Solve for x tan(x)=5/12

Problem

tan(x)=5/12

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 the equation to solve for the principal value of x

x=arctan(5/12)

3. Account for the period of the tangent function, which is π To find all possible solutions, add integer multiples of π to the principal value.

x=arctan(5/12)+n*π

4. Define the variable n as any integer to represent the general solution set.

n∈ℤ

Final Answer

tan(x)=5/12⇒x=arctan(5/12)+n*π,n∈ℤ

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