Find the Reference Angle (19pi)/4

Problem

(19*π)/4

Solution

1. Identify the given angle θ=(19*π)/4 and determine its position relative to a full circle.

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

2*π=(8*π)/4

3. Subtract 2*π twice from the original angle.

(19*π)/4−2*(2*π)=(19*π)/4−(16*π)/4

(19*π)/4−(16*π)/4=(3*π)/4

4. Determine the quadrant for the coterminal angle (3*π)/4 Since π/2<(3*π)/4<π the angle is in Quadrant II.

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

θ′=π−(3*π)/4

6. Calculate the final value.

θ′=(4*π)/4−(3*π)/4=π/4

Final Answer

Reference Angle of (19*π)/4=π/4

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