Whakaoti i te y=2sin5x

$$y = 2 \sin 5 x$$

Whakaoti mō x (complex solution)

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

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

Whakaoti mō x

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

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

Whakaoti mō y

$$y=2\sin(5x)$$