Simplify tan(-150)

Problem

tan(−150)

Solution

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

tan(−150)=−tan(150)

2. Find the reference angle for 150 by subtracting it from 180 since it is in the second quadrant.

Reference Angle=180−150=30

3. Determine the sign of the tangent function in the second quadrant. Since tangent is negative in the second quadrant, tan(150)=−tan(30)

−tan(150)=−(−tan(30))

4. Simplify the signs to show that the expression is equivalent to the tangent of the reference angle.

−(−tan(30))=tan(30)

5. Evaluate the exact value of tan(30) using the unit circle or special triangles.

tan(30)=1/√(,3)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

1/√(,3)=√(,3)/3

Final Answer

tan(−150)=√(,3)/3

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