Find the Quadrant of the Angle (5pi)/6

Problem

(5*π)/6

Solution

1. Identify the standard range for each quadrant in radians.

0<θ<π/2⇒Quadrant I

π/2<θ<π⇒Quadrant II

π<θ<(3*π)/2⇒Quadrant III

(3*π)/2<θ<2*π⇒Quadrant IV

2. Compare the given angle (5*π)/6 to the quadrant boundaries.

π/2=(3*π)/6

π=(6*π)/6

3. Determine the position of the angle by observing that (3*π)/6<(5*π)/6<(6*π)/6

π/2<(5*π)/6<π

4. Conclude that since the angle is between π/2 and π it lies in the second quadrant.

Final Answer

(5*π)/6∈Quadrant II

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