\begin{exercice}
Un carré rouge et un dodécagone regulier vert sont inscrits dans le cercle trigonométrique suivant :\vspace{-2mm}
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\end{center}\vspace{-9mm}
\begin{enumerate}
\item Associer à chaque point une mesure en radians.
\item Donner les valeurs exactes de :\vspace{1mm}
\begin{colenumerate}{4}
\item $\sin \dfrac{2\pi}{3}$
\item $\cos \dfrac{5\pi}{4}$
\item $\sin \dfrac{11\pi}{2}$
\item $\cos \dfrac{7\pi}{6}$
\end{colenumerate}\vspace{1mm}
\item Résoudre les équations  sur $[0~;~2\pi]$.
\begin{colenumerate}{3}
\item $\cos x  =  \dfrac{1}{2}$
\item $\sin x  =  \dfrac{\sqrt{3}}{2}$
\item $\cos x\! =\!  -\dfrac{\sqrt{2}}{2}$
\end{colenumerate}
\end{enumerate}
  \begin{corrige}
  \begin{enumerate}
\item Avec les mesures principales : $P(-\frac{5\pi}{6})$ $Q(-\frac{3\pi}{4})$ $R(-\frac{2\pi}{3})$ $J'(-\frac{\pi}{2})$ $S(-\frac{\pi}{3})$ $T(-\frac{\pi}{4})$ $U(-\frac{\pi}{6})$ $I(0)$ $A(\frac{\pi}{6})$ $B(\frac{\pi}{4})$ $C(\frac{\pi}{3})$ $J(\frac{\pi}{2})$ $D(\frac{2\pi}{3})$ $E(\frac{3\pi}{4})$ $F(\frac{5\pi}{6})$ $I'(\pi)$.
\item
\begin{enumerate}
\item $\sin \frac{2\pi}{3}=\frac{\sqrt{3}}{2}$
\item $\cos \frac{5\pi}{4}=-\frac{\sqrt{2}}{2}$
\item $\sin \frac{11\pi}{2}=-1$
\item $\cos \frac{7\pi}{6}-\frac{\sqrt{3}}{2}$
\end{enumerate}
\item \begin{enumerate}
\item $\{\frac{\pi}{3}~;~\frac{5\pi}{3}\}$
\item $\{\frac{\pi}{3}~;~\frac{2\pi}{3}\}$
\item $\{\frac{3\pi}{4}~;~\frac{5\pi}{4}\}$
\end{enumerate}
\end{enumerate}
\end{corrige}
   \end{exercice}\vspace{-4mm}

