Find the Reference Angle -(2pi)/3

Problem

−(2*π)/3

Solution

1. Identify the given angle θ=−(2*π)/3

2. Find a coterminal angle in the interval [0,2*π) by adding 2*π to the negative angle.

(θ_c)=−(2*π)/3+2*π

(θ_c)=−(2*π)/3+(6*π)/3

(θ_c)=(4*π)/3

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

4. Apply the reference angle formula for Quadrant III, which is θ′=(θ_c)−π

θ′=(4*π)/3−π

θ′=(4*π)/3−(3*π)/3

θ′=π/3

Final Answer

θ′=π/3

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