Find the Exact Value cot(30)

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. Substitute the specific angle θ=30 into the definition.

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

3. Recall the exact values for the sine and cosine of 30 from the unit circle.

cos(30)=√(,3)/2

sin(30)=1/2

4. Substitute these values into the expression and simplify the fraction.

cot(30)=√(,3)/2/1/2

5. Multiply by the reciprocal of the denominator to find the final value.

cot(30)=√(,3)/2⋅2/1

cot(30)=√(,3)

Final Answer

cot(30)=√(,3)

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