Solve y=ayoperatorname{csin}x

$$y = a y \operatorname { csin } x$$

Solve for a

$$\left\{\begin{matrix}a=\frac{1}{c\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }c\neq 0\\a\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

The equation is in standard form.

$$cy\sin(x)a=y$$

Divide both sides by yc\sin(x).

$$\frac{cy\sin(x)a}{cy\sin(x)}=\frac{y}{cy\sin(x)}$$

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

$$a=\frac{y}{cy\sin(x)}$$

Divide y by yc\sin(x).

$$a=\frac{1}{c\sin(x)}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{1}{a\sin(x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }a\neq 0\\c\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

The equation is in standard form.

$$ay\sin(x)c=y$$

Divide both sides by ay\sin(x).

$$\frac{ay\sin(x)c}{ay\sin(x)}=\frac{y}{ay\sin(x)}$$

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

$$c=\frac{y}{ay\sin(x)}$$

Divide y by ay\sin(x).

$$c=\frac{1}{a\sin(x)}$$