Find the Quadrant of the Angle (5pi)/4

Problem

(5*π)/4

Solution

1. Convert the angle from radians to degrees to make it easier to visualize on the coordinate plane.

(5*π)/4⋅180/π

2. Simplify the expression by canceling π and performing the multiplication.

5⋅45=225

3. Compare the angle to the standard quadrant boundaries in degrees: Quadrant I (0 to 90, Quadrant II (90 to 180, Quadrant III (180 to 270, and Quadrant IV (270 to 360.

180<225<270

4. Determine the quadrant based on the comparison. Since 225 falls between 180 and 270 it lies in the third quadrant.

Final Answer

Quadrant of (5*π)/4=Quadrant III

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