Вычислите cosa, если sina=-8/17, 180°<a<270°.

\[\sin\alpha = - \frac{8}{17};\ \ \]

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

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

\[= \sqrt{1 - \left( - \frac{8}{17} \right)^{2}} = \sqrt{1 - \frac{64}{289}} =\]

\[= \sqrt{\frac{225}{289}} = \left| \frac{15}{17} \right| = - \frac{15}{17}\ \]