Verify the Identity tan(theta)=1

Problem

tan(θ)=1

Solution

1. Identify the equation as a trigonometric equation to solve for the variable θ within a standard interval, typically [0,2*π)

2. Recall the definition of the tangent function in terms of the unit circle, where tan(θ)=y/x

3. Determine the angles where the ycoordinate and xcoordinate are equal, which occurs in Quadrant I and Quadrant III.

4. Find the reference angle by calculating arctan(1) which results in π/4 (or 45.

5. Apply the periodicity of the tangent function, which is π to find all solutions.

Final Answer

θ=π/4+n*π,n∈ℤ

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