Simplify arctan(0)

Problem

arctan(0)

Solution

1. Identify the definition of the inverse tangent function, where y=arctan(x) means 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)=0

3. Recall the trigonometric identity tan(y)=sin(y)/cos(y)

4. Solve for y by finding where sin(y)=0 within the restricted range (−π/2,π/2)

5. Determine that sin(0)=0 which satisfies the condition.

Final Answer

arctan(0)=0

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