\[\tan\alpha =\dfrac{\sin\alpha}{\cos\alpha}\]
Variazione della funzione tangente
\[\tan0=\tan0^{\circ}=0\]
\[\tan\left(\dfrac{\pi}{2}-\varepsilon\right)=\tan(90^{\circ}-\varepsilon)=+\infty\]
\[\tan\left(\dfrac{\pi}{2}+\varepsilon\right)=\tan(90^{\circ}+\varepsilon)=-\infty\]
\[\tan\pi=\tan180^{\circ}=0\]
\[\tan\left(\dfrac{3}{2}\pi-\varepsilon\right)=\tan(270^{\circ}-\varepsilon)=+\infty\]
\[\tan\left(\dfrac{3}{2}\pi+\varepsilon\right)=\tan(270^{\circ}+\varepsilon)=-\infty\]
\[\tan2\pi=\tan360^{\circ}=0\]
con \(-\infty\leq\tan\alpha\leq+\infty\).
Cotangente
\[\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}=\dfrac{1}{\tan\alpha}\]
Variazione della funzione cotangente
\[\cot\left(0+\varepsilon\right)=\cot(0^{\circ}+\varepsilon)=+\infty\]
\[\cot\left(0-\varepsilon\right)=\cot(0^{\circ}-\varepsilon)=-\infty\]
\[\cot\dfrac{\pi}{2}=\cot90^{\circ}=0\]
\[\cot\left(\pi-\varepsilon\right)=\cot(180^{\circ}-\varepsilon)=-\infty\]
\[\cot\left(\pi+\varepsilon\right)=\cot(180^{\circ}+\varepsilon)=+\infty\]
\[\cot\dfrac{3}{2}\pi=\cot270^{\circ}=0\]
\[\cot(2\pi-\varepsilon)=\cot(360^{\circ}-\varepsilon)=-\infty\]
\[\cot(2\pi+\varepsilon)=\cot(360^{\circ}+\varepsilon)=+\infty\]
con \(-\infty\leq\cot\alpha\leq+\infty\).