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**Refresh my memory plz, Inverse Trig**

[tex]x=\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)[/tex]

Inverse sine is defined from [tex]-\frac{\pi}{2}[/tex] to [tex]\frac{\pi}{2}[/tex] which lies in the 1st and 4th quadrant.

So [tex]x=-\frac{\pi}{4}[/tex]