From the unit circle:
we can see that angle
[tex]\frac{3\pi}{4}=135\text{ degre}es[/tex]
so this angle is in the quadrant II.
The second angle
[tex]\frac{57\pi}{8}=1282.5\text{ degre}es[/tex]
which is equivalent to
[tex]202.5\text{ degre}es[/tex]
which is on quadrant III.
The next angle is
[tex]\begin{gathered} \frac{13\pi}{6}=390\text{ degre}es \\ or\text{ equivalently} \\ 30\text{ degr}ees \end{gathered}[/tex]
which is on quadrant I.
The next angle is
[tex]-\frac{35\pi}{6}=-1050\text{ degre}es[/tex]
which is equivalent to
[tex]-330\text{ degre}es=30\text{ degre}es[/tex]
which is on quadrant I.
The next angle is
[tex]-\frac{5\pi}{6}=-150\text{ degre}es[/tex]
which is on quadrant III.
And finally, the angle
[tex]-\frac{5\pi}{11}=-81.81\text{ degre}es[/tex]
which is on quadrant IV
In summary, the answers are:
Quadrant I:
[tex]\frac{13\pi}{6},-\frac{35\pi}{6},[/tex]
Quadrant II:
[tex]\frac{3\pi}{4}[/tex]
Quadrant III:
[tex]\frac{57\pi}{8},-\frac{5\pi}{6}[/tex]
Quadrant IV:
[tex]-\frac{5\pi}{11}[/tex]
