Cho góc \(\alpha\) thỏa \(c{\rm{os}}\alpha  =  - \frac{4}{5},\,\,\frac{\pi }{2}...

* Hướng dẫn giải

\(\frac{\pi }{2} < \alpha  < \pi  \Rightarrow \sin \alpha  > 0\)

\(\begin{array}{l}
{\sin ^2}\alpha  + c{\rm{o}}{{\rm{s}}^2}\alpha  = 1\\
 \Rightarrow {\sin ^2}\alpha  = 1 - c{\rm{o}}{{\rm{s}}^2}\alpha  = 1 - {\left( { - \frac{4}{5}} \right)^2} = \frac{9}{{25}} \Rightarrow \sin \alpha  = \frac{3}{5}\\
\tan \,\alpha  = \frac{{ - 3}}{4};\\
\cot \,\alpha  = \frac{{ - 4}}{3}.
\end{array}\)