Find the Exact Value arctan(-1)

Problem

arctan(−1)

Solution

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

2. Set up the equation tan(y)=−1 where y must be within the interval (−π/2,π/2)

3. Recall the unit circle values for the tangent function, noting that tan(π/4)=1

4. Apply the odd function property of tangent, tan(−y)=−tan(y) to determine that tan(−π/4)=−1

5. Verify that −π/4 falls within the required range (−π/2,π/2)

Final Answer

arctan(−1)=−π/4

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