Вычислите ctga, если sina=-1/2 и π<a<3π/2.

\[\sin a = - \frac{1}{2};\ \ \ \]

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

\[ctg\ a > 0.\]

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

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

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

\[ctg\ a = \frac{\cos a}{\sin a} =\]

\[= - \frac{\sqrt{3}}{2}\ :\left( - \frac{1}{2} \right) = \sqrt{3}\text{.\ \ }\]