Find the Exact Value tan(-120 degrees )

Problem

tan(−120^∘)

Solution

1. Apply the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−120^∘)=−tan(120^∘)

2. Find the reference angle for 120^∘ Since 120^∘ is in the second quadrant, the reference angle is 180^∘−120^∘=60^∘

Reference Angle=60^∘

3. Determine the sign of the tangent function in the second quadrant. Tangent is negative in the second quadrant.

tan(120^∘)=−tan(60^∘)

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

tan(120^∘)=−√(,3)

5. Combine the results to find the final value.

tan(−120^∘)=−(−√(,3))

tan(−120^∘)=√(,3)

Final Answer

tan(−120^∘)=√(,3)

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