Find the Quadrant of the Angle (11pi)/4

Problem

(11*π)/4

Solution

1. Identify the angle in radians and determine if it is within the standard range of [0,2*π)

2. Subtract multiples of 2*π to find the coterminal angle within the first rotation.

2*π=(8*π)/4

(11*π)/4−(8*π)/4=(3*π)/4

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

Quadrant I: *0<θ<π/2

Quadrant II: π/2<θ<π

Quadrant III: *π<θ<(3*π)/2

Quadrant IV: (3*π)/2<θ<2*π

4. Determine the location since π/2<(3*π)/4<π

Final Answer

(11*π)/4∈Quadrant II

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