Find the Reference Angle -230 degrees

Problem

−230^∘

Solution

1. Find a coterminal angle between 0^∘ and 360^∘ by adding 360^∘ to the given angle.

−230^∘+360^∘=130^∘

2. Identify the quadrant where the terminal side of the angle lies. Since 90^∘<130^∘<180^∘ the angle is in Quadrant II.

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

θ^′=180^∘−130^∘

4. Subtract to find the final reference angle.

θ^′=50^∘

Final Answer

Reference Angle of −230^∘=50^∘

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