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.

tan(π/3)=√(,3)

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

Quadrant II:x=π−π/3=(2*π)/3

Quadrant IV:x=2*π−π/3=(5*π)/3

3. Generalize the solution by accounting for the period of the tangent function, which is π

x=(2*π)/3+n*π

Final Answer

tan(x)=−√(,3)⇒x=(2*π)/3+n*π

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