Evaluate arctan(1)

Problem

arctan(1)

Solution

1. Identify the definition of the inverse tangent function, where y=arctan(x) means that tan(y)=x for y in the interval (−π/2,π/2)

2. Set up the equation to find the angle y such that tan(y)=1

3. Recall the unit circle values or trigonometric identities to determine which angle in the specified interval has a tangent value of 1

4. Determine that tan(π/4)=1 because sin(π/4)=√(,2)/2 and cos(π/4)=√(,2)/2 and tan(θ)=sin(θ)/cos(θ)

5. Conclude that since π/4 falls within the range (−π/2,π/2) it is the correct value.

Final Answer

arctan(1)=π/4

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