Find the Reference Angle -(7pi)/6

Problem

−(7*π)/6

Solution

1. Find a coterminal angle between 0 and 2*π by adding 2*π to the given angle.

−(7*π)/6+2*π=−(7*π)/6+(12*π)/6

(5*π)/6

2. Determine the quadrant where the angle (5*π)/6 terminates. Since π/2<(5*π)/6<π the angle is in Quadrant II.

(5*π)/6∈Quadrant II

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

θ′=π−(5*π)/6

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

θ′=(6*π)/6−(5*π)/6

θ′=π/6

Final Answer

θ′=π/6

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