Løs 4sin3x+2m=3

$$4 \sin 3 x + 2 m = 3$$

Løs for m

$$m=\frac{-4\sin(3x)+3}{2}$$

Vejledning i at løse lineær ligning

Subtraher 4\sin(3x) fra begge sider.

$$2m=3-4\sin(3x)$$

Ligningen er nu i standardform.

$$2m=-4\sin(3x)+3$$

Divider begge sider med 2.

$$\frac{2m}{2}=\frac{-4\sin(3x)+3}{2}$$

Division med 2 annullerer multiplikationen med 2.

$$m=\frac{-4\sin(3x)+3}{2}$$

Løs for x (complex solution)

$$x=\left(-\frac{1}{3}i\right)\ln(\left(-\frac{1}{2}i\right)m+\frac{3}{4}i+\left(-\frac{1}{4}i\right)\left(-7+\left(-12\right)m+4m^{2}\right)^{\frac{1}{2}})+\frac{2}{3}\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-\frac{1}{3}i\right)\ln(\left(-\frac{1}{2}i\right)m+\frac{3}{4}i+\frac{1}{4}i\left(-7+\left(-12\right)m+4m^{2}\right)^{\frac{1}{2}})+\frac{2}{3}\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

Løs for x

$$x=\frac{\arcsin(\frac{3-2m}{4})+2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{-\arcsin(\frac{3-2m}{4})+2\pi n_{2}+\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }m\geq -\frac{1}{2}\text{ and }m\leq \frac{7}{2}$$