Simplify tan(240)

Problem

tan(240)

Solution

1. Identify the reference angle by determining the quadrant of 240 Since 180<240<270 the angle is in the third quadrant.

2. Calculate the reference angle (θ_R) using the formula for the third quadrant: (θ_R)=θ−180

(θ_R)=240−180=60

3. Determine the sign of the tangent function in the third quadrant. In the third quadrant, tangent is positive.

4. Apply the reference angle to the tangent function.

tan(240)=tan(60)

5. Evaluate the exact value of tan(60) using the unit circle or special triangles.

tan(60)=√(,3)

Final Answer

tan(240)=√(,3)

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