[tex]sin\alpha = \frac{2}{9}\\\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\\\cos^{2}\alpha = 1 - sin^{2}\alpha = 1-(\frac{2}{9})^{2} = \frac{81}{81} - \frac{4}{81}=\frac{77}{81}\\\\cos\alpha = \sqrt{\frac{77}{81}} = \frac{\sqrt{77}}{\sqrt{81}}\\\\cos\alpha = \frac{\sqrt{77}}{9}[/tex]
[tex]tg\alpha = \frac{sin\alpha}{cos\alpha} =\frac{\frac{2}{9}}{\frac{\sqrt{77}}{9}} = \frac{2}{\sqrt{77}}\cdot\frac{\sqrt{77}}{\sqrt{77}}\\\\tg\alpha = \frac{2\sqrt{77}}{77}\\\\\\ctg\alpha = \frac{1}{tg\alpha}\\\\ctg\alpha = \frac{\sqrt{77}}{2}}[/tex]
