Find the Reference Angle 1589

Problem

1589

Solution

1. Find the coterminal angle within the range [0,360) by dividing the given angle by 360 and finding the remainder.

1589÷360=4* R *149

2. Identify the quadrant where the coterminal angle 149 lies.

90<149<180

The angle is in Quadrant II.

3. Apply the reference angle formula for Quadrant II, which is θ′=180−θ

θ′=180−149

4. Subtract to find the final value.

θ′=31

Final Answer

Reference Angle of *1589=31

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