Angles orientés et repérage, cours, première S - MathsFG

(O;~ i;~ j)
(O;~ OI;~ OJ)
DI(OI)
(I;~ IK)IK = 1
x N x
(I;~ IK)D D
CM
x IM
\
IOM
x

•
•π
•π
3= 60◦
•3 = 3
π×180◦≈171◦
(O;~ i;~ j)
M N x y
O(~ OM;~ ON)
y−x+ 2kπ k ∈Z
(~ OM;~ ON) = y−x

M N O
(~ OM;~ ON)a
]−π;π]
(~ OM;~ ON)\ MON
|a|
x+ 2kπ k ∈Z
k−π≤x+ 2kπ ≤π−π−x≤2kπ ≤π−x−pi+x
2π≤k≤π−x 2π
−1
2−x 2π≤k≤1 2−x 2πk
−π π
~u ~v M N
~
OM ~u ~ ON
~v
(~u;~v)
(~ OM;~ ON)
~u ~v ~w
(~u;~v) = (~u;~w)+(~w;~v)

~u ~v
•~u ~v (~u;~v)=0
•~u ~v (~u;~v) = π
~u ~v
•(~v;~u) = −(~u;~v)
•(~u;−~v) = (~u;~v) + π
•(−~u;~v) = (~u;~v) + π
•(−~u;−~v)=(~u;~v)
•(~u;~u) = 0 (~u;~u)=(~u;~v)+(~v;~u) (~u;~v) = −(~v;~u)
•(~u;−~v) = (~u;~v)+(~v;−~v)=(~u;~v) + π
•
•(−~u;−~v)=(−~u;~u)+(~u;~v)+(~v;−~v) = π+ (~u;~v) + π= (~u;~v)
(~ AB;~ AC) + ( ~ AC;~ BC) + ( ~ BC;~ BA) = ( ~ AB;~ AB) = 0
(~ AB;~ AC) + ( ~ BC;~ BA) + ( ~ CA;~ CB)=( ~ AB;~ AC) + ( ~ AC;~ BC) + ( ~ BC;~ BA) + π=π
π
(O:~ i;~ j)C
Cx
•xcos(x)
•xsin(x)