Find the Quadrant of the Angle 4pi

Problem

4*π

Solution

1. Identify the angle in terms of full rotations. Since one full rotation in radians is 2*π we can divide the given angle by 2*π

2. Calculate the number of rotations by evaluating 4*π/2*π=2 This means the angle represents exactly two full counter-clockwise revolutions.

3. Determine the terminal side position. An angle that is an integer multiple of 2*π terminates on the positive x-axis.

4. Conclude the location. Angles that terminate exactly on an axis are called quadrantal angles and do not lie within a specific quadrant.

Final Answer

4*π* is a quadrantal angle (positive x-axis)

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