Résoudre g=sin(x+1)

$$g = \sin ( x + 1 )$$

Calculer g (solution complexe)

$$g=\frac{ie^{-ix-i}-ie^{ix+i}}{2}$$

Calculer x (solution complexe)

$$x=-i\ln(\sqrt{1-g^{2}}+ig)+2\pi n_{1}-1\text{, }n_{1}\in \mathrm{Z}$$

$$x=-i\ln(-\sqrt{1-g^{2}}+ig)+2\pi n_{2}-1\text{, }n_{2}\in \mathrm{Z}$$

Calculer g

$$g=\sin(x+1)$$

Calculer x

$$x=\arcsin(g)+2\pi n_{1}-1\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\arcsin(g)+2\pi n_{2}+\pi -1\text{, }n_{2}\in \mathrm{Z}\text{, }|g|\leq 1$$