Cotangente
cot α
=
jambe adjacente
jambe opposée
=
OA
AB
=
A"B"
OA"
=
xB
yB
Si hypoténuse (OB, OA", R) = 1,
cot α = A"B"
Fonction
`y = cot x`
Domaine
`D(cot x) = R - {pin (n in Z)}`
Plage de valeurs
`E(cot x) = R`
Parité
`étrange`
Périodicité
`T = pi`
Zéros
`cot x = 0, x=pi/2 + pin, n in Z`
Intervalles de constance
`cot x > 0, x in (pin, pi/2 + pin), n in Z`
`cot x < 0, x in (-pi/2 + pin, pin), n in Z`
Intervalles de monotonie
`darrdarrdarr x in D`
Extrêmes
`non`
Points d'inflections
`y=0, x = pi/2 + pin, n in Z`
`cot alpha = cos alpha / sin alpha`
`cot alpha = 1/(tan alpha)`
`cot alpha = - tan(alpha + pi/2) = - tan(alpha - pi/2)`
`cot alpha = sqrt(1/sin^2alpha - 1)`
`-cot alpha = cot(-alpha)`
`(cot alpha)^' =-1/sin^2 alpha`
`int cot(alpha)dalpha = -ln |sin alpha| + C`