Find the Quadrant of the Angle -150 degrees

Problem

−150

Solution

1. Identify the direction of the angle. Since the angle −150 is negative, it is measured clockwise from the positive x-axis.

2. Determine the coterminal angle in the standard range [0,360) by adding 360 to the given angle.

−150+360=210

3. Compare the angle to the standard quadrant boundaries: Quadrant I is (0,90) Quadrant II is (90,180) Quadrant III is (180,270) and Quadrant IV is (270,360)

4. Conclude that since 180<210<270 the angle lies in the third quadrant.

Final Answer

Quadrant of −150=Quadrant III

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