Find the Quadrant of the Angle -(2pi)/3

Problem

−(2*π)/3

Solution

1. Convert the angle to a positive coterminal angle by adding 2*π to determine its position within the standard 0 to 2*π range.

−(2*π)/3+2*π=−(2*π)/3+(6*π)/3

(4*π)/3

2. Compare the coterminal angle (4*π)/3 to the quadrant boundaries in radians.

π<(4*π)/3<(3*π)/2

3. Identify the quadrant based on the boundaries. Since the angle is between π (180 degrees) and (3*π)/2 (270 degrees), it lies in the third quadrant.

Quadrant III

Final Answer

The angle −(2*π)/3* is in Quadrant III

Want more problems? Check here!