frac{5}{4}\pi\text{ and }\pi<\frac{5\pi}{4}<\frac{3\pi}{2}, \\ -\frac{5}{6}\pi\rightarrow\frac{7\pi}{6}\text{ and }\pi<\frac{7\pi}{6}<\frac{3\pi}{2}, \\ -\frac{5}{11}\pi\rightarrow\frac{17}{11}\pi\text{ and }\frac{3\pi}{2}<\frac{17\pi}{11}<2\pi\text{.} \end{gathered}[/tex]
Therefore the fulfilled table is:
Answer:
