Simplify 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 standard trigonometric values for the sine function within this range.

3. Determine the angle θ such that sin(θ)=−√(,2)/2

4. Recognize that since sin(π/4)=√(,2)/2 and the sine function is odd, sin(−π/4)=−√(,2)/2

5. Verify that −π/4 falls within the required interval [−π/2,π/2]

Final Answer

arcsin(−√(,2)/2)=−π/4

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