![image](https://tex.z-dn.net/?f=%5Csin+a%3D-3%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B10%7D%3B%5C%5C%0A%28-3%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B10%7D%29%5E2%3D%5Cfrac%7B9%5Ccdot11%7D%7B100%7D%3D%5Cfrac%7B99%7D%7B100%7D%3C1%21%21%21%21%5C%5C%0Aa%5Cin%28%5Cpi%3B%5Cfrac%7B3%5Cpi%7D%7B2%7D%29%3B%3D%3D%3E%5Csin+a%5Cleq0%3B%5Ccos+a%5Cleq0%3B%5C%5C%0A%5Ccos%5E2a%2B%5Csin%5E2a%3D1%3B%5C%5C%0A%5Ccos%5E2a%3D1-%5Csin%5E2a%3B%5C%5C%0A%5Ccos+a%3D-%5Csqrt%7B1-%5Csin%5E2a%7D%3D-%5Csqrt%7B1-%28-3%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B10%7D%29%5E2%7D%3D-%5Csqrt%7B1-%5Cfrac%7B99%7D%7B100%7D%7D%3D%5C%5C%0A%3D-%5Csqrt%7B%5Cfrac%7B100-99%7D%7B100%7D%7D%3D-%5Csqrt%7B%5Cfrac%7B1%7D%7B100%7D%7D%3D-%5Cfrac%7B1%7D%7B10%7D%3B%5C%5C%0A%5Ccos+a%3D-%5Cfrac%7B1%7D%7B10%7D%3B%5C%5C)
\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">