Вычислите sina, если cosa=-4/5, 90°<a<180°.

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

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

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

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

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