Find the Reference Angle (11pi)/3

Problem

(11*π)/3

Solution

1. Find the coterminal angle within the range [0,2*π) by subtracting multiples of 2*π

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(11*π)/3−(6*π)/3=(5*π)/3

2. Determine the quadrant for the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle lies in Quadrant IV.

3. Apply the reference angle formula for Quadrant IV, which is θ′=2*π−θ

θ′=2*π−(5*π)/3

4. Simplify the expression to find the final reference angle.

θ′=(6*π)/3−(5*π)/3

θ′=π/3

Final Answer

Reference Angle of (11*π)/3=π/3

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