Evaluate arctan(-1/3)

Problem

arctan(−1/3)

Solution

1. Identify the range of the inverse tangent function. The value y=arctan(x) must lie in the interval (−π/2,π/2)

2. Recognize that −1/3 is not a standard value associated with common angles like 30 45 or 60

3. Apply the property of odd functions for inverse tangent, which states arctan(−x)=−arctan(x)

4. Express the result in terms of the positive argument.

Final Answer

arctan(−1/3)=−arctan(1/3)

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