Đáp án:
\(\tan \alpha = - \dfrac{{\sqrt 7 }}{3};\,\,\,\cot \alpha = - \dfrac{{3\sqrt 7 }}{7}\)
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{3\pi }}{2} < \alpha < 2\pi \Rightarrow \sin \alpha < 0\\
{\sin ^2}\alpha + {\cos ^2}\alpha = 1\\
\Leftrightarrow {\sin ^2}\alpha + {\left( {\dfrac{3}{4}} \right)^2} = 1\\
\Leftrightarrow {\sin ^2}\alpha + \dfrac{9}{{16}} = 1\\
\Leftrightarrow {\sin ^2}\alpha = \dfrac{7}{{16}}\\
\sin \alpha < 0 \Rightarrow \sin \alpha = - \dfrac{{\sqrt 7 }}{4}\\
\Rightarrow \left\{ \begin{array}{l}
\tan \alpha = \dfrac{{\sin \alpha }}{{\cos \alpha }} = - \dfrac{{\sqrt 7 }}{3}\\
\cot \alpha = \dfrac{1}{{\tan a}} = - \dfrac{3}{{\sqrt 7 }} = \dfrac{{ - 3\sqrt 7 }}{7}
\end{array} \right.
\end{array}\)
