Find the Exact Value tan(240 degrees )

Problem

tan(240^∘)

Solution

1. Identify the reference angle by determining how far 240^∘ is from the nearest xaxis.

240^∘−180^∘=60^∘

2. Determine the quadrant in which the angle 240^∘ lies.

180^∘<240^∘<270^∘

The angle is in Quadrant III.

3. Determine the sign of the tangent function in Quadrant III.

In Quadrant III, tangent is positive.

4. Apply the reference angle to find the exact value.

tan(240^∘)=tan(60^∘)

5. Evaluate the tangent of the reference angle using known trigonometric values.

tan(60^∘)=√(,3)

Final Answer

tan(240^∘)=√(,3)

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