Find the Exact Value arctan(1)

Problem

arctan(1)

Solution

1. Identify the definition of the inverse tangent function, which asks for an angle θ in the interval (−π/2,π/2) such that tan(θ)=1

2. Recall the trigonometric values for common angles within the unit circle.

3. Determine the angle where the sine and cosine values are equal, since tan(θ)=sin(θ)/cos(θ)

4. Evaluate the expression by noting that tan(π/4)=1 and π/4 falls within the required range (−π/2,π/2)

Final Answer

arctan(1)=π/4

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