Find the Reference Angle -(19pi)/6

Problem

−(19*π)/6

Solution

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

−(19*π)/6+2*π=−(19*π)/6+(12*π)/6=−(7*π)/6

−(7*π)/6+2*π=−(7*π)/6+(12*π)/6=(5*π)/6

2. Identify the quadrant where the angle (5*π)/6 terminates. Since π/2<(5*π)/6<π the angle is in 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=π/6

Final Answer

Reference Angle of −(19*π)/6=π/6

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