[tex]sin\alpha=\frac15\\\alpha \in (90; 180)\\sin^2\alpha+cos^2\alpha=1\\cos^2\alpha = 1-sin^2\alpha\\cos^2\alpha=1-(\frac15)^2\\cos^2\alpha=1-\frac1{25}\\cos^2\alpha=\frac{24}{25}\\cos\alpha=-\sqrt{\frac{24}{25}}=-\frac{2\sqrt6}5\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg\alpha=\frac{\frac15}{-\frac{2\sqrt6}5}=\frac15*(-\frac5{2\sqrt6})=-\frac1{2\sqrt6}=-\frac{\sqrt6}{2*6}=-\frac{\sqrt6}{12}\\ctg\alpha=\frac{cos\alpha}{sin\alpha}\\ctg\alpha=\frac{-\frac{2\sqrt6}5}{\frac15}=-\frac{2\sqrt6}5*5=-2\sqrt6[/tex]
