[tex]sin\alpha= \frac{1}{2}\\\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\\\cos^{2}\alpha = 1 - sin^{2}\alpha = 1 - (\frac{1}{2})^{2} = \frac{4}{4}-\frac{1}{4} = \frac{3}{4}\\\\cos\alpha = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}\\\\\\tg\alpha = \frac{sin\alpha}{cos\alpha} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}=\frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}\\\\\\ct\alpha = \frac{1}{tg\alpha} = \sqrt{3}[/tex]
