Solve y=2-3sin(pi/4left(x-1right))

$$y = 2-3 \sin ( \frac{ \pi }{ 4 } \left( x-1 \right) )$$

Solve for x (complex solution)

$$x=\frac{-4i\ln(\frac{-i\sqrt{\left(y-5\right)\left(y+1\right)}-iy+2i}{3})+\pi }{\pi }+8n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{-4i\ln(\frac{i\sqrt{\left(y-5\right)\left(y+1\right)}-iy+2i}{3})+\pi }{\pi }+8n_{2}\text{, }n_{2}\in \mathrm{Z}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{4\arcsin(\frac{2-y}{3})}{\pi }+8n_{1}+9\text{, }n_{1}\in \mathrm{Z}\text{, }&y=5\text{ or }y=-1\\x=\frac{4\arcsin(\frac{2-y}{3})}{\pi }+8n_{2}+1\text{, }n_{2}\in \mathrm{Z}\text{; }x=-\frac{4\arcsin(\frac{2-y}{3})}{\pi }+8n_{3}+5\text{, }n_{3}\in \mathrm{Z}\text{, }&y\geq -1\text{ and }y\leq 5\end{matrix}\right.$$

Solve for y

$$y=-3\sin(\frac{\pi \left(x-1\right)}{4})+2$$