Find the Exact Value arccos(( square root of 2)/2)

Problem

arccos(√(,2)/2)

Solution

1. Identify the definition of the inverse cosine function, where y=arccos(x) means cos(y)=x for y in the interval [0,π]

2. Set up the equation to find the angle y such that cos(y)=√(,2)/2

3. Recall the unit circle values for the cosine function, noting that cos(π/4)=√(,2)/2

4. Verify that the angle π/4 falls within the restricted range of the arccosine function, which is [0,π]

Final Answer

arccos(√(,2)/2)=π/4

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