Επίλυση y^2=sin(log_{10}({1/x^2}))

$${ y }^{ 2 } = \sin ( \log_{ 10 }({ \frac{ 1 }{ { x }^{ 2 } } }) )$$

Λύση ως προς y (complex solution)

$$y=-\sqrt{\sin(\log(\frac{1}{x^{2}}))}$$

$$y=\sqrt{\sin(\log(\frac{1}{x^{2}}))}\text{, }x\neq 0$$

Λύση ως προς x

$$x=-10^{\frac{\arcsin(y^{2})-2\pi n_{1}-\pi }{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x=10^{\frac{\arcsin(y^{2})-2\pi n_{2}-\pi }{2}}\text{, }n_{2}\in \mathrm{Z}$$

$$x=-10^{\frac{-\arcsin(y^{2})-2\pi n_{3}}{2}}\text{, }n_{3}\in \mathrm{Z}$$

$$x=10^{\frac{-\arcsin(y^{2})-2\pi n_{4}}{2}}\text{, }n_{4}\in \mathrm{Z}\text{, }|y|\leq 1$$

Λύση ως προς y

$$y=\sqrt{-\sin(\log(x^{2}))}$$

$$y=-\sqrt{-\sin(\log(x^{2}))}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\left(\left(x>100^{\frac{\pi n_{1}}{2}}\text{ and }x<10^{\pi n_{1}+\frac{\pi }{2}}\right)\text{ or }\left(x>-10^{\pi n_{1}+\frac{\pi }{2}}\text{ and }x<-100^{\frac{\pi n_{1}}{2}}\right)\right)\text{ and }x\neq 0$$