Find the Quadrant of the Angle -5pi

Problem

−5*π

Solution

1. Identify the angle in standard position. The given angle is −5*π radians.

2. Find a coterminal angle within the standard range of [0,2*π) by adding multiples of 2*π

3. Add 2*π repeatedly:

−5*π+2*π=−3*π

−3*π+2*π=−π

−π+2*π=π

4. Determine the location of the angle π The angle π (or 180 lies exactly on the negative x-axis.

5. Conclude that because the angle lies on an axis, it is a quadrantal angle and does not belong to any specific quadrant.

Final Answer

−5*π* is a quadrantal angle (on the negative x-axis)

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