Find the Quadrant of the Angle -120

Problem

−120^∘

Solution

1. Identify the direction of the angle. Since the angle −120^∘ is negative, it is measured clockwise from the positive x-axis.

2. Determine the range for each quadrant when measuring clockwise. The first quadrant clockwise (Quadrant IV) is 0^∘ to −90^∘ and the second quadrant clockwise (Quadrant III) is −90^∘ to −180^∘

3. Compare the given angle to these ranges. Since −180^∘<−120^∘<−90^∘ the angle lies in the third quadrant.

4. Verify by finding a coterminal angle. Add 360^∘ to the angle to find its positive equivalent.

−120^∘+360^∘=240^∘

5. Locate the coterminal angle. An angle of 240^∘ is between 180^∘ and 270^∘ which corresponds to Quadrant III.

Final Answer

−120^∘* is in Quadrant III

Want more problems? Check here!