Solve for x tan(x)=2/3

Problem

tan(x)=2/3

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose tangent is 2/3

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

arctan(tan(x))=arctan(2/3)

3. Simplify the left side using the property of inverse functions.

x=arctan(2/3)

4. Account for the period of the tangent function, which is π to find the general solution.

x=arctan(2/3)+n*π

5. Specify that n must be an integer.

n∈ℤ

Final Answer

x=arctan(2/3)+n*π

Want more problems? Check here!