An angle's quadrant in the Cartesian coordinate system is determined by its measure: Quadrant I (0-90 degrees), II (90-180), III (180-270), IV (270-360). Angles measured counterclockwise from the positive x-axis.
The quadrant in which the terminal side of an angle in standard position lies is determined by the sign of its corresponding angle measure. In the Cartesian coordinate system, angles in standard position are measured counterclockwise from the positive x-axis.
Quadrant I (0 to 90 degrees):
If the angle measure θ is between 0 and 90 degrees, inclusive, the terminal side lies in Quadrant I.
Quadrant II (90 to 180 degrees):
If θ is between 90 and 180 degrees, exclusive, the terminal side is in Quadrant II.
Quadrant III (180 to 270 degrees):
If θ is between 180 and 270 degrees, exclusive, the terminal side falls in Quadrant III.
Quadrant IV (270 to 360 degrees):
If θ is between 270 and 360 degrees, exclusive, the terminal side lies in Quadrant IV.