Résoudre (x-2)sinygeq0

$$( x - 2 ) \sin y \geq 0$$

Calculer x

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\geq 2\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }\left(y\geq 2\pi n_{1}\text{ and }y\leq 2\pi n_{1}+\pi \right)\\x\leq 2\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(y\geq 2\pi n_{2}+\pi \text{ and }y\leq 2\pi n_{2}+2\pi \right)\\x\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}\end{matrix}\right,$$

Calculer y

$$\left\{\begin{matrix}\\y=\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=2\\y\in \begin{bmatrix}2\pi n_{1}+\pi ,2\pi n_{1}+2\pi \end{bmatrix}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\leq 2\\y\in \begin{bmatrix}2\pi n_{2},2\pi n_{2}+\pi \end{bmatrix}\text{, }n_{2}\in \mathrm{Z}\text{, }&x\geq 2\end{matrix}\right,$$