Find the Exact Value arccos(cos(pi/3))

Problem

arccos(cos(π/3))

Solution

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

2. Determine if the input angle π/3 lies within the interval [0,π]

3. Compare the value: since 0≤π/3≤π the composition arccos(cos(θ)) simplifies directly to θ

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

Final Answer

arccos(cos(π/3))=π/3

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