Résoudre y=5/2sin(4x+2pi/3)

$$y = \frac { 5 } { 2 } \sin ( 4 x + \frac { 2 \pi } { 3 } )$$

Calculer x (solution complexe)

$$x=-\frac{i\ln(\frac{i\sqrt{4y^{2}-25}+2iy}{5})}{4}+\frac{\pi n_{1}}{2}-\frac{\pi }{6}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{i\ln(\frac{-i\sqrt{4y^{2}-25}+2iy}{5})}{4}+\frac{\pi n_{2}}{2}-\frac{\pi }{6}\text{, }n_{2}\in \mathrm{Z}$$

Calculer y (solution complexe)

$$y=\frac{5ie^{-4ix-\frac{2i\pi }{3}}-5ie^{4ix+\frac{2i\pi }{3}}}{4}$$

Calculer x

$$x=\frac{3\arcsin(\frac{2y}{5})+6\pi n_{1}-2\pi }{12}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{-3\arcsin(\frac{2y}{5})+6\pi n_{2}+\pi }{12}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq \frac{5}{2}$$

Calculer y

$$y=\frac{5\sin(\frac{2\left(6x+\pi \right)}{3})}{2}$$