Solve \( 5 \cos (2 \alpha)=5 \cos ^{2}(\alpha)-4 \) for all solutions \( 0 \leq \alpha<2 \pi \) \( \alpha=\square \) Give your answers accurate to at least 2 decimal places and in a list separated by commas.

13. Calcule \( \sin \left(\frac{\pi}{4}\right) \)

13. Obtenha as menores determinaçôes não negativas dos arcos. a) \( 1300^{\circ} \) b) \( 1440^{\circ} \) c) \( 170^{\circ} \) d) \( \frac{11 \pi}{2} \mathrm{rad} \) e) \( \frac{43 \pi}{5} \mathrm{rad} \) f) \( -1200^{\circ} \)

1) \( y=-9 \cos x \)

13. Obtenha as menores determinaçőes não negativas dos arcos. a) \( 1300^{\circ} \) b) \( 1440^{\circ} \) c) \( 170^{\circ} \) d) \( \frac{11 \pi}{2} \mathrm{rad} \) min e) \( \frac{43 \pi}{5} \mathrm{rad} \) f) \( -1200^{\circ} \)

1) Soit \( k \in Z \) Montrer que: \( \left(\frac{2 \pi}{3}+k \pi\right) \in\left[\frac{-\pi}{3}, \frac{5 \pi}{3}\right] \Longleftrightarrow k \in\{-1 ; 0 ; 1\} \) 2) Montrer que: \( (\forall a \in \mathbb{R}) ;|a-2| \leq \frac{2}{3} \Longleftrightarrow \frac{1}{10} \leq \frac{1}{3 a+2} \leq \frac{1}{6} \)