I. Résultats usuels de trigonométrie
II. Inversion des fonctions circulaires
III. Fonctions hyperboliques

• Valeurs particulières - Cercle trigonométrique

  q ° rad	0° 0	30° p/6	45° p/4	60° p/3	90° p/2
  sin	0				1
  cos	1				0
  tan	0		1		non défini

  cos(x) = sin(x) = 1 = sin²(q) + cos²(q)
  

  sin(-q) = -sin(q) sin(q + p) = -sin(q) sin(p - q) = sin(q)

  cos(-q) = cos(q) cos(q + p) = -cos(q) cos(p - q) = -cos(q)

  tan(-q) = -tan(q) tan(q + p) = tan(q) tan(p - q) = -tan(q)

  sin() = cos(q) sin() = cos(q)

  cos() = -sin(q) cos() = sin(q)

  
  
  

• Formules de transformations produits-sommes

  - Addition

  cos(A + B) = cos(A).cos(B) - sin(A).sin(B)

  cos(A - B) = cos(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 appliquées à l'angle double

  sin(2.q) = 2.sin(q).cos(q)

  cos(2.q) = cos²(q) - sin²(q) = 2.cos²(q) - 1 = 1 - 2.sin²(q)

  tan(2.q) =
  

  - Transformation d'une somme en produit

  cos(p) + cos(q) = 2.cos().cos()

  cos(p) - cos(q) = -2.sin().sin()

  sin(p) + sin(q) = 2.sin().cos()

  sin(p) - sin(q) = 2.cos().sin()
  

  - Transformation d'un produit en somme

  cos(p).cos(q) = .[cos(p-q) + cos(p+q)]

  sin(p).sin(q) = .[cos(p-q) - cos(p+q)]

  sin(p).cos(q) = .[sin(p+q) + sin(p-q)]
  

• Arccos

  x R, p = Arccos(-x) + Arccos(x)
  

  x [-1,1] , sin(Arccos(x)) =
  

  (Arccos)'(x) =
  

• Arcsin

  x [-1,1], cos(Arcsin(x)) =
  

  = Arccos(x) + Arcsin(x)
  

  (Arcsin)'(x) =
  

• Arctan

  x 0, Arctan(x) + Arctan() = (signe(x)).
  

  cos(Arctan(x)) =

  sin(Arctan(x)) =
  

  (Arctan)'(x) =

• Directes

  - Généralités

  ch(x) = sh(x) = th(x) =
  

  ch(-x) = ch(x) sh(-x) = -sh(x)

  ch(x) + sh(x) = ex ch(x) - sh(x) = e-x

  ch²(x) - sh²(x) = 1 1 - th²(x) =
  

  (ch)'(x) = sh(x) (sh)'(x) = ch(x)
  

  - Addition
  

  ch(A + B) = ch(A).ch(B) + sh(A).sh(B)

  ch(A - B) = ch(A).ch(B) - sh(A).sh(B)
  

  sh(A + B) = sh(A).ch(B) + sh(B).ch(A)

  sh(A - B) = sh(A).ch(B) - sh(B).ch(A)
  

  th(A + B) = th(A - B) =
  

• Inverses

  - Argch

  Argch(x) = Ln(x + )
  

  (Argch)'(x) =
  

  - Argsh

  Argsh(x) = Ln(x + )
  

  (Argsh)'(x) =
  

  - Argth

  Argth(x) =
  

  (Argth)'(x) =