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

Problem

−(4*π)/3

Solution

1. Convert to a positive coterminal angle by adding 2*π to the given angle to make it easier to visualize on the unit circle.

−(4*π)/3+2*π

2. Find a common denominator to perform the addition.

−(4*π)/3+(6*π)/3

3. Simplify the expression to find the coterminal angle.

(2*π)/3

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

π/2<(2*π)/3<π

Final Answer

The angle −(4*π)/3* is in Quadrant II

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