Løs 7I=2cosT+2sint

$$7 I = 2 \cos T + 2 \sin t$$

Løs for I

$$I=\frac{2\left(\sin(t)+\cos(T)\right)}{7}$$

Vejledning i at løse lineær ligning

Ligningen er nu i standardform.

$$7I=2\sin(t)+2\cos(T)$$

Divider begge sider med 7.

$$\frac{7I}{7}=\frac{2\left(\sin(t)+\cos(T)\right)}{7}$$

Division med 7 annullerer multiplikationen med 7.

$$I=\frac{2\left(\sin(t)+\cos(T)\right)}{7}$$

Løs for T (complex solution)

$$T=\left(-i\right)\ln(\frac{7}{2}I+\frac{1}{2}ie^{it}+\left(-\frac{1}{2}i\right)e^{\left(-i\right)t}+\left(-\frac{1}{2}\right)\left(\left(\left(-7\right)I+\left(-i\right)e^{it}+ie^{\left(-i\right)t}\right)^{2}-4\right)^{\frac{1}{2}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$T=\left(-i\right)\ln(\frac{7}{2}I+\frac{1}{2}ie^{it}+\left(-\frac{1}{2}i\right)e^{\left(-i\right)t}+\frac{1}{2}\left(\left(\left(-7\right)I+\left(-i\right)e^{it}+ie^{\left(-i\right)t}\right)^{2}-4\right)^{\frac{1}{2}})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$