Find the Quadrant of the Angle (11pi)/8

Problem

(11*π)/8

Solution

1. Identify the standard quadrant boundaries in radians.

Q*1:0<θ<π/2

Q*2:π/2<θ<π

Q*3:π<θ<(3*π)/2

Q*4:(3*π)/2<θ<2*π

2. Convert the boundaries to have a common denominator of 8 to compare with the given angle.

π=(8*π)/8

(3*π)/2=(12*π)/8

3. Compare the given angle (11*π)/8 to the boundaries of the third quadrant.

(8*π)/8<(11*π)/8<(12*π)/8

4. Determine the quadrant based on the comparison.

π<(11*π)/8<(3*π)/2

Final Answer

Quadrant of (11*π)/8=Quadrant III

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