\[\boxed{\mathbf{994.}}\]
\[1)\cos a,\ если\sin a = \frac{2\sqrt{3}}{5}:\]
\[\cos a = \pm \sqrt{1 - \sin^{2}a}\]
\[\cos a = \pm \sqrt{1 - \left( \frac{2\sqrt{3}}{5} \right)^{2}} =\]
\[= \pm \sqrt{\frac{25}{25} - \frac{12}{25}} = \pm \sqrt{\frac{13}{25}} = \pm \frac{\sqrt{13}}{5}\]
\[Ответ:\ \ \pm \frac{\sqrt{13}}{5}.\]
\[2)\sin a,\ если\cos a = - \frac{1}{\sqrt{5}}:\]
\[\sin a = \pm \sqrt{1 - \cos^{2}a}\]
\[\sin a = \pm \sqrt{1 - \left( - \frac{1}{\sqrt{5}} \right)^{2}} =\]
\[= \pm \sqrt{\frac{5}{5} - \frac{1}{5}} = \pm \sqrt{\frac{4}{5}} = \pm \frac{2}{\sqrt{5}}\]
\[Ответ:\ \ \pm \frac{2}{\sqrt{5}}.\]
\[3)\sin a,\ если\cos a = \frac{2}{3}:\]
\[\sin a = \pm \sqrt{1 - \cos^{2}a}\]
\[\sin a = \pm \sqrt{1 - \left( \frac{2}{3} \right)^{2}} =\]
\[= \pm \sqrt{\frac{9}{9} - \frac{4}{9}} = \pm \sqrt{\frac{5}{9}} = \pm \frac{\sqrt{5}}{3}\]
\[Ответ:\ \ \pm \frac{\sqrt{5}}{3}.\]
\[4)\cos a,\ если\sin a = - \frac{1}{\sqrt{3}}:\]
\[\cos a = \pm \sqrt{1 - \sin^{2}a}\]
\[\cos a = \pm \sqrt{1 - \left( - \frac{1}{\sqrt{3}} \right)^{2}} =\]
\[= \pm \sqrt{\frac{3}{3} - \frac{1}{3}} = \pm \sqrt{\frac{2}{3}} =\]
\[= \pm \sqrt{\frac{6}{9}} = \pm \frac{\sqrt{6}}{3}\]
\[Ответ:\ \ \pm \frac{\sqrt{6}}{3}.\]