Find the Exact Value arccos(cos(-(3pi)/5))

Problem

arccos(cos(−(3*π)/5))

Solution

1. Apply the property of cosine for negative angles, cos(−θ)=cos(θ) because cosine is an even function.

cos(−(3*π)/5)=cos((3*π)/5)

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

3. Check the angle (3*π)/5 to see if it falls within the interval [0,π]

0≤(3*π)/5≤π

4. Apply the identity arccos(cos(θ))=θ for θ in the interval [0,π]

arccos(cos((3*π)/5))=(3*π)/5

Final Answer

arccos(cos(−(3*π)/5))=(3*π)/5

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