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

Problem

cot(x)=√(,3)

Solution

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

1/tan(x)=√(,3)

2. Solve for tan(x) by taking the reciprocal of both sides.

tan(x)=1/√(,3)

3. Rationalize the denominator to identify the value more easily.

tan(x)=√(,3)/3

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

x=π/6

5. Determine the general solution by adding the period of the tangent function, which is π where n is any integer.

x=π/6+n*π

Final Answer

cot(x)=√(,3)⇒x=π/6+n*π

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