Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\alpha < \pi < \frac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin \alpha < 0\\
\cos \alpha < 0
\end{array} \right.\\
\tan \alpha = 3 \Leftrightarrow \left\{ \begin{array}{l}
\frac{{\sin \alpha }}{{\cos \alpha }} = 3 \Leftrightarrow \sin \alpha = 3\cos \alpha \\
\cot \alpha = \frac{1}{{\tan \alpha }} = \frac{1}{3}
\end{array} \right.\\
{\sin ^2}\alpha + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\left( {3\cos \alpha } \right)^2} + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\cos ^2}\alpha = \frac{1}{{10}}\\
\cos \alpha < 0 \Rightarrow \cos \alpha = - \frac{{\sqrt {10} }}{{10}}\\
\sin \alpha = 3.\cos \alpha = - \frac{{3\sqrt {10} }}{{10}}
\end{array}\)
