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

Problem

arccos(−√(,2)/2)

Solution

1. Identify the range of the inverse cosine function, which is [0,π]

2. Recall the unit circle values for the cosine function where cos(θ)=√(,2)/2 which occurs at θ=π/4

3. Apply the property for negative arguments in inverse cosine, which states arccos(−x)=π−arccos(x)

4. Substitute the known value into the property: π−π/4

5. Subtract the fractions to find the final angle: (4*π)/4−π/4=(3*π)/4

Final Answer

arccos(−√(,2)/2)=(3*π)/4

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