Evaluate arccos(-( square root of 3)/2)

Problem

arccos(−√(,3)/2)

Solution

1. Identify the range of the inverse cosine function, which is [0,π]

2. Recall the reference angle in the first quadrant where the cosine value is √(,3)/2

3. Determine the reference angle (θ_ref) such that cos((θ_ref))=√(,3)/2 which is π/6

4. Apply the property for negative arguments in inverse cosine, arccos(−x)=π−arccos(x)

5. Calculate the final value by subtracting the reference angle from π

π−π/6=(5*π)/6

Final Answer

arccos(−√(,3)/2)=(5*π)/6

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