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