Add or subtract multiplies of 360° until the angle is in the range [0, 360). Then, compare to ...
.. 0-90 . . . . . .. quadrant I
.. 90-180 . . . .. quadrant II
.. 180-270 . . .. quadrant III
.. 270-360 . . . quadrant IV
1. 520° ~ 160° . . . Q2
2. 690° ~ 330° . . Q4
3. -61° ~ 299° . . . Q4
4. -574° ~ 146° . . Q2
5. -105° ~ 255° . . Q3
Multiply by 180/π and proceed as above.
11. -π/3 ~ 300° . . . . Q4
12. π/3 ~ 60° . . . . .. Q1
13. -7π/12 ~ 255° . . Q3
14. -π/12 ~ 345° . . . Q4
15. -53π/18 ~ 190° .. Q3