Resolver {l}{tanx=1/2}{y=cos(x-pi/2)}

$$\left\{ \begin{array} { l } { \tan x = \frac { 1 } { 2 } } \\ { y = \cos ( x - \frac { \pi } { 2 } ) } \end{array} \right.$$

Ebatzi: x, y (complex solution)

$$x=\pi n_{1}+\arctan(\frac{1}{2})$$

$$n_{1}\in \mathrm{Z}$$

$$y=\frac{\sqrt{5}\left(-1\right)^{n_{1}}}{5}$$

$$n_{1}\in \mathrm{Z}$$

Ebatzi: x, y

$$x=2\pi n_{1}+\arcsin(\frac{\sqrt{5}}{5})+\pi \text{, }n_{1}\in \mathrm{Z}\text{, }y=-\frac{\sqrt{5}}{5}\approx -0.447213595$$

$$x=2\pi n_{2}+\arcsin(\frac{\sqrt{5}}{5})\text{, }n_{2}\in \mathrm{Z}\text{, }y=\frac{\sqrt{5}}{5}\approx 0.447213595$$