Simplify sin(arccos(( square root of 2)/2))

Problem

sin(arccos(√(,2)/2))

Solution

1. Evaluate the inner inverse trigonometric function arccos(√(,2)/2)

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

3. Determine that θ=π/4 because cos(π/4)=√(,2)/2

4. Substitute the angle back into the outer function to get sin(π/4)

5. Calculate the value of sin(π/4) which is √(,2)/2

Final Answer

sin(arccos(√(,2)/2))=√(,2)/2

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