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

Problem

sin(arccos(−√(,2)/2))

Solution

1. Identify the inner value arccos(−√(,2)/2) The range of the arccosine function is [0,π]

2. Determine the angle θ such that cos(θ)=−√(,2)/2 within the interval [0,π]

3. Calculate the angle using the unit circle, which gives θ=(3*π)/4

4. Substitute the angle back into the outer function to find sin((3*π)/4)

5. Evaluate the sine of (3*π)/4 which is √(,2)/2

Final Answer

sin(arccos(−√(,2)/2))=√(,2)/2

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