Solve for x tan(x)=1/2

Problem

tan(x)=1/2

Solution

1. Identify the equation as a basic trigonometric equation where the tangent of an angle x is equal to a constant.

2. Apply the inverse tangent function to both sides of the equation to isolate x for the principal value.

x=arctan(1/2)

3. Determine the general solution by accounting for the periodicity of the tangent function, which has a period of π

x=arctan(1/2)+n*π

4. Specify the domain for the integer n which represents any integer value.

n∈ℤ

Final Answer

tan(x)=1/2⇒x=arctan(1/2)+n*π,n∈ℤ

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