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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