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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