Evaluate tan(120 degrees )

Problem

tan(120^∘)

Solution

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

(θ_ref)=180^∘−120^∘=60^∘

2. Determine the quadrant of the angle 120^∘

Quadrant II

3. Determine the sign of the tangent function in the second quadrant.

tan(θ)<0

4. Apply the reference angle property for tangent.

tan(120^∘)=−tan(60^∘)

5. Substitute the known value for tan(60^∘)

tan(60^∘)=√(,3)

6. Combine the sign and the value to find the final result.

tan(120^∘)=−√(,3)

Final Answer

tan(120^∘)=−√(,3)

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