Find the Exact Value 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. Substitute the specific angle 30^∘ into the identity.

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

cot(30^∘)=√(,3)/2/1/2

cot(30^∘)=√(,3)/2⋅2/1

cot(30^∘)=√(,3)

Final Answer

cot(30^∘)=√(,3)

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