Which quadrant does the given angle -127 degrees lie?

1 Answer
Nov 1, 2016

3rd Quadrant.

#-127° " rotation " = +233°# rotation

#" "127° "clockwise" = 233° # anticlockwise

Explanation:

#-127° " rotation " = +233°# rotation

#" "127° "clockwise" = 233° " anticlockwise "# rotation

Positive rotations are in an anticlockwise direction, so rotations are through the 1st, 2nd, 3rd and finally 4th quadrants to return to the 0° position.

Anticklockwise:
Rotation of #0° to 90°# 1st quadrant
Rotation of #90° to 180°# 2nd quadrant
Rotation of #180° to 270°# 3rd quadrant
Rotation of #270° to 360°# 4th quadrant

Negative rotations are in an clockwise direction, so the angles are through the 4th, 3rd, 2nd and finally 1st quadrant before returning to the 0° position.

A rotation of #-127°# is more than 90°, which means it is in the 3rd quadrant:

#-127° " rotation " = +233°# rotation

Clockwise:
Rotation of #0° to -90°# 4th quadrant
Rotation of #-90° to -180°# 3rd quadrant
Rotation of #-180° to -270°# 2nd quadrant
Rotation of #-270° to -360°# 1st quadrant