Définitions via sin⁡\sin et cos⁡\cos
tan⁡x=sin⁡xcos⁡x\tan x=\dfrac{\sin x}{\cos x}, D(tan⁡): x≠π2+πk, k∈ZD(\tan):\ x\neq \dfrac{\pi}{2}+\pi k,\ k\in\mathbb{Z}. cot⁡x=cos⁡xsin⁡x\cot x=\dfrac{\cos x}{\sin x}, D(cot⁡): x≠πk, k∈ZD(\cot):\ x\neq \pi k,\ k\in\mathbb{Z}. Les deux fonctions ont un point π\pi (le moins positif sur les domaines respectifs) et sont impairs.
Asymptotes verticales : pour tan⁡x\tan x quand cos⁡x=0\cos x=0 ; pour cot⁡x\cot x quand sin⁡x=0\sin x=0
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