Find the Value Using the Unit Circle cot(30 degrees )

Problem

cot(30)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Determine the coordinates on the unit circle for the angle 30

(x,y)=(cos(30),sin(30))

3. Substitute the known values for cos(30) and sin(30) from the unit circle.

cos(30)=√(,3)/2

sin(30)=1/2

4. Calculate the ratio by dividing the cosine value by the sine value.

cot(30)=√(,3)/2/1/2

5. Simplify the fraction by multiplying by the reciprocal of the denominator.

cot(30)=√(,3)/2⋅2/1

cot(30)=√(,3)

Final Answer

cot(30)=√(,3)

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