Find the Reference Angle -(5pi)/6

Problem

−(5*π)/6

Solution

1. Find the coterminal angle within the range [0,2*π) by adding 2*π to the given negative angle.

θ=−(5*π)/6+2*π

θ=−(5*π)/6+(12*π)/6

θ=(7*π)/6

2. Identify the quadrant where the angle (7*π)/6 terminates. Since π<(7*π)/6<(3*π)/2 the angle is in Quadrant III.

π<(7*π)/6<(3*π)/2

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

θ′=(7*π)/6−π

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

θ′=(7*π)/6−(6*π)/6

θ′=π/6

Final Answer

Reference Angle of −(5*π)/6=π/6

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