Simplify cot(pi/3)

Problem

cot(π/3)

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/3 into the trigonometric functions.

cot(π/3)=cos(π/3)/sin(π/3)

3. Evaluate the exact values for the cosine and sine of π/3 using the unit circle or a special right triangle.

cos(π/3)=1/2

sin(π/3)=√(,3)/2

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

cot(π/3)=1/2⋅2/√(,3)

cot(π/3)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

cot(π/3)=(1⋅√(,3))/(√(,3)⋅√(,3))

cot(π/3)=√(,3)/3

Final Answer

cot(π/3)=√(,3)/3

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