Simplify tan(210)

Problem

tan(210)

Solution

1. Identify the reference angle by determining the quadrant of 210 Since 180<210<270 the angle is in the third quadrant.

2. Calculate the reference angle by subtracting 180 from the given angle.

(θ_ref)=210−180=30

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

tan(210)=tan(30)

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

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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