Find the Reference Angle tan(150)

Problem

tan(150^∘)

Solution

1. Identify the quadrant in which the given angle 150^∘ lies. Since 90^∘<150^∘<180^∘ the angle is in the second quadrant.

2. Apply the formula for the reference angle θ^′ in the second quadrant. The reference angle is the positive acute angle formed by the terminal side of the angle and the x-axis.

3. Calculate the reference angle using the formula θ^′=180^∘−θ

180^∘−150^∘=30^∘

Final Answer

θ^′=30^∘

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