Find the Reference Angle -(5pi)/4

Problem

−(5*π)/4

Solution

1. Find a coterminal angle between 0 and 2*π by adding 2*π to the given angle.

θ=−(5*π)/4+2*π

θ=−(5*π)/4+(8*π)/4

θ=(3*π)/4

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

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

θ′=π−(3*π)/4

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

θ′=(4*π)/4−(3*π)/4

θ′=π/4

Final Answer

Reference Angle=π/4

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