Solve y=sin(pi/3-2x)dx

$$y = \sin ( \frac { \pi } { 3 } - 2 x ) d x$$

Solve for d

$$\left\{\begin{matrix}d=\frac{y}{x\sin(\frac{\pi -6x}{3})}\text{, }&x\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{6}\\d\in \mathrm{R}\text{, }&\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{6}\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sin(\frac{\pi }{3}-2x)dx=y$$

The equation is in standard form.

$$x\sin(-2x+\frac{\pi }{3})d=y$$

Divide both sides by \sin(\frac{1}{3}\pi -2x)x.

$$\frac{x\sin(-2x+\frac{\pi }{3})d}{x\sin(-2x+\frac{\pi }{3})}=\frac{y}{x\sin(-2x+\frac{\pi }{3})}$$

Dividing by \sin(\frac{1}{3}\pi -2x)x undoes the multiplication by \sin(\frac{1}{3}\pi -2x)x.

$$d=\frac{y}{x\sin(-2x+\frac{\pi }{3})}$$

Divide y by \sin(\frac{1}{3}\pi -2x)x.

$$d=\frac{y}{x\sin(\frac{\pi -6x}{3})}$$