\begin{questions}
\item D'après le cours,
\begin{align*}
\cos^2\alpha + \sin^2\alpha = 1 & \iff \left(\frac{\sqrt5}{3}\right)^2 + \sin^2\alpha=1\\
& \iff \frac{5}{9} + \sin^2\alpha = 1\\
& \iff \sin^2\alpha = 1-\frac{5}{9} = \frac{4}{9}\\
& \iff \sin\alpha = \sqrt{\frac{4}{9}}\\
& \iff \sin\alpha = \frac{2}{3}.
\end{align*}

\item À la calculatrice, on trouve:
\[
\alpha=\arccos\left(\frac{\sqrt5}{3}\right) \approx 42^\circ.
\]
\end{questions}
