[tex]0^{o} < \alpha < 90^{o}\\\\cos\alpha = \frac{1}{\sqrt{5}}\\\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\\\sin^{2}\alpha = 1 - cos^{2}\alpha = 1 - (\frac{1}{\sqrt{5}})^{2} = 1-\frac{1}{5} = \frac{5}{5}-\frac{1}{5} = \frac{4}{5}\\\\sin\alpha = \sqrt{\frac{4}{5}}=\frac{\sqrt{4}}{\sqrt{5}} = \frac{2}{\sqrt{5}}\\\\\\tg\alpha = \frac{sin\Alpha}{cos\alpha}=\frac{\frac{2}{\sqrt{5}}}{\frac{1}{\sqrt{5}}} = 2\\\\\\ctg\alpha = \frac{1}{tg\alpha} = \frac{1}{2}[/tex]
