Solve for x cot(x)=-1/( square root of 3)

Problem

cot(x)=−1/√(,3)

Solution

1. Identify the equivalent tangent value by using the reciprocal identity tan(x)=1/cot(x)

tan(x)=−√(,3)

2. Determine the reference angle by finding the value of θ such that tan(θ)=√(,3) in the first quadrant.

θ=π/3

3. Apply the properties of the tangent function, noting that tan(x) is negative in the second and fourth quadrants.

x=π−π/3=(2*π)/3

x=2*π−π/3=(5*π)/3

4. Generalize the solution by adding multiples of the period of the cotangent function, which is π

x=(2*π)/3+n*π

Final Answer

cot(x)=−1/√(,3)⇒x=(2*π)/3+n*π

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