Solve for x tan(x)=3.5

Problem

tan(x)=3.5

Solution

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

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

x=arctan(3.5)

3. Calculate the principal value using a calculator in radian mode.

x≈1.2925

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

x=arctan(3.5)+n*π

Final Answer

tan(x)=3.5⇒x=arctan(3.5)+n*π

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