Вычислите sina, tga, ctga, если cosa=-5/13 и 90°<a<180°.

\[\cos\alpha = - \frac{5}{13};\ \ \ \ \]

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

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

\[\sin\alpha = \sqrt{1 - \cos^{2}\alpha} =\]

\[= \sqrt{1 - \left( - \frac{5}{13} \right)^{2}} = \sqrt{1 - \frac{25}{169}} =\]

\[= \sqrt{\frac{144}{169}} = \left| \frac{12}{13} \right| = \frac{12}{13}\]

\[tg\ \alpha = \frac{12}{13}\ :\left( - \frac{5}{13} \right) = - \frac{12}{5} =\]

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

\[ctg\ \alpha = - \frac{5}{13}\ :\frac{12}{13} = - \frac{5}{12}.\]