Вычислите cosa, tga, ctga, если sina=-4/5 и 180°<a<270°.

\[\sin\alpha = - \frac{4}{5};\ \ \]

\[180{^\circ} < \alpha < 270{^\circ} \Longrightarrow \cos\alpha < 0;\ \ \]

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

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

\[= \sqrt{1 - \left( - \frac{4}{5} \right)^{2}} = \sqrt{1 - \frac{16}{25}} =\]

\[= \sqrt{\frac{9}{25}} = \left| \frac{3}{5} \right| = - \frac{3}{5}\]

\[tg\ \alpha = - \frac{4}{5}\ :\left( - \frac{3}{5} \right) = \frac{4}{3} = 1\frac{1}{3}\]

\[ctg\ \alpha = - \frac{3}{5}\ :\left( - \frac{4}{5} \right) = \frac{3}{4}.\]