[tex]cos\alpha = \frac{2}{3}\\sin^2\alpha + cos^2\alpha = 1\\sin^2\alpha + (\frac{2}{3})^2=1\\sin^2\alpha = 1 - \frac{4}{9}\\sin^2\alpha = \frac{5}{9}\\sin\alpha = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\tg\alpha = \frac{\sqrt{5}}{3} * \frac{3}{2} = \frac{\sqrt{5}}{2}\\ctg\alpha = \frac{cos\alpha}{sin\alpha}\\ctg\alpha= \frac{2}{3} * \frac{3}{\sqrt{5}} = \frac{6}{3\sqrt{5}}*\frac{\sqrt{5}}{\sqrt{5}} = \frac{6\sqrt{5}}{3*5} = \frac{6\sqrt{5}}{15}=\frac{2\sqrt{5}}{5}[/tex]
