Find the Quadrant of the Angle (13pi)/6

Problem

(13*π)/6

Solution

1. Identify the angle in radians and determine its size relative to a full rotation of 2*π

2. Find the coterminal angle by subtracting 2*π from the given angle to bring it within the standard range of [0,2*π)

2*π=(12*π)/6

(13*π)/6−(12*π)/6=π/6

3. Determine the quadrant by comparing the coterminal angle π/6 to the quadrant boundaries.

0<π/6<π/2

4. Conclude that since the angle is between 0 and π/2 radians, it lies in the first quadrant.

Final Answer

Quadrant of (13*π)/6=Quadrant I

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