Find the Exact Value tan(240)

Problem

tan(240)

Solution

1. Identify the reference angle by finding the distance from the nearest x-axis. Since 240 is in the third quadrant, subtract 180 from the angle.

(θ_ref)=240−180=60

2. Determine the sign of the tangent function in the third quadrant. In the third quadrant, both sine and cosine are negative, which makes the tangent function positive.

tan(240)=tan(60)

3. Evaluate the exact value of the tangent of the reference angle using the unit circle or special right triangles.

tan(60)=√(,3)

Final Answer

tan(240)=√(,3)

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