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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