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 reference angle for which the cosine value is √(,2)/2

3. Determine the reference angle (θ_ref)=π/4 because cos(π/4)=√(,2)/2

4. Apply the property of inverse cosine for negative values, arccos(−x)=π−arccos(x) since the cosine function is negative in the second quadrant.

5. Calculate the final value by subtracting the reference angle from π

π−π/4=(3*π)/4

Final Answer

arccos(−√(,2)/2)=(3*π)/4

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