Find the Reference Angle (29pi)/4

Problem

(29*π)/4

Solution

1. Find the coterminal angle within the interval [0,2*π) by dividing the coefficient by 2*π

(29*π)/4÷2*π=29/8=3.625

2. Subtract the number of full rotations (3 full rotations) from the original angle to find the coterminal angle θ

θ=(29*π)/4−3*(2*π)

θ=(29*π)/4−(24*π)/4

θ=(5*π)/4

3. Determine the quadrant for the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle lies in Quadrant III.

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

θ′=(5*π)/4−π

θ′=(5*π)/4−(4*π)/4

θ′=π/4

Final Answer

Reference Angle of (29*π)/4=π/4

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