Solve for x tan(x)=1

Problem

tan(x)=1

Solution

1. Identify the basic reference angle where the tangent function equals 1 within the first quadrant.

tan(π/4)=1

2. Determine the period of the tangent function, which is π This means the solution repeats every π radians.

Period=π

3. Generalize the solution by adding integer multiples of the period to the reference angle.

x=π/4+n*π

4. Specify that n must be an integer to cover all possible solutions on the unit circle.

n∈ℤ

Final Answer

tan(x)=1⇒x=π/4+n*π,n∈ℤ

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