\[\begin{array}{l}
\tan a = - 2\\
= > \frac{{\sin a}}{{\cos a}} = - 2\left( {\cos a \ne 0} \right)\\
= > \sin a = - 2\cos a\\
Co:{\sin ^2}a + {\cos ^2}a = 1\\
= > {\left( { - 2\cos a} \right)^2} + {\cos ^2}a = 1\\
= > 5{\cos ^2}a = 1\\
= > {\cos ^2}a = \frac{1}{5}\\
= > \left[ \begin{array}{l}
\cos a = \frac{1}{{\sqrt 5 }}\\
\cos a = \frac{{ - 1}}{{\sqrt 5 }}
\end{array} \right.\\
+ )\cos a = \frac{1}{{\sqrt 5 }}\\
= > \sin a = \left( { - 2} \right).\frac{1}{{\sqrt 5 }} = \frac{{ - 2}}{{\sqrt 5 }}\\
\cot a = \frac{1}{{\tan a}} = \frac{{ - 1}}{2}\\
+ )\cos a = \frac{{ - 1}}{{\sqrt 5 }}\\
= > \sin a = \left( { - 2} \right).\frac{{ - 1}}{{\sqrt 5 }} = \frac{2}{{\sqrt 5 }}\\
\cot a = \frac{1}{{\tan a}} = \frac{{ - 1}}{2}\\
vay:\sin a = \frac{{ - 2}}{{\sqrt 5 }};\cos a = \frac{1}{{\sqrt 5 }};\tan a = - 2;\cot a = \frac{{ - 1}}{2}\\
hoac:\sin a = \frac{2}{{\sqrt 5 }};\cos a = \frac{{ - 1}}{{\sqrt 5 }};\tan a = - 2;\cot a = \frac{{ - 1}}{2}
\end{array}\]