Find the Quadrant of the Angle -pi/3

Problem

−π/3

Solution

1. Identify the direction of the angle. Since the angle −π/3 is negative, it is measured clockwise from the positive xaxis.

2. Convert the angle to its positive coterminal equivalent to easily identify the quadrant. Add 2*π to the angle:

−π/3+2*π=−π/3+(6*π)/3

(5*π)/3

3. Compare the angle to the standard quadrant boundaries in radians. The boundaries for the four quadrants are:

• Quadrant I: 0<θ<π/2

• Quadrant II: π/2<θ<π

• Quadrant III: π<θ<(3*π)/2

• Quadrant IV: (3*π)/2<θ<2*π

4. Determine the location. Since (3*π)/2 is (4.5*π)/3 and (5*π)/3 is greater than (4.5*π)/3 but less than 2*π the angle lies in the fourth quadrant.

Final Answer

Quadrant of −π/3=Quadrant IV

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