Find the Exact Value 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 values of the tangent function for standard angles within this range.

3. Determine the angle θ such that tan(θ)=−√(,3)

4. Use the property that tan(π/3)=√(,3)

5. Apply the odd function property of tangent, tan(−θ)=−tan(θ) to find that tan(−π/3)=−√(,3)

6. Verify that −π/3 falls within the interval (−π/2,π/2)

Final Answer

arctan(−√(,3))=−π/3

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