Solve y=operatorname{sir}(sinx)

$$y = \operatorname { sir } ( \sin x )$$

Solve for r

$$\left\{\begin{matrix}r=-\frac{iy}{s\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }s\neq 0\\r\in \mathrm{C}\text{, }&\left(s=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$sir\sin(x)=y$$

The equation is in standard form.

$$is\sin(x)r=y$$

Divide both sides by is\sin(x).

$$\frac{is\sin(x)r}{is\sin(x)}=\frac{y}{is\sin(x)}$$

Dividing by is\sin(x) undoes the multiplication by is\sin(x).

$$r=\frac{y}{is\sin(x)}$$

Divide y by is\sin(x).

$$r=-\frac{iy}{s\sin(x)}$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{iy}{r\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }r\neq 0\\s\in \mathrm{C}\text{, }&\left(r=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$sir\sin(x)=y$$

The equation is in standard form.

$$ir\sin(x)s=y$$

Divide both sides by ir\sin(x).

$$\frac{ir\sin(x)s}{ir\sin(x)}=\frac{y}{ir\sin(x)}$$

Dividing by ir\sin(x) undoes the multiplication by ir\sin(x).

$$s=\frac{y}{ir\sin(x)}$$

Divide y by ir\sin(x).

$$s=-\frac{iy}{r\sin(x)}$$