$\begin{array}{l}
0 < \alpha < \dfrac{\pi }{2} \to \sin \alpha > 0,\cos \alpha > 0,\tan \alpha > 0,\cot \alpha > 0\\
\sin \alpha = \sqrt {1 - {{\cos }^2}\alpha } = \sqrt {1 - {{\left( {\dfrac{1}{2}} \right)}^2}} = \dfrac{{\sqrt 3 }}{2}\\
\tan \alpha = \dfrac{{\sin \alpha }}{{\cos \alpha }} = \sqrt 3 ,\cot \alpha = \dfrac{1}{{\tan \alpha }} = \dfrac{{\sqrt 3 }}{3}\\
7)\dfrac{{3\pi }}{2} < \alpha < 2\pi \to \cos \alpha > 0,\sin \alpha < 0,\tan \alpha < 0,\cot \alpha < 0\\
\cos \alpha = \sqrt {1 - {{\sin }^2}\alpha } = \sqrt {1 - {{\left( { - \dfrac{1}{2}} \right)}^2}} = \dfrac{{\sqrt 3 }}{2}\\
\Rightarrow \tan \alpha = \dfrac{{\sin \alpha }}{{\cos \alpha }} = - \dfrac{{\sqrt 3 }}{3},\cot \alpha = \dfrac{1}{{\tan \alpha }} = - \sqrt 3
\end{array}$
