Вычислите sina, cosa, ctga, если tga =-8/15 и 270°<a<360°.

\[tg\ \alpha = - \frac{8}{15};\ \ \ \]

\[270{^\circ} < \alpha < 360{^\circ} \Longrightarrow \sin\alpha < 0;\ \]

\[\cos\alpha > 0;\ \ ctg\ \alpha < 0\]

\[ctg\ \alpha = \frac{1}{\text{tg\ α}} = 1\ :\left( - \frac{8}{15} \right) =\]

\[= - \frac{15}{8} = - 1\frac{7}{8}\]

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

\[= \sqrt{\frac{1}{\left( - \frac{8}{15} \right)^{2} + 1}} = \sqrt{\frac{1}{\frac{64}{225} + 1}} =\]

\[= \sqrt{\frac{1}{\frac{289}{225}}} = \sqrt{\frac{225}{289}} = \left| \frac{15}{17} \right| = \frac{15}{17}\ \]

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

\[= - \frac{8}{15} \cdot \frac{15}{17} = - \frac{8}{17}.\]