Solve 1/n=sin(x)

$$\frac { 1 } { n } = \sin ( x )$$

Solve for n

$$n=\frac{1}{\sin(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$1=n\sin(x)$$

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

$$n\sin(x)=1$$

The equation is in standard form.

$$\sin(x)n=1$$

Divide both sides by \sin(x).

$$\frac{\sin(x)n}{\sin(x)}=\frac{1}{\sin(x)}$$

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

$$n=\frac{1}{\sin(x)}$$

Variable n cannot be equal to 0.

$$n=\frac{1}{\sin(x)}\text{, }n\neq 0$$

Solve for x (complex solution)

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

$$x=2\pi n_{2}-i\ln(\frac{\sqrt{n^{2}-1}+i}{n})\text{, }n_{2}\in \mathrm{Z}\text{, }n\neq 0$$