Find all solutions of the equation. \[ \sin x=-\frac{\sqrt{3}}{2} \]

1. Calcola il valore delle seguenti espressioni, usando le formule di addizione e sottrazione e le \( ^{-125} \) formule di duplicazione: a. \( \frac{1}{2} \cos 15^{\circ}+\frac{\sqrt{3}}{2} \sin 15^{\circ} \) b. \( \sin 150^{\circ}-\cos 120^{\circ} \)

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) \( -1200^{\circ} \)

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) \( -1200^{\circ} \)

Determine las soluciones en \( \mathbb{R} \) de la siguiente ecuación trigonométrica: \[ \sec ^{2}(x)-\sec (x)-2=0 \] a. \( S=\left\{\frac{\pi}{3}+2 k \pi, \frac{5 \pi}{3}+2 k \pi,(2 k+1) \pi: k \in \mathbb{Z}\right\} \) b. \( S=\left\{2 k \pi, \frac{2 \pi}{3}+2 k \pi, \frac{\pi}{6}+2 k \pi: k \in \mathbb{Z}\right\} \) c. \( S=\left\{k \pi, \frac{\pi}{6}+2 k \pi, \frac{5 \pi}{6}+2 k \pi \quad: \quad k \in \mathbb{Z}\right\} \) d. Ninguna de las anteriores