Simplify cot(pi/6)

Problem

cot(π/6)

Solution

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

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle π/6 into the expression.

cot(π/6)=cos(π/6)/sin(π/6)

3. Evaluate the trigonometric values for the standard angle π/6 (which is 30.

cos(π/6)=√(,3)/2

sin(π/6)=1/2

4. Simplify the resulting fraction by dividing the numerator by the denominator.

√(,3)/2/1/2=√(,3)/2⋅2/1

√(,3)/2⋅2/1=√(,3)

Final Answer

cot(π/6)=√(,3)

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