Find the Exact Value arccos(cos((5pi)/6))

Problem

arccos(cos((5*π)/6))

Solution

1. Identify the range of the principal inverse cosine function, arccos(x) which is [0,π]

2. Determine if the input angle (5*π)/6 falls within the interval [0,π]

3. Compare the values: since 0≤(5*π)/6≤π the composition arccos(cos(θ)) simplifies directly to θ

4. Apply the property arccos(cos(θ))=θ for θ∈[0,π]

Final Answer

arccos(cos((5*π)/6))=(5*π)/6

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