Find the Exact Value 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

3. Determine the angle in the second quadrant (since the value is negative) that corresponds to a reference angle of π/4

4. Calculate the specific angle using the formula θ=π−π/4

5. Simplify the expression to find the exact value.

Final Answer

arccos(−√(,2)/2)=(3*π)/4

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