Find the Quadrant of the Angle (10pi)/3

Problem

(10*π)/3

Solution

1. Convert to a mixed fraction to determine how many full rotations are contained in the angle.

(10*π)/3=3*π+π/3

2. Find the coterminal angle within the standard range of [0,2*π) by subtracting 2*π (one full rotation).

(10*π)/3−2*π=(10*π)/3−(6*π)/3

(10*π)/3−2*π=(4*π)/3

3. Identify the quadrant by comparing the coterminal angle to the quadrantal boundaries.

π<(4*π)/3<(3*π)/2

4. Conclude that since the angle is between 180 (π and 270 ((3*π)/2, it lies in the third quadrant.

Final Answer

Quadrant of (10*π)/3=Quadrant III

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