\sin a\leq0;\cos a\leq0;\\
\cos^2a+\sin^2a=1;\\
\cos^2a=1-\sin^2a;\\
\cos a=-\sqrt{1-\sin^2a}=-\sqrt{1-(-3\frac{\sqrt{11}}{10})^2}=-\sqrt{1-\frac{99}{100}}=\\
=-\sqrt{\frac{100-99}{100}}=-\sqrt{\frac{1}{100}}=-\frac{1}{10};\\
\cos a=-\frac{1}{10};\\" alt="\sin a=-3\frac{\sqrt{11}}{10};\\
(-3\frac{\sqrt{11}}{10})^2=\frac{9\cdot11}{100}=\frac{99}{100}<1!!!!\\
a\in(\pi;\frac{3\pi}{2});==>\sin a\leq0;\cos a\leq0;\\
\cos^2a+\sin^2a=1;\\
\cos^2a=1-\sin^2a;\\
\cos a=-\sqrt{1-\sin^2a}=-\sqrt{1-(-3\frac{\sqrt{11}}{10})^2}=-\sqrt{1-\frac{99}{100}}=\\
=-\sqrt{\frac{100-99}{100}}=-\sqrt{\frac{1}{100}}=-\frac{1}{10};\\
\cos a=-\frac{1}{10};\\" align="absmiddle" class="latex-formula">