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

Problem

(2*π)/3

Solution

1. Identify the angle in radians and compare it to the standard quadrant boundaries.

2. Determine the decimal or fractional value of the coefficient of π

3. Compare the value 2/3 to the boundaries: 0 to 1/2 is Quadrant I, 1/2 to 1 is Quadrant II, 1 to 3/2 is Quadrant III, and 3/2 to 2 is Quadrant IV.

4. Observe that 1/2<2/3<1 which corresponds to the range π/2<(2*π)/3<π

5. Conclude that the angle lies in the second quadrant.

Final Answer

(2*π)/3∈Quadrant II

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