Find the Exact Value arccos(cos(-pi/4))

Problem

arccos(cos(−π/4))

Solution

1. Evaluate the inner cosine function using the even-odd property cos(−θ)=cos(θ)

cos(−π/4)=cos(π/4)

2. Determine the exact value of cos(π/4) using the unit circle.

cos(π/4)=√(,2)/2

3. Substitute this value back into the inverse cosine function.

arccos(√(,2)/2)

4. Identify the angle θ in the restricted range of arccosine, [0,π] such that cos(θ)=√(,2)/2

θ=π/4

Final Answer

arccos(cos(−π/4))=π/4

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