Find the Exact Value tan(120 degrees )

Problem

tan(120^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the x-axis. Since 120^∘ is in the second quadrant, the reference angle is 180^∘−120^∘=60^∘

2. Determine the sign of the tangent function in the second quadrant. In the second quadrant, sine is positive while cosine and tangent are negative.

3. Apply the reference angle property tan(θ)=−tan(180^∘−θ) for angles in the second quadrant.

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

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

Final Answer

tan(120^∘)=−√(,3)

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