Solve for x tan(x)=3

Problem

tan(x)=3

Solution

1. Identify the equation as a basic trigonometric equation of the form tan(x)=a

2. Apply the inverse tangent function to both sides to find the principal value of x

x=arctan(3)

3. Determine the general solution by adding the period of the tangent function, which is n*π where n is any integer.

x=arctan(3)+n*π

4. Calculate the numerical value of the principal solution in radians if a decimal approximation is required.

arctan(3)≈1.249

Final Answer

tan(x)=3⇒x=arctan(3)+n*π

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