5.2 Determine the following with the aid of a calculator 5.2.1 \( \quad \) the size of the angle \( \alpha \). 5.2.2 the area of the \( \triangle P O X \) if it given that \( \mathrm{X}(2 ; 0) \)

1. \( -1450^{\circ} \) nin esas ölçüsü aşağıdakilerden hangisi- dir? \( \begin{array}{lllll}\text { A) } 10^{\circ} & \text { B) } 40^{\circ} & \text { C) } 105^{\circ} & \text { D) } 150^{\circ} & \text { E) } 350^{\circ}\end{array} \)

सिद्ध करें कि \( \frac{\tan \theta}{1-\cot }+\frac{\cot \theta}{1-\tan }=1+\sec \theta \cdot \operatorname{cosec} \theta \)

3. \[ \begin{array}{l} a=\cos 100^{\circ} \\ b=\sin 140^{\circ} \\ c=\cos 70^{\circ} \\ d=\tan 230^{\circ} \end{array} \] olduğuna göre, aşağıdaki sıralamalardan hangisi doğrudur? A) b \( > \) a \( > \) c \( > \) d B) \( b>c>d>a \) C) \( b>d>c>a \) D) \( d> \) c \( > \) b \( > \) a E) \( d>b>c>a \)

1.2 Produit scalaire et vectoriel A) Soient \( \bar{i} \) et \( \hat{\theta} \) deux vecteurs du plan ou de l'espace muni d'un repère orthonormé où \( \theta \) est I angle entre \( \hat{\theta} \) et \( \hat{\theta} \). Calculez ิ \( \cdot \mathrm{I}^{-1} \) si 1) \( |\vec{u}|=3,|\vec{u}|=5 \mathrm{et} \theta=60^{\circ} \) 2) \( \|\tilde{u}\|=\frac{3}{2},\|\vec{v}\|=4 \mathrm{et} \theta=\frac{\pi}{4} \) 3) \( |\vec{u}|=\frac{1}{\sqrt{3}},|v|=3 \mathrm{et} \theta=\frac{5 \pi}{6} \) 4) \( |\vec{u}|=\frac{1}{3} \cdot|\bar{v}|=2 \mathrm{cl} \theta=\frac{\pi}{2} \) 5) \( |\vec{u}|=4,|\bar{v}|=1 \mathrm{et} \theta=135^{\circ} \)

\( \frac{\cos 150^{\circ} \cdot \cos 45^{\circ}}{\sin 30^{\circ}-\tan 135^{\circ}} \) işleminin sonucu kaçtır? \( \begin{array}{lllll}\text { A) }-2 & \text { B) }-\sqrt{3} & \text { C) }-\frac{\sqrt{6}}{6} & \text { D) } \frac{1}{4} & \text { E) } \frac{\sqrt{2}}{4}\end{array} \)