Вычислите sina, если tga=корень из 3 и π<a<3π/2.

\[tg\ a = \sqrt{3};\ \ \ \ \ \]

\[\pi < a < \frac{3\pi}{2} \Longrightarrow \cos a < 0;\ \]

\[\sin a < 0\]

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

\[= \sqrt{\frac{1}{\left( \sqrt{3} \right)^{2} + 1}} = \sqrt{\frac{1}{3 + 1}} =\]

\[= \sqrt{\frac{1}{4}} = \left| \frac{1}{2} \right| = - \frac{1}{2}\]

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

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

\[= \sqrt{\frac{3}{4}} = \left| \frac{\sqrt{3}}{2} \right| = - \frac{\sqrt{3}}{2}\text{.\ }\]