Trigonométrie 𝜋 2 Le cercle trigonométrique 𝐿 α = 𝑅 angle en Radians (rad). L R α sin θ cos² α + sin² α = 1 π 0 cos θ Points particuliers θ rad 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2 cos θ 1 √2 2 1 2 0 sin θ 0 √3 2 1 2 √2 2 √3 2 1 tan θ 0 1 1 √3 / √3 Rotations sur le cercle cos(-x) = cos(x) cos(x + π) = –cos(x) cos(x + 2π) = cos(x) cos(x – π) = –cos(x) 𝜋 cos(x + 2 ) = –sin(x) sin(-x) = –sin(x) sin(x + π) = –sin(x) sin(x + 2π) = sin(x) sin(x – π) = –sin(x) 𝜋 sin(x + 2 ) = cos(x) tan(-x) = –tan(x) tan(x + π) = tan(x) tan(x + 2π) = tan(x) tan(x – π) = tan(x) 𝜋 −1 tan(x + 2 ) = tan(𝑥) cos(2 – x) = sin(x) sin(2 – x) = –cos(x) tan(2 – x) = tan(𝑥) 𝜋 𝜋 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) 𝜋 sin(a + b) = sin(a) cos(b) + sin(b) cos(a) sin(a – b) = sin (a) cos(b) – sin(b) cos(a) tan(𝑎)+tan(𝑏) tan(a + b) = 1−tan(𝑎)tan(𝑏) tan(𝑎)−tan(𝑏) tan(a – b) = 1+tan(𝑎)tan(𝑏) Formules de l’angle double cos(2a) = cos²(a) – sin²(a) = 2cos²(a) – 1 −1 sin(2a) = 2 sin(a) cos(a) 2 tan(𝑎) tan(2a) = 1−tan²(𝑎) Formules de linéarisation 1+cos(2𝑎) cos²(a) = 2 sin²(a) = 1−cos(2𝑎) 𝑠𝑖𝑛²(𝑎) 1−cos(2𝑎) tan²(a) = 𝑐𝑜𝑠²(𝑎) = 1+cos(2𝑎) 2 Produits de cosinus et sinus cos(a) cos(b) = cos(𝑎+𝑏)+cos(𝑎−𝑏) sin(a) sin(b) = 2 cos(a) sin(b) = cos(𝑎+𝑏)−cos(𝑎−𝑏) sin(𝑎+𝑏)−sin(𝑎−𝑏) 2 2 Additions de cosinus et sinus cos( cos(p) + cos(q) = 2 cos( cos(p) – cos(q) = 2 sin( p+q 2 p+q 2 p+q 2 ) cos( ) sin( ) cos( p−q 2 p−q 2 ) ) p−q 2 cos(p)+cos(q) ) = 2 sin(p) + sin(q) = 2 cos( sin(p) – sin(q) = 2 cos( p−q p+q 2 p+q 2 p−q 2 2 ) sin( ) sin( ) )