Løs y=|3cos2x-1|

$$y = | 3 \cos 2 x - 1 |$$

Løs for x

$$\left\{\begin{matrix}x=\frac{\arccos(\frac{1-y}{3})+2\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}\text{; }x=\frac{-\arccos(\frac{1-y}{3})+2\pi n_{2}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&y\geq 0\text{ and }y\leq 4\\x=\frac{\arccos(\frac{y+1}{3})+2\pi n_{3}}{2}\text{, }n_{3}\in \mathrm{Z}\text{; }x=\frac{-\arccos(\frac{y+1}{3})+2\pi n_{4}}{2}\text{, }n_{4}\in \mathrm{Z}\text{, }&y\geq 0\text{ and }y\leq 2\end{matrix}\right,$$

Løs for y

$$y=|3\cos(2x)-1|$$