Find the Exact Value tan(-210 degrees )

Problem

tan(−210^∘)

Solution

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

tan(−210^∘)=−tan(210^∘)

2. Find the reference angle for 210^∘ Since 210^∘ is in the third quadrant, subtract 180^∘ from the angle.

Reference Angle=210^∘−180^∘=30^∘

3. Determine the sign of the tangent function in the third quadrant. Tangent is positive in the third quadrant.

tan(210^∘)=tan(30^∘)

4. Substitute the known value for tan(30^∘) which is √(,3)/3

tan(210^∘)=√(,3)/3

5. Apply the negative sign from the first step to find the final value.

−tan(210^∘)=−√(,3)/3

Final Answer

tan(−210^∘)=−√(,3)/3

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