Find the Exact Value arccos(sin(pi/4))

Problem

arccos(sin(π/4))

Solution

1. Evaluate the inner function by finding the sine of π/4 using the unit circle or special triangles.

sin(π/4)=√(,2)/2

2. Substitute the value back into the inverse cosine function.

arccos(√(,2)/2)

3. Determine the angle θ in the interval [0,π] such that cos(θ)=√(,2)/2

cos(π/4)=√(,2)/2

4. Identify the result as the angle that satisfies the condition within the restricted range of the arccosine function.

θ=π/4

Final Answer

arccos(sin(π/4))=π/4

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