Find the Quadrant of the Angle (4pi)/3

Problem

(4*π)/3

Solution

1. Identify the standard range for each quadrant in radians.

0<θ<π/2* is Quadrant I

π/2<θ<π* is Quadrant II

π<θ<(3*π)/2* is Quadrant III

(3*π)/2<θ<2*π* is Quadrant IV

2. Compare the given angle (4*π)/3 to the boundary values.

π=(3*π)/3

(3*π)/2=(4.5*π)/3

3. Determine the position of the angle based on the comparisons.

(3*π)/3<(4*π)/3<(4.5*π)/3

π<(4*π)/3<(3*π)/2

4. Conclude that since the angle is between π and (3*π)/2 it lies in the third quadrant.

Final Answer

(4*π)/3* is in Quadrant III

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