Find the Reference Angle -(5pi)/6

Problem

negative 5 pi over 6

Solution

1. Find the coterminal angle within the range the interval from 0 to 2 pi including 0 but not including 2 pi by adding 2 pi to the given negative angle.

theta equals negative 5 pi over 6 plus 2 pi

theta equals negative 5 pi over 6 plus 12 pi over 6

theta equals 7 pi over 6

2. Identify the quadrant where the angle 7 pi over 6 terminates. Since pi is less than 7 pi over 6 is less than 3 pi over 2 the angle is in Quadrant III.

pi is less than 7 pi over 6 is less than 3 pi over 2

3. Apply the reference angle formula for Quadrant III, which is theta prime equals theta minus pi

theta prime equals 7 pi over 6 minus pi

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

theta prime equals 7 pi over 6 minus 6 pi over 6

theta prime equals pi over 6

Final Answer

Reference Angle of minus 5 pi over 6 equals pi over 6

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