Find the Quadrant of the Angle (5pi)/2

Problem

(5*π)/2

Solution

1. Convert the angle to a more familiar form by identifying how many full rotations (2*π radians) it contains.

2. Divide the numerator by the denominator to express the fraction as a mixed number.

(5*π)/2=2.5*π

3. Subtract the largest multiple of 2*π that is less than the given angle to find the coterminal angle within the range [0,2*π)

2.5*π−2*π=0.5*π

4. Simplify the coterminal angle.

0.5*π=π/2

5. Identify the location of the angle π/2 on the coordinate plane. Since π/2 corresponds to 90 it lies exactly on the positive y-axis.

6. Determine the quadrant. Angles that fall exactly on the axes are called quadrantal angles and do not belong to any specific quadrant.

Final Answer

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

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