Find the Reference Angle -30

Problem

−30^∘

Solution

1. Identify the given angle as θ=−30^∘

2. Find a coterminal angle within the range [0^∘,360^∘) by adding 360^∘ to the negative angle.

−30^∘+360^∘=330^∘

3. Determine the quadrant in which the angle 330^∘ lies. Since 270^∘<330^∘<360^∘ the angle is in Quadrant IV.

4. Apply the formula for the reference angle θ^′ in Quadrant IV, which is θ^′=360^∘−θ

θ^′=360^∘−330^∘

5. Calculate the final value.

θ^′=30^∘

Final Answer

θ^′=30^∘

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