Trigonométrie

Trigonométrie
Le cercle trigonométrique
α = 
 angle en Radians (rad). L R
α sin θ
cos² α + sin² α = 1
π 0
cos θ
Points particuliers
θ rad
0
cos θ
1
0
sin θ
0
1
tan θ
0
1
/
Rotations sur le cercle
cos(-x) = cos(x)
cos(x + π) = –cos(x)
cos(x + 2π) = cos(x)
cos(x – π) = –cos(x)
cos(x + 
) = –sin(x)
cos(
 – x) = sin(x)
sin(-x) = –sin(x)
sin(x + π) = –sin(x)
sin(x + 2π) = sin(x)
sin(x – π) = –sin(x)
sin(x + 
) = cos(x)
sin(
 – x) = –cos(x)
tan(-x) = –tan(x)
tan(x + π) = tan(x)
tan(x + 2π) = tan(x)
tan(x – π) = tan(x)
tan(x + 
) = 
tan(
 – x) = 
Formules d’addition
cos(a + b) = cas(a) cos(b) – sin(a) sin(b)
cos(a – b) = cas(a) cos(b) + sin(a) sin(b)
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
sin(a – b) = sin (a) cos(b) – sin(b) cos(a)
tan(a + b) = 
tan(a – b) = 
Formules de l’angle double
cos(2a) = cos²(a) – sin²(a) = 2cos²(a) – 1 sin(2a) = 2 sin(a) cos(a)
tan(2a) =  

Formules de linéarisation
cos²(a) =  sin²(a) = 
tan²(a) = 
 = 
Produits de cosinus et sinus
cos(a) cos(b) = 
 sin(a) sin(b) = 
cos(a) sin(b) = 
Additions de cosinus et sinus
cos
 cos  =
cos(p) + cos(q) = 2 cos
 cos
cos(p) – cos(q) = 2 sin
 sin
sin(p) + sin(q) = 2 cos
 sin
sin(p) – sin(q) = 2 cos
 sin