Réitigh (2y-2)=sin(1.5x+1)

$$( 2 y - 2 ) = \sin ( 1.5 x + 1 )$$

Réitigh do y. (complex solution)

$$y=-\frac{ie^{\frac{3ix}{2}+i}}{4}+\frac{ie^{-\frac{3ix}{2}-i}}{4}+1$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Cuir 2 leis an dá thaobh.

$$2y=\sin(1.5x+1)+2$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$2y=\sin(\frac{3x}{2}+1)+2$$

Roinn an dá thaobh faoi 2.

$$\frac{2y}{2}=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Má roinntear é faoi 2 cuirtear an iolrúchán faoi 2 ar ceal.

$$y=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Roinn \sin(\frac{3x}{2}+1)+2 faoi 2.

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

Réitigh do y.

$$y=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Cuir 2 leis an dá thaobh.

$$2y=\sin(1.5x+1)+2$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$2y=\sin(\frac{3x}{2}+1)+2$$

Roinn an dá thaobh faoi 2.

$$\frac{2y}{2}=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Má roinntear é faoi 2 cuirtear an iolrúchán faoi 2 ar ceal.

$$y=\frac{\sin(\frac{3x}{2}+1)+2}{2}$$

Roinn \sin(\frac{3x}{2}+1)+2 faoi 2.

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

Réitigh do x. (complex solution)

$$x=-\frac{2i\ln(\sqrt{-4y^{2}+8y-3}+2iy-2i)}{3}+\frac{4\pi n_{1}}{3}-\frac{2}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{2i\ln(-\sqrt{-4y^{2}+8y-3}+2iy-2i)}{3}+\frac{4\pi n_{2}}{3}-\frac{2}{3}\text{, }n_{2}\in \mathrm{Z}$$

Réitigh do x.

$$x=\frac{2\left(-\arcsin(2\left(1-y\right))+2\pi n_{1}-1\right)}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{2\left(\arcsin(2\left(1-y\right))+2\pi n_{2}+\pi -1\right)}{3}\text{, }n_{2}\in \mathrm{Z}\text{, }y\geq \frac{1}{2}\text{ and }y\leq \frac{3}{2}$$