حل y=5sin(2x-3.14)+1

$$y=5 \sin ( 2x-3.14 ) +1$$

حل مسائل x (complex solution)

$$x=-\frac{i\ln(\frac{i\sqrt{y^{2}-2y-24}}{5}+\frac{iy}{5}-0.2i)}{2}+\pi n_{1}+1.57\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{i\ln(-\frac{i\sqrt{y^{2}-2y-24}}{5}+\frac{iy}{5}-0.2i)}{2}+\pi n_{2}+1.57\text{, }n_{2}\in \mathrm{Z}$$

حل مسائل y (complex solution)

$$y=-\frac{5ie^{2ix-3.14i}}{2}+\frac{5ie^{3.14i-2ix}}{2}+1$$

حل مسائل x

$$x=\frac{-50\arcsin(\frac{1-y}{5})+100\pi n_{1}+157}{100}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{50\arcsin(\frac{1-y}{5})+100\pi n_{2}+157-50\pi }{100}\text{, }n_{2}\in \mathrm{Z}$$

حل مسائل y

$$y=5\sin(2x-3.14)+1$$