Fiche de révision - trigonométrie

TRIGONOMÉTRIE I
sin arcsin
R→[−1;1] [−1;1] →[−π
2;π 2]
sin(x)
dx =cos(x)arcsin(x) dx =1
1−x2
sin(x) dx =−cos(x)+c t e arcsin(x) dx =xarcsin(x)+p1−x2+c t e
cos arccos
R→[−1;1] [−1;1] →[0;π]
cos(x)
dx =−sin(x)arccos(x) dx =−1
1−x2
cos(x) dx =sin(x)+c t e arccos(x) dx =xarccos(x)−p1−x2+c t e
tan arctan
R\{4kπ
2,∀k∈Z}→R R →]−π 2;π 2[
tan(x)
dx =1
cos2(x)
arctan(x)
dx =1
1+x2
tan(x) dx =−ln(cos(x)) arcsin(x) dx =xarctan(x)−1
2ln¡1+x2¢+c t e