Find the Quadrant of the Angle -pi/4

Problem

−π/4

Solution

1. Identify the direction of the angle. Since the angle −π/4 is negative, it is measured clockwise from the positive xaxis.

2. Convert the angle to its positive coterminal equivalent if necessary to visualize its position. Adding 2*π gives:

−π/4+2*π=(7*π)/4

3. Determine the range of the quadrants in radians. Quadrant I is 0 to π/2 Quadrant II is π/2 to π Quadrant III is π to (3*π)/2 and Quadrant IV is (3*π)/2 to 2*π

4. Compare the angle to the quadrant ranges. Since (3*π)/2<(7*π)/4<2*π the angle lies in the fourth quadrant.

Final Answer

Quadrant of −π/4=Quadrant IV

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