Evaluate tan(120)

Problem

tan(120^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis.

(θ_ref)=180^∘−120^∘=60^∘

2. Determine the quadrant of the angle 120^∘

Quadrant II

3. Apply the sign of the tangent function in the second quadrant, where tangent is negative.

tan(120^∘)=−tan(60^∘)

4. Substitute the known value for the tangent of 60^∘

tan(60^∘)=√(,3)

Final Answer

tan(120^∘)=−√(,3)

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