Find the Reference Angle -(3pi)/4

Problem

−(3*π)/4

Solution

1. Find a coterminal angle in the interval [0,2*π] by adding 2*π to the given angle.

θ=−(3*π)/4+2*π

θ=−(3*π)/4+(8*π)/4

θ=(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

θ′=(5*π)/4−(4*π)/4

θ′=π/4

Final Answer

θ′=π/4

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