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

Problem

cot(x)=−√(,3)

Solution

1. Identify the equivalent equation using the tangent function by taking the reciprocal of both sides.

tan(x)=−1/√(,3)

2. Determine the reference angle by finding the value of α such that tan(α)=1/√(,3) in the first quadrant.

α=π/6

3. Locate the quadrants where the cotangent (and tangent) function is negative, which are Quadrant II and Quadrant IV.

x=π−π/6=(5*π)/6

x=2*π−π/6=(11*π)/6

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

x=(5*π)/6+n*π

Final Answer

cot(x)=−√(,3)⇒x=(5*π)/6+n*π,n∈ℤ

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