\(\left\{{}\begin{matrix}tan\alpha=-\dfrac{7}{3}\\sin^2\alpha+cos^2\alpha=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{sin\alpha}{cos\alpha}=-\dfrac{7}{3}\\sin^2\alpha+cos^2\alpha=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin\alpha=-\dfrac{7}{3}cos\alpha\\sin^2\alpha+cos^2\alpha=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin\alpha=-\dfrac{7}{3}cos\alpha\\\dfrac{49}{9}cos^2\alpha+cos^2\alpha=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin\alpha=-\dfrac{7}{3}cos\alpha\\cos^2\alpha=\dfrac{9}{58}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}sin\alpha=-\dfrac{7}{3}cos\alpha\\cos\alpha=\dfrac{3}{\sqrt{58}}\end{matrix}\right.\) (Vì \(\dfrac{3\pi}{2}< \alpha< 2\pi\Rightarrow cos\alpha>0\))
\(\Leftrightarrow\left\{{}\begin{matrix}sin\alpha=-\dfrac{7}{\sqrt{58}}\\cos\alpha=\dfrac{3}{\sqrt{58}}\end{matrix}\right.\)
\(cot\alpha=\dfrac{1}{tan\alpha}=-\dfrac{3}{7}\)
