Find the Quadrant of the Angle (3pi)/2

Problem

(3*π)/2

Solution

1. Identify the angle in radians. The given angle is (3*π)/2

2. Convert the angle to degrees if necessary to visualize its position. Since π radians is 180 we calculate (3⋅180)/2=270

3. Determine the boundary positions of the quadrants. Quadrant I is 0<θ<π/2 Quadrant II is π/2<θ<π Quadrant III is π<θ<(3*π)/2 and Quadrant IV is (3*π)/2<θ<2*π

4. Conclude the location of the angle. Because the angle is exactly (3*π)/2 (or 270, it lies exactly on the negative y-axis. Angles that fall on the axes are called quadrantal angles and do not belong to any specific quadrant.

Final Answer

(3*π)/2=Quadrantal Angle (Negative y-axis)

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