Find the Reference Angle (10pi)/3

Problem

(10*π)/3

Solution

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

(10*π)/3−2*π=(10*π)/3−(6*π)/3

(10*π)/3−(6*π)/3=(4*π)/3

2. Determine the quadrant for the angle (4*π)/3 Since π<(4*π)/3<(3*π)/2 the angle lies in Quadrant III.

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

θ′=(4*π)/3−π

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

θ′=(4*π)/3−(3*π)/3

θ′=π/3

Final Answer

Reference Angle of (10*π)/3=π/3

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