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