Find the Quadrant of the Angle (17pi)/6

Problem

(17*π)/6

Solution

1. Identify the angle in radians and determine its position relative to a full circle, which is 2*π radians.

2. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

2*π=(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

3. Compare the coterminal angle (5*π)/6 to the quadrantal boundaries: 0 π/2 π and (3*π)/2

π/2<(5*π)/6<π

(3*π)/6<(5*π)/6<(6*π)/6

4. Determine the quadrant based on these boundaries. Since the angle is between π/2 and π it lies in the second quadrant.

Final Answer

Quadrant of (17*π)/6=Quadrant II

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