Evaluate tan(210 degrees )

Problem

tan(210)

Solution

1. Identify the reference angle by finding the difference between 210 and the nearest x-axis, which is 180

(θ_ref)=210−180=30

2. Determine the quadrant of the angle 210 which lies in the third quadrant (Quadrant III).

3. Apply the sign rule for the tangent function in the third quadrant, where tangent is positive.

tan(210)=tan(30)

4. Evaluate the exact value of tan(30) using the unit circle or special triangles.

tan(30)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan(210)=√(,3)/3

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