Find the Quadrant of the Angle (9pi)/2

Problem

(9*π)/2

Solution

1. Convert the angle to a mixed number to identify the number of full rotations.

(9*π)/2=4*π+π/2

2. Identify the number of full revolutions. Since 2*π represents one full circle, 4*π represents two full revolutions.

4*π=2*(2*π)

3. Determine the coterminal angle by removing the full revolutions.

(9*π)/2−4*π=π/2

4. Locate the position of the coterminal angle on the coordinate plane. The angle π/2 (or 90 lies exactly on the positive y-axis.

5. Conclude that because the angle lies on an axis, it is a quadrantal angle and does not belong to a specific quadrant.

Final Answer

(9*π)/2=Quadrantal angle (positive y-axis)

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