Solve -j=sin4x

$$- j = \sin 4 x$$

Solve for j

$$j=-\sin(4x)$$

Steps for Solving Linear Equation

The equation is in standard form.

$$-j=\sin(4x)$$

Divide both sides by -1.

$$\frac{-j}{-1}=\frac{\sin(4x)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$j=\frac{\sin(4x)}{-1}$$

Divide \sin(4x) by -1.

$$j=-\sin(4x)$$

Solve for x (complex solution)

$$x=-\frac{i\ln(\sqrt{1-j^{2}}-ij)}{4}+\frac{\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{i\ln(-\sqrt{1-j^{2}}-ij)}{4}+\frac{\pi n_{2}}{2}\text{, }n_{2}\in \mathrm{Z}$$

Solve for x

$$x=\frac{-\arcsin(j)+2\pi n_{1}}{4}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{\arcsin(j)+2\pi n_{2}+\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }|j|\leq 1$$