Find the Quadrant of the Angle (5pi)/3

Problem

(5*π)/3

Solution

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

(5*π)/3⋅180^∘/π

2. Simplify the expression by dividing 180^∘ by 3 and multiplying by 5

5⋅60^∘=300^∘

3. Identify the standard ranges for each quadrant in degrees.

Quadrant I: *0^∘<θ<90^∘

Quadrant II: *90^∘<θ<180^∘

Quadrant III: *180^∘<θ<270^∘

Quadrant IV: *270^∘<θ<360^∘

4. Compare the given angle to the quadrant ranges.

270^∘<300^∘<360^∘

Final Answer

(5*π)/3∈Quadrant IV

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