Find the Exact Value cot(210 degrees )

Problem

cot(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 Since 180<210<270 the angle lies in Quadrant III.

3. Determine the sign of the cotangent function in Quadrant III. In this quadrant, both sine and cosine are negative, so their ratio (cotangent) is positive.

cot(210)=cot(30)

4. Evaluate the cotangent of the reference angle using the definition cot(θ)=cos(θ)/sin(θ)

cos(30)=√(,3)/2

sin(30)=1/2

5. Calculate the final ratio.

cot(30)=√(,3)/2/1/2=√(,3)

Final Answer

cot(210)=√(,3)

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