Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
\pi < \alpha < \frac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin \alpha < 0\\
\cos \alpha < 0
\end{array} \right.\\
\cos \alpha < 0 \Rightarrow \cos \alpha = - \sqrt {1 - {{\sin }^2}\alpha } = - \sqrt {1 - {{\left( { - \frac{1}{3}} \right)}^2}} = - \frac{{2\sqrt 2 }}{3}\\
\tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} = \frac{1}{{2\sqrt 2 }}\\
\cot \alpha = \frac{{\cos \alpha }}{{\sin \alpha }} = 2\sqrt 2 \\
b,\\
\frac{{3\pi }}{2} < \alpha < 2\pi \Rightarrow \left\{ \begin{array}{l}
\sin \alpha < 0\\
\cos \alpha > 0
\end{array} \right.\\
\sin \alpha < 0 \Rightarrow \sin \alpha = - \sqrt {1 - {{\cos }^2}\alpha } = - \frac{{\sqrt {21} }}{5}\\
\tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} = \frac{{ - \sqrt {21} }}{2}\\
\cot \alpha = \frac{{\cos \alpha }}{{\sin \alpha }} = - \frac{2}{{\sqrt {21} }}
\end{array}\)
