Tangent and cotangent/Real/Definition

Tangent

The function

$\mathbb {R} \setminus {\left({\frac {\pi }{2}}+\mathbb {Z} \pi \right)}\longrightarrow \mathbb {R} ,x\longmapsto \tan x={\frac {\sin x}{\cos x}},$

is called tangent, and the function

$\mathbb {R} \setminus \mathbb {Z} \pi \longrightarrow \mathbb {R} ,x\longmapsto \cot x={\frac {\cos x}{\sin x}},$

is called cotangent.