Find the Quadrant of the Angle (11pi)/3

Problem

(11*π)/3

Solution

1. Convert to a mixed number to determine how many full rotations are contained within the angle.

(11*π)/3=32/3*π

2. Find the coterminal angle within the standard range of [0,2*π) by subtracting the largest possible multiple of 2*π

32/3*π−2*π=12/3*π

(5*π)/3

3. Identify the quadrant by comparing the coterminal angle to the quadrantal boundaries.

(3*π)/2<(5*π)/3<2*π

4. Conclude that since the angle lies between (3*π)/2 (270 and 2*π (360, it is in the fourth quadrant.

Final Answer

Quadrant of (11*π)/3=Quadrant IV

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