Odpowiedź:
[tex]sin \alpha = \frac{6}{7}\\tg \alpha = \frac{\sqrt{13}}{6} \\ctg \alpha = \frac{6\sqrt{13} }{13}[/tex]
Szczegółowe wyjaśnienie:
[tex]cos \alpha = \frac{\sqrt{13} }{7}\\sin^{2} \alpha + cos^{2} \alpha = 1\\cos^{2} \alpha = ( \frac{\sqrt{13} }{7} )^{2} = \frac{13}{49} \\sin^{2} \alpha = 1 - \frac{13}{49} = \frac{36}{49} \\sin \alpha = \sqrt{\frac{36}{49} } = \frac{6}{7} \\[/tex]
[tex]tg \alpha = \frac{sin \alpha }{cos \alpha } = \frac{\frac{\sqrt{13} }{7} }{\frac{6}{7} } \\tg\alpha = \frac{\sqrt{13} }{7} * \frac{7}{6} = \frac{\sqrt{13} }{6}[/tex]
[tex]ctg\alpha = \frac{1}{tg\alpha } = \frac{1}{\frac{\sqrt{13} }{6} } = \frac{6}{\sqrt{13} } \\ctg \alpha = \frac{6\sqrt{13} }{13}[/tex]
Pozdrawiam.
