Find the Reference Angle (23pi)/6

Problem

(23*π)/6

Solution

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

(23*π)/6−2*π=(23*π)/6−(12*π)/6

(23*π)/6−(12*π)/6=(11*π)/6

2. Determine the quadrant for the angle (11*π)/6 Since (3*π)/2<(11*π)/6<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−(11*π)/6

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

θ′=(12*π)/6−(11*π)/6

θ′=π/6

Final Answer

Reference Angle of (23*π)/6=π/6

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