Find the Quadrant of the Angle (13pi)/4

Problem

(13*π)/4

Solution

1. Identify the angle in radians and determine its position relative to a full circle. A full rotation is 2*π radians, which is equivalent to (8*π)/4

2. Subtract multiples of 2*π to find the coterminal angle within the interval [0,2*π)

(13*π)/4−2*π=(13*π)/4−(8*π)/4

(13*π)/4−(8*π)/4=(5*π)/4

3. Determine the quadrant by comparing the coterminal angle (5*π)/4 to the standard quadrant boundaries: Quadrant I (0,π/2) Quadrant II (π/2,π) Quadrant III (π,(3*π)/2) and Quadrant IV ((3*π)/2,2*π)

4. Compare the values. Since π<(5*π)/4<(3*π)/2 (which is (4*π)/4<(5*π)/4<(6*π)/4, the angle lies in the third quadrant.

Final Answer

Quadrant of (13*π)/4=Quadrant III

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