Simplify tan(120)

Problem

tan(120^∘)

Solution

1. Identify the angle in the unit circle. The angle 120^∘ is in the second quadrant.

2. Determine the reference angle. For an angle θ in the second quadrant, the reference angle θ^′ is 180^∘−θ

3. Calculate the reference angle: 180^∘−120^∘=60^∘

4. Determine the sign of the tangent function. In the second quadrant, the tangent of an angle is negative.

5. Apply the trigonometric identity: tan(120^∘)=−tan(60^∘)

6. Substitute the known value for tan(60^∘) which is √(,3)

Final Answer

tan(120^∘)=−√(,3)

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