Find the Exact Value tan(120)

Problem

tan(120)

Solution

1. Identify the reference angle by finding the distance from the angle to the x-axis. Since 120 is in the second quadrant, the reference angle is 180−120=60

2. Determine the sign of the tangent function in the second quadrant. In the second quadrant, sine is positive while cosine and tangent are negative.

3. Apply the reference angle property for tangent.

tan(120)=−tan(60)

4. Substitute the known exact value for tan(60) which is √(,3)

tan(120)=−√(,3)

Final Answer

tan(120)=−√(,3)

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