Find the Quadrant of the Angle (7pi)/6

Problem

(7*π)/6

Solution

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

Q*1:0<θ<π/2

Q*2:π/2<θ<π

Q*3:π<θ<(3*π)/2

Q*4:(3*π)/2<θ<2*π

2. Compare the given angle (7*π)/6 to the boundary values.

π=(6*π)/6

(3*π)/2=(9*π)/6

3. Determine the position of the angle by checking the inequality.

(6*π)/6<(7*π)/6<(9*π)/6

π<(7*π)/6<(3*π)/2

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

Final Answer

Quadrant of (7*π)/6=Quadrant III

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