Find the Exact Value tan(-150)

Problem

tan(−150^∘)

Solution

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

tan(−150^∘)=−tan(150^∘)

2. Determine the reference angle for 150^∘ Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

Reference Angle=30^∘

3. Identify the sign of the tangent function in the second quadrant. In Quadrant II, tangent is negative.

tan(150^∘)=−tan(30^∘)

4. Substitute the known value for tan(30^∘) which is √(,3)/3 or 1/√(,3)

tan(150^∘)=−√(,3)/3

5. Combine the results by substituting the value of tan(150^∘) back into the expression from step 1.

tan(−150^∘)=−(−√(,3)/3)

6. Simplify the signs to find the final exact value.

tan(−150^∘)=√(,3)/3

Final Answer

tan(−150^∘)=√(,3)/3

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