Simplify arctan(-1/( square root of 3))

Problem

arctan(−1/√(,3))

Solution

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

2. Apply the property of odd functions for arctangent, which states arctan(−x)=−arctan(x)

arctan(−1/√(,3))=−arctan(1/√(,3))

3. Determine the angle θ in the interval (0,π/2) such that tan(θ)=1/√(,3)

tan(π/6)=1/√(,3)

4. Substitute the value back into the expression to find the final result.

−arctan(1/√(,3))=−π/6

Final Answer

arctan(−1/√(,3))=−π/6

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