Find the Quadrant of the Angle -(5pi)/3

Problem

−(5*π)/3

Solution

1. Convert to a positive coterminal angle by adding 2*π to the given angle to make it easier to identify the quadrant.

−(5*π)/3+2*π

2. Find a common denominator to perform the addition.

−(5*π)/3+(6*π)/3

3. Simplify the expression to find the coterminal angle in the standard interval [0,2*π)

π/3

4. Identify the quadrant by comparing the angle to the standard quadrant boundaries: Quadrant I is (0,π/2) Quadrant II is (π/2,π) Quadrant III is (π,(3*π)/2) and Quadrant IV is ((3*π)/2,2*π)

0<π/3<π/2

Final Answer

Quadrant of −(5*π)/3=Quadrant I

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