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

Problem

tan(x)=−√(,3)/3

Solution

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

θ=π/6

2. Determine the quadrants where the tangent function is negative. Tangent is negative in Quadrant II and Quadrant IV.

Quadrant II and Quadrant IV

3. Calculate the specific solutions within the interval [0,2*π) using the reference angle.

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 tangent function, which is π

x=(5*π)/6+n*π

Final Answer

tan(x)=−√(,3)/3⇒x=(5*π)/6+n*π

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