Evaluate tan(-30 degrees )

Problem

tan(−30)

Solution

1. Apply the odd-even identity for the tangent function, which states that tan(−θ)=−tan(θ)

tan(−30)=−tan(30)

2. Identify the value of tan(30) using the unit circle or a special right triangle (30−60−90.

tan(30)=1/√(,3)

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

1/√(,3)=√(,3)/3

4. Substitute the value back into the expression from step 1.

−tan(30)=−√(,3)/3

Final Answer

tan(−30)=−√(,3)/3

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