Find the Quadrant of the Angle (7pi)/3

Problem

(7*π)/3

Solution

1. Identify the angle in radians and determine its position relative to a full circle. A full rotation is 2*π radians.

2. Convert the angle to a mixed number or subtract 2*π to find the coterminal angle within the standard range [0,2*π)

(7*π)/3=2*π+π/3

3. Determine the coterminal angle. Since (7*π)/3 is one full rotation plus π/3 the angle terminates in the same position as π/3

(7*π)/3−2*π=π/3

4. Locate the quadrant for π/3 Since 0<π/3<π/2 the angle lies in the first quadrant.

Final Answer

Quadrant of (7*π)/3=Quadrant I

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