3.
b)
[tex]0^{o} < \alpha < 90^{o}\\\\tg\alpha = 2\frac{2}{5} = \frac{12}{5}\\\\tg\alpha = \frac{sin\alpha}{cos\alpha}\\\\\frac{sin\alpha}{cos\alpha} = \frac{12}{5}\\\\12cos\alpha = 5sin\alpha \ \ /:12\\\\cos\alpha = \frac{5}{12}sin\alpha\\\\sin^{2}\alpha+cos^{2}\alpha = 1\\\\sin^{2}\alpha + (\frac{5}{12}sin\alpha)^{2} = 1\\\\sin^{2}\alpha + \frac{25}{144}sin^{2}\alpha = 1\\\\\frac{169}{144}sin^{2}\alpha = 1 \ \ /\cdot\frac{144}{169}\\\\sin^{2}\alpha = \frac{144}{169}\\\\sin\alpha = \sqrt{\frac{144}{169}}[/tex]
[tex]\boxed{sin\alpha = \frac{12}{13}}[/tex]
[tex]cos\alpha = \frac{5}{12}sin\alpha\\\\cos\alpha = \frac{5}{12}\cdot\frac{12}{13}\\\\\boxed{cos\alpha =\frac{5}{13}}\\\\ctg\alpha = \frac{1}{tg\alpha}\\\\ctg\alpha = \frac{1}{\frac{12}{5}}\\\\\boxed{ctg\alpha = \frac{5}{12}}[/tex]
