Chapitre 4

(O;~u;~v)
O1

2π
ππ
2
CO[OI]
IC(I;A)IA =OI = 1
C[IA)
[IA0)

N ϑ M
C
ϑ M
RC
•ϑ
ICx
M
•ϑ
ICx
M
•P π K
K π
_
IK π
•L−π
2
B0
_
IL π
2
M l
_
IM
d\ IOM d =180×l
π
M ϑ
ϑ0ϑ0=ϑ+ (2π)×k=ϑ+ 2kπ k
Jπ
2
π
2+ 2π=5π 2
π
2+ 4π
π
2+ 2kπ π 2−2π=−3π 2
π
2−4ππ 2−2kπ

ABC B
cos(\ BAC) = BA
AC sin(\
BAC) = BC
AC tan(\
BAC) = BC
BA
arccos arcsin arctan
cos−1sin−1tan−1

CO I
I0J J0
M ϑ
ϑcos(ϑ)M(O;I;J)
ϑsin(ϑ)M(O;I;J)
ϑ
•(cos(ϑ))2+ (sin(ϑ))2= 1
• −1≤cos(ϑ)≤1
• −1≤sin(ϑ)≤1
•(O;I;J)M(cos(ϑ); sin(ϑ)) OM2=
(xM−0)2+ (yM−0)2
OM2=x2
M+y2 M= (cos(ϑ))2+ (sin(ϑ))2
OM = 1 (cos(ϑ))2+ (sin(ϑ))2= 1
•I1I0−1M
−1≤xM≤1