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

Problem

tan(x)=−√(,3)

Solution

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

θ=π/3

2. Determine the quadrants where the tangent function is negative. Tangent is negative in the second and fourth quadrants.

Quadrant II and Quadrant IV

3. Calculate the general solutions within one period of the tangent function, which has a period of π

x=π−π/3=(2*π)/3

4. Apply the periodicity of the tangent function to find all possible values for x where k is any integer.

x=(2*π)/3+k*π

Final Answer

tan(x)=−√(,3)⇒x=(2*π)/3+k*π,k∈ℤ

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