Find the Quadrant of the Angle (7pi)/2

Problem

(7*π)/2

Solution

1. Identify the angle in terms of its position on the unit circle.

2. Convert the angle to a coterminal angle within the standard range [0,2*π) by subtracting multiples of 2*π

2*π=(4*π)/2

3. Subtract the full rotation from the given angle.

(7*π)/2−(4*π)/2=(3*π)/2

4. Determine the location of the coterminal angle (3*π)/2

5. Observe that (3*π)/2 corresponds to 270 which lies exactly on the negative y-axis.

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

Final Answer

(7*π)/2=Quadrantal angle (negative y-axis)

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