Find the Reference Angle (13pi)/4

Problem

(13*π)/4

Solution

1. Find the coterminal angle within the range [0,2*π) by subtracting multiples of 2*π

(13*π)/4−2*π=(13*π)/4−(8*π)/4

(13*π)/4−(8*π)/4=(5*π)/4

2. Identify the quadrant where the angle (5*π)/4 terminates. Since π<(5*π)/4<(3*π)/2 the angle is in Quadrant III.

3. Apply the reference angle formula for Quadrant III, which is θ′=θ−π

θ′=(5*π)/4−π

4. Simplify the expression to find the final reference angle.

θ′=(5*π)/4−(4*π)/4

θ′=π/4

Final Answer

Reference Angle of (13*π)/4=π/4

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