Solve for x cot(x)=( square root of 3)/3

Problem

cot(x)=√(,3)/3

Solution

1. Rewrite the equation in terms of the tangent function using the reciprocal identity cot(x)=1/tan(x)

tan(x)=3/√(,3)

2. Rationalize the denominator of the right side by multiplying the numerator and denominator by √(,3)

tan(x)=(3√(,3))/3

tan(x)=√(,3)

3. Identify the reference angle in the first quadrant where the tangent is √(,3)

x=π/3

4. Determine the general solution by adding multiples of the period of the tangent function, which is π

x=π/3+n*π

Final Answer

cot(x)=√(,3)/3⇒x=π/3+n*π,n∈ℤ

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