Odpowiedź:
[tex] \sin\alpha = \frac{5}{7} \\ \\ { \sin }^{2} \alpha + { \cos}^{2} \alpha = 1 \\ ( \frac{5}{7} {)}^{2} + { \cos}^{2} \alpha = 1 \\ \frac{25}{49} + { \cos}^{2} \alpha = 1 \\ { \cos}^{2} \alpha = \frac{24}{49} \\ \cos \alpha = \frac{2 \sqrt{6} }{7} \\ \\ \tg \alpha = \frac{ \sin \alpha }{ \cos \alpha } = \frac{ \frac{5}{7} }{ \frac{2 \sqrt{6} }{7} } = \frac{5}{7} \times \frac{7}{2 \sqrt{6} } = \frac{5}{2 \sqrt{6} } = \frac{5 \sqrt{6} }{12} \\ \\ \ctg\alpha = \frac{1}{tg \alpha } = \frac{1}{ \frac{5}{2 \sqrt{6} } } = \frac{2 \sqrt{6} }{5} [/tex]
