Solve for x tan(x)=4/5

Problem

tan(x)=4/5

Solution

1. Identify the goal, which is to isolate x by applying the inverse tangent function to both sides of the equation.

2. Apply the inverse function to both sides to undo the tangent operation.

x=arctan(4/5)

3. Consider the general solution because the tangent function is periodic with a period of π

x=arctan(4/5)+n*π

4. Evaluate the principal value using a calculator if a decimal approximation is required.

arctan(4/5)≈0.6747

Final Answer

x=arctan(4/5)+n*π

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