Trigonométrie
I - Généralités
1.1/ Relations fondamentales tan(x) = sin(x)/cos(x)
Petite astuce de Nelly: Pour se souvenir de la formule précédente, perso je me dis que tangente c'est Soleil sur Carottes ! D'où sin sur cos...si ça peut aider! sin²(x) + cos²(x) = 1 sin²(x) = tan²(x) / (1 + tan²(x)) cos²(x) = 1 / (1 + tan²(x))
1.2/ Transformations remarquables sin(2 + x) = sin(x) cos(2 + x) = cos(x) tan(2 + x) = tan(x)

sin( -x) = - sin(x) cos( -x) = cos(x) tan( -x) = - tan(x)

sin( - x) = sin(x) cos( - x) = - cos(x) tan( - x) = - tan(x)

sin( + x) = - sin(x) cos( + x) = - cos(x) tan( + x) = tan(x)

sin(/2 - x) = cos(x) cos(/2 - x) = sin(x) tan(/2 - x) = 1/tan(x)

sin(/2 + x) = cos(x) cos(/2 + x) = - sin(x) tan(/2 + x) = -1/tan(x)

sin(3/2 - x) = - cos(x) cos(3/2 - x) = - sin(x) tan(3/2 - x) = 1/tan(x)

sin(3/2 + x) = - cos(x) cos(3/2 + x) = sin(x) tan(3/2 + x) = -1/tan(x)
1.3/ Angles remarquables x | sin(x) | cos(x) | tan(x) | cotan(x) | 0 | 0 | 1 | 0 | / | /6 | 1/2 | (3)/2 | (3)/3 | (3) | /4 | (2)/2 | (2)/2 | 1 | 1 | /3 | (3)/2 | 1/2 | (3) | (3)/3 | /2 | 1 | 0 | / | 0 | | 0 | -1 | 0 | / |
1.4/ Equations trigonométriques k appartient à Z

sin(a) = sin(b) alors a = b + 2k ou a = - b + 2k

cos(a) = cos(b) alors a = b + 2k ou a = -b + 2k

tan(a) = tan(b) alors a = b + k
II - Formules d'addition sin(a + b) = sin(a)cos(b) + sin(b)cos(a) sin(a - b) = sin(a)cos(b) - sin(b)cos(a) cos(a + b) = cos(a)cos(b) - sin(a)sin(b) cos(a - b) = cos(a)cos(b) + sin(a)sin(b) tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b)) tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

sin(p) + sin(q) = 2sin((p + q)/2)cos((p - q)/2) sin(p) - sin(q) = 2sin((p - q)/2)cos((p + q)/2) cos(p) + cos(q) = 2cos((p + q)/2)cos((p - q)/2) cos(p) - cos(q) = -2sin((p + q)/2)sin((p - q)/2) tan(p) + tan(q) = sin(p + q) / (cos(p)cos(q)) tan(p) - tan(q) = sin(p - q) / (cos(p)cos(q))

sin(a)sin(b) = (1/2)(cos(a - b) - cos(a + b))