Solve for x
x=\frac{-4\arcsin(y)+8\pi n_{1}+3\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0
x=\frac{4\arcsin(y)-8\pi n_{1}-3\pi }{4}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0
x=\frac{4\arcsin(y)+8\pi n_{2}-\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(n_{2}>-1\text{ and }y\leq 1\text{ and }y\geq \frac{\sqrt{2}}{2}\right)
x=\frac{-4\arcsin(y)-8\pi n_{2}+\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(n_{2}>-1\text{ and }y\leq 1\text{ and }y\geq \frac{\sqrt{2}}{2}\right)\text{, }|y|\leq 1
Solve for y
y=\sin(\frac{4|x|+\pi }{4})
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