Cosinus
cos α
=
jambe adjacente
hypoténuse
=
OA
OB
=
xB
R
Si hypoténuse (OB, R) = 1,
cos α = jambe adjacente (OA, xB)
Fonction
`y = cos x`
Domaine
`D(cos x) = R`
Plage de valeurs
`E(cos x) = [-1, 1]`
Parité
`Même`
Périodicité
`T = 2pi`
Zéros
`cos x = 0, x=pi/2+pin, n in Z`
Intervalles de constance
`cos x > 0, x in (-pi/2 + 2pin, pi/2 + 2pin), n in Z`
`cos x < 0, x in (pi/2 + 2pin, (3pi)/2 + 2pin), n in Z`
Intervalles de monotonie
`uarruarruarr x in [-pi + 2pin, 2pin], n in Z`
`darrdarrdarr x in [2pin, pi + 2pin], n in Z`
Extrêmes
`y_min = -1, x = pi+2pin, n in Z`
`y_max = 1, x = 2pin, n in Z`
Points d'inflections
`y=0, x = pi/2 + pin, n in Z`
`cos alpha = sin(alpha + pi/2)`
`cos alpha = +- sqrt(1 - sin^2alpha)`
`cos alpha = sin alpha * text(cot α)`
`cos alpha = sin alpha / text(tan α)`
`cos alpha = cos(-alpha)`
`(cos alpha)^' =- sin alpha`
`int cos (alpha)dalpha = sin alpha + C`