Find the Reference Angle -150 degrees

Problem

−150^∘

Solution

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

−150^∘+360^∘=210^∘

2. Identify the quadrant where the angle 210^∘ terminates. Since 180^∘<210^∘<270^∘ the angle is in Quadrant III.

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

θ^′=210^∘−180^∘

4. Calculate the final value.

θ^′=30^∘

Final Answer

Reference Angle of −150^∘=30^∘

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