Вычислите tga, если cosa=-1/2 и π/2<a<π.

\[\cos\alpha = - \frac{1}{2};\ \ \ \]

\[\frac{\pi}{2} < \alpha < \pi \Longrightarrow \sin\alpha > 0;\ \ \ \]

\[tg\alpha < 0.\]

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

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

\[= \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}\]

\[tg\alpha = \frac{\sin\alpha}{\cos\alpha} = \frac{\sqrt{3}}{2}\ :\left( - \frac{1}{2} \right) =\]

\[= - \sqrt{3}.\]