[tex]cos\alpha = \frac{3}{4}\\\\sin^{2}\alpha + cos^{2}\alpha = 1\\\\sin^{2}\alpha = 1 - cos^{2}\alpha = 1 - (\frac{3}{4})^{2} = \frac{16}{16} - \frac{9}{16} = \frac{7}{16}\\\\sin\alpha = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{\sqrt{16}}=\frac{\sqrt{7}}{4}\\\\tg\alpha = \frac{sin\alpha}{cos\alpha} = \frac{\frac{\sqrt{7}}{4}}{\frac{3}{4}}=\frac{\sqrt{7}}{3}\\\\ctg\alpha = \frac{1}{tg\alpha} = \frac{3}{\sqrt{7}}\cdot\frac{\sqrt{7}}{\sqrt{7}} = \frac{3\sqrt{7}}{7}[/tex]