Evaluate tan(240 degrees )

Problem

tan(240)

Solution

1. Identify the reference angle by finding the difference between 240 and the nearest x-axis, which is 180

(θ_ref)=240−180=60

2. Determine the quadrant of the angle. Since 240 is between 180 and 270 it lies in Quadrant III.

3. Determine the sign of the tangent function in Quadrant III. In this quadrant, both sine and cosine are negative, so tangent is positive.

tan(240)=tan(60)

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

tan(60)=√(,3)

Final Answer

tan(240)=√(,3)

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