Find the Exact Value cot(210)

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 which lies in Quadrant III.

3. Determine the sign of the cotangent function in Quadrant III, where both sine and cosine are negative, making cotangent positive.

cot(210)=cot(30)

4. Apply the definition of cotangent as the ratio of cosine to sine for the reference angle.

cot(30)=cos(30)/sin(30)

5. Substitute the known values for cos(30)=√(,3)/2 and sin(30)=1/2

cot(30)=√(,3)/2/1/2

6. Simplify the fraction by canceling the denominators.

cot(30)=√(,3)

Final Answer

cot(210)=√(,3)

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