Find the Reference Angle (8pi)/3

Problem

(8*π)/3

Solution

1. Find a coterminal angle between 0 and 2*π by subtracting multiples of 2*π

(8*π)/3−2*π=(8*π)/3−(6*π)/3

(8*π)/3−(6*π)/3=(2*π)/3

2. Determine the quadrant of the coterminal angle (2*π)/3 Since π/2<(2*π)/3<π the angle lies in Quadrant II.

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

θ′=π−(2*π)/3

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

θ′=(3*π)/3−(2*π)/3

θ′=π/3

Final Answer

Reference Angle of (8*π)/3=π/3

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