sin\alpha=\frac{\sqrt6}{3}
sin^2\alpha+cos^2\alpha=1
(\frac{\sqrt6}{3})^2+cos^2\alpha=1
\frac{6}{9}+cos^2\alpha=1
\frac{2}{3}+cos^2\alpha=1
cos\alpha=\sqrt{1-\frac{2}{3}}=\sqrt{\frac{1}{3}}=\frac{1*\sqrt3}{\sqrt3*\sqrt3}=\frac{\sqrt3}{3}
tg\alpha=\frac{sin\alpha}{cos\alpha}=\frac{\sqrt6}{3}:\frac{\sqrt3}{3}=\frac{\sqrt6*3}{3*\sqrt3}=\sqrt2
ctg\alpha=\frac{1}{tg\alpha}=\frac{1*\sqrt2}{\sqrt2*\sqrt2}=\frac{\sqrt2}{2}