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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