Find the Exact Value tan(210)

Problem

tan(210)

Solution

1. Identify the reference angle by determining how far 210 is from the xaxis.

(θ_ref)=210−180=30

2. Determine the quadrant in which the angle 210 lies. Since 180<210<270 the angle is 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(210)=tan(30)

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

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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