Вычислите sina, cosa, tga, если ctga=-5/12 и 90°<a<180°.

\[ctg\ \alpha = - \frac{5}{12};\ \ \ \]

\[90{^\circ} < \alpha < 180{^\circ} \Longrightarrow \sin\alpha > 0;\ \]

\[\cos\alpha < 0;\ \ tg\ \alpha < 0.\]

\[tg\ \alpha = \frac{1}{\text{ctg\ α}} = 1\ :\left( - \frac{5}{12} \right) =\]

\[= - \frac{12}{5} = - 2\frac{2}{5}\]

\[\cos\alpha = \sqrt{\frac{1}{tg^{2}\alpha + 1}} =\]

\[= \sqrt{\frac{1}{\left( - \frac{12}{5} \right)^{2} + 1}} = \sqrt{\frac{1}{\frac{144}{25} + 1}} =\]

\[= \sqrt{\frac{1}{\frac{169}{25}}} = \sqrt{\frac{25}{169}} =\]

\[= \left| \frac{5}{13} \right| = - \frac{5}{13}\]

\[\sin\alpha = tg\ \alpha \cdot \cos\alpha =\]

\[= - \frac{12}{5} \cdot \left( - \frac{5}{13} \right) = \frac{12}{13}\]