\begin{enumerate}
\item $\cos\left(2x+\dfrac{\pi}{6}\right)<\dfrac{1}{2} \iff 
\dfrac{\pi}{3}+2k\pi < 2x+\dfrac{\pi}{6} < \dfrac{5\pi}{3}+2k\pi,\quad k\in\Z$ :
\begin{center}
\begin{tikzpicture}[scale=0.5, every node/.style={scale=0.75}]
\draw (0,0) circle (2cm);
\draw[->,>=latex] (-3,0) -- (3,0) node[right] {cos};
\draw[->,>=latex] (0,-3) -- (0,3) node[right] {sin};
\node[below left] at (0,0) {O};
\draw[violet,very thick] (60:2cm) node[above right] {$\frac{\pi}{3}$} arc (60:300:2cm) node[below right] {$\frac{5\pi}{3}$};
\draw[dashed] (60:2) -- (300:2);
\node[below right] at (1,0) {$\frac{1}{2}$};
\end{tikzpicture}
\end{center}
Donc :
\begin{align*}
\cos\left(2x+\dfrac{\pi}{6}\right)<\dfrac{1}{2} & \iff \dfrac{\pi}{3}-\dfrac{\pi}{6}+2k\pi < 2x+\dfrac{\pi}{6}-\dfrac{\pi}{6} < \dfrac{5\pi}{3}-\dfrac{\pi}{6}+2k\pi,\quad k\in\Z\\
& \iff \dfrac{\pi}{6}+2k\pi < 2x  < \dfrac{3\pi}{2}+2k\pi,\quad k\in\Z\\
& \iff \dfrac{\pi}{12}+k\pi < x  < \dfrac{3\pi}{4}+k\pi,\quad k\in\Z
\end{align*}

\begin{center}
\begin{tikzpicture}[scale=0.75, every node/.style={scale=0.75},baseline]
\draw (0,0) circle (2cm);
\draw[->,>=latex] (-3,0) -- (3,0) node[right] {cos};
\draw[->,>=latex] (0,-3) -- (0,3) node[right] {sin};
\node[below left] at (0,0) {O};
\draw[violet,very thick] ({180/12}:2cm) node[above right] {$\frac{\pi}{12}$} arc ({180/12}:{9*180/12}:2cm) node[above left] {$\frac{3\pi}{4}$};
\draw[violet,very thick] ({-9*180/12}:2cm) node[below left] {$-\frac{3\pi}{4}$} arc ({-9*180/12}:{-180/12}:2cm) node[below right] {$-\frac{\pi}{12}$};
\end{tikzpicture}
\qquad $\boxed{\mathcal{S}=\intervOO{-\dfrac{3\pi}{4}}{-\dfrac{\pi}{12}}\cup\intervOO{\dfrac{\pi}{12}}{\dfrac{3\pi}{4}}}$
\end{center}

\item $\begin{aligned}[t]
\sin\left(3x-\dfrac{\pi}{7}\right)\leqslant-\dfrac{\sqrt{2}}{2}
& \iff -\dfrac{3\pi}{4}+2k\pi \leqslant 3x-\dfrac{\pi}{7} \leqslant -\dfrac{\pi}{4}+2k\pi,\quad k\in\Z \\
& \iff -\dfrac{3\pi}{4}+\dfrac{\pi}{7}+2k\pi \leqslant 3x \leqslant -\dfrac{\pi}{4}+\dfrac{\pi}{7}+2k\pi,\quad k\in\Z \\
& \iff -\dfrac{17\pi}{28}+2k\pi \leqslant 3x \leqslant -\dfrac{3\pi}{28}+2k\pi,\quad k\in\Z  \\
& \iff -\dfrac{17\pi}{84}+\dfrac{2k\pi}{3} \leqslant x \leqslant -\dfrac{\pi}{28}+ \dfrac{2k\pi}{3},\quad k\in\Z
\end{aligned}$
\[
\boxed{\mathcal{S}=\intervFF{-\dfrac{73\pi}{84}}{-\dfrac{59\pi}{84}} \cup \intervFF{-\dfrac{17\pi}{84}}{-\dfrac{\pi}{28}} \cup \intervFF{\dfrac{13\pi}{28}}{\dfrac{53\pi}{84}}}
\]
\begin{center}
\begin{tikzpicture}[scale=0.75, every node/.style={scale=0.75}]
\draw (0,0) circle (2cm);
\draw[->,>=latex] (-3,0) -- (3,0) node[right] {cos};
\draw[->,>=latex] (0,-3) -- (0,3) node[right] {sin};
\node[below left] at (0,0) {O};
\draw[red,very thick] ({-17*180/84}:2cm) node[below right] {$-\frac{17\pi}{84}$} arc ({-17*180/84}:{-1*180/28}:2cm) node[below right] {$-\frac{\pi}{28}$};
\draw[red,very thick] ({13*180/28}:2cm) node[above right] {$\frac{13\pi}{28}$} arc ({13*180/28}:{53*180/84}:2cm) node[above left] {$\frac{53\pi}{84}$};
\draw[red,very thick] ({-73*180/84}:2cm) node[below left] {$-\frac{73\pi}{84}$} arc ({-73*180/84}:{-59*180/84}:2cm) node[below left] {$-\frac{59\pi}{84}$};
\end{tikzpicture}
\end{center}
\end{enumerate}
\newpage