# Which quadrant does the given angle -127 degrees lie?

Nov 1, 2016

-127° " rotation " = +233° rotation

" "127° "clockwise" = 233°  anticlockwise

#### Explanation:

-127° " rotation " = +233° rotation

$\text{ "127° "clockwise" = 233° " anticlockwise }$ 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