Answer
-90$^{\circ}$ is between 3rd and 4th quadrants.
Work Step by Step
Coterminal angles always in the same quadrant with original angle, therefore
-90$^{\circ}$+360$^{\circ}$=270$^{\circ}$
-90$^{\circ}$-360$^{\circ}$=-450$^{\circ}$
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