2. \( 2 \sin 2 x-3 \cdot \cos y \) ifadesinin alabileceği en küçük tam sayı değeri kaçtır? \( \begin{array}{lllll}\text { A) }-5 & \text { B) }-4 & \text { C) }-3 & \text { D) }-2 & \text { E) }-1\end{array} \)

EXERCICE3: (5 points) 1. Résous dams R, requation \( 2 t^{2}+\sqrt{3} t-3=0 \) 2. Détermine les nombres réels \( A \) et \( B \) tels que pourt tout \( x \in \mathbb{R} \), on ait: \[ \sqrt{3} \cos x+\sin x=A \sin (x+B) \] 3. a. Utilise les résultats des questions 1. et 2. pour résoudre dans l'intervalle ] \( -\pi \); \( \pi \) ] léquation \( (E)=\left(2 \cos ^{2} x+\sqrt{3} \cos x-3\right)(\sqrt{3} \cos x+\sin x-\sqrt{3})=0 \) 4. Reprisente les images des solutions de (E) sur un cercle trigonométrique.

\( \sin 15+i \cos 15)^{2} \) equals to: \( \frac{\sqrt{3}+i}{2} \) \( \frac{1+\sqrt{3} i}{2} \)

Ex.2; Find Own Ship's New Course \( \mathrm{C}_{0}=010^{\circ}, \mathrm{V}_{0}=12 \mathrm{kn} \). Radar observations in fogs \( 1030 \mathrm{D}=8^{\prime}, 0, \mathrm{~T} \mathrm{~B}=038^{\circ} \); \( 1036 \mathrm{D}=7^{\prime}, 0, \mathrm{~T} \mathrm{~B}=038^{\circ} \); \( 1042 \mathrm{D}=6^{\prime}, 0, \mathrm{~T} \mathrm{~B}=038^{\circ} \); Own ship will alter course to starboard in 9 minutes to make the desired \( \mathrm{DCPA}=2^{\prime}, 0 \). Requireds 1. The target ship's course and speed. 2. Own ship's new course and new TCPA 4

\( \left. \begin{array} { l } { \frac { \sin 210 ^ { \circ } \cos 300 ^ { \circ } \tan 240 ^ { \circ } } { \cos 120 ^ { \circ } \tan 150 ^ { \circ } \sin 330 ^ { \circ } } } \\ { [ \sin ( - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] } \end{array} \right. \)

If \( \sin \theta+\cos \theta=x \), then find the value of \( \sin ^{8} \theta+\sin ^{4} \theta+ \) \( \cos ^{6} \theta+\cos ^{4} \theta \).