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$^{\circ}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.