Evaluate arctan(- square root of 3)

Problem

arctan(−√(,3))

Solution

1. Identify the range of the inverse tangent function, which is (−π/2,π/2)

2. Recall the tangent values for common angles in the first quadrant, specifically that tan(π/3)=√(,3)

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

4. Calculate the value by substituting the known angle into the property.

arctan(−√(,3))=−arctan(√(,3))

arctan(−√(,3))=−π/3

Final Answer

arctan(−√(,3))=−π/3

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