Find the Quadrant of the Angle (11pi)/6

Problem

(11*π)/6

Solution

1. Identify the standard range for the four quadrants in radians within one full rotation from 0 to 2*π

2. Compare the given angle (11*π)/6 to the quadrant boundaries: Quadrant I is (0,π/2) Quadrant II is (π/2,π) Quadrant III is (π,(3*π)/2) and Quadrant IV is ((3*π)/2,2*π)

3. Convert the boundaries to a common denominator of 6 to make comparison easier.

4. Determine that (3*π)/2=(9*π)/6 and 2*π=(12*π)/6

5. Observe that (9*π)/6<(11*π)/6<(12*π)/6 which places the angle in the fourth quadrant.

Final Answer

Quadrant of (11*π)/6=Quadrant IV

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