Find the Exact Value tan(210 degrees )

Problem

tan(210)

Solution

1. Identify the quadrant of the angle. Since 180<210<270 the angle 210 lies in the third quadrant (Quadrant III).

2. Determine the reference angle. In the third quadrant, the reference angle (θ_ref) is calculated as θ−180

(θ_ref)=210−180=30

3. Determine the sign of the tangent function. In Quadrant III, both sine and cosine are negative, which means the tangent function (sin(θ)/cos(θ) 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

Want more problems? Check here!