۴. $\sin^{2} 47^{\circ} + \cos^{2} 47^{\circ} = 1$ $1 + \tan^{2} 47^{\circ} = \frac{1}{\cos^{2} 47^{\circ}}$ $\sin 47^{\circ} = \sqrt{1 - \cos^{2} 47^{\circ}} = \sqrt{1 - (\frac{1}{2})^{2}} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$ $\cot 47^{\circ} = \frac{1}{\tan 47^{\circ}}$

۵. $\sin 20^{\circ} \simeq 0.34 \Rightarrow \cos 20^{\circ} = \sqrt{1 - \sin^{2} 20^{\circ}} = \sqrt{1 - (0.34)^{2}} \simeq 0.94$ $\tan 20^{\circ} = \frac{AC}{BC} \simeq \frac{0.34}{0.94}$ $AC = BC \times \tan 20^{\circ} = 2000 \times \frac{0.34}{0.94} \simeq 72$ متر

۶. الف) $\frac{1}{\cos \theta} \frac{1}{\tan \theta} = \frac{\sin \theta}{\cos \theta} \frac{1}{\sin \theta} \frac{1}{\tan \theta} = \frac{1}{\frac{\sin \theta}{\cos \theta}} = \frac{\cos \theta}{\sin \theta}$