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

Problem

tan(x)=√(,3)/3

Solution

1. Identify the standard value for the tangent function. The value √(,3)/3 is equivalent to 1/√(,3)

2. Determine the reference angle. In the unit circle, tan(θ)=1/√(,3) when θ=π/6 (or 30^∘.

3. Consider the period of the tangent function. The tangent function has a period of π meaning it repeats its values every π radians.

4. Write the general solution. To account for all possible angles where the tangent is √(,3)/3 add integer multiples of the period to the reference angle.

Final Answer

x=π/6+n*π,n∈ℤ

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