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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