Find the Exact Value arcsin(-( square root of 2)/2)

Problem

arcsin(−√(,2)/2)

Solution

1. Identify the range of the inverse sine function, which is [−π/2,π/2]

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

3. Apply the property of odd functions for inverse sine, arcsin(−x)=−arcsin(x) to account for the negative sign.

4. Determine the angle within the restricted range such that sin(θ)=−√(,2)/2 which results in θ=−π/4

Final Answer

arcsin(−√(,2)/2)=−π/4

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