T RIGONOMÉTRIE I
sin
R → [−1; 1]
sin(x)
dx
= cos(x)
arcsin
[−1; 1] → [− π2 ; π2 ]
arcsin(x)
dx
1
= 1−x
2
sin(x) dx = − cos(x) + c t e
p
arcsin(x) dx = x arcsin(x) + 1 − x 2 + c t e
cos
R → [−1; 1]
arccos
[−1; 1] → [0; π]
cos(x)
dx
= − sin(x)
cos(x) dx = sin(x) + c t e
R\{4k π2 ,
tan(x)
dx
tan
∀k ∈ Z} → R
= cos12 (x)
tan(x) dx = − ln(cos(x))
arccos(x)
dx
−1
= 1−x
2
p
arccos(x) dx = x arccos(x) − 1 − x 2 + ct e
arctan
R →] − π2 ; π2 [
arctan(x)
dx
1
= 1+x
2
¡
¢
arcsin(x) dx = x arctan(x) − 21 ln 1 + x 2 + ct e