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

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