Lignes trigonométriques	Lignes hyperboliques
fonctions
cos x =	ch x = ch x pair et chx ≥ 1
sin x =	sh x = sh x impair
Tan x =	Th x = -1 <th x <+1
Arc cos x [-1 , 1] → [0 , π] symétrie / (0, π/2)	Arg ch x =ln(x+) (≥ 0 pour x ≥ 1)
Arc sin x [-1 , 1] → [ ] symétrie / (0, 0)	Arg sh x =ln(x+) impaire
Arc tan x R →] [ symétrie / (0, 0)	Arg th x = impaire pour -1 < x < +1
Informatique : Arc cos x = arc tan (-x/)+2arc tan (1) Arc sin x = arc tan (x / )
Dérivées
Cos ‘ x = – sin x	Ch ‘ x = sh x
Sin ‘ x = cos x	Sh ‘ x = ch x
Tan ‘ x = 1/cos^2x = 1+ tan^2 x	Th ‘ x = 1/ ch^2 x = 1 – th^2 x
Arc cos ‘ x = – 1 /	Arg ch ‘ x = 1 /
Arc sin ‘ x = 1 /	Arg sh ‘ x = 1 /
Arc tg x = 1 / (1+x^2 )	Arg th ‘ x = 1 / (1-x^2)
Relation fondamentale
Cos^2 x + sin ^2 x = 1	Ch^2x – sh^2 x = 1
Addition
Cos (a+b) = cos a cos b – sin a sin b	Ch (a+b) = cha ch b + sh a sh b
Sin (a+b) = cos a sin b + cos b sin a	Sh (a+b) = cha sh b + sh a ch b
Tan (a+b) = (tan a + tan b) / (1–tan a tan b)	Th (a+b) = (th a + th b ) / (1 + th a th b )
Cos 2x = cos^2 x – sin^2 x	Ch 2x = ch^2 x + sh^2 x
Sin 2x = 2 cos x sin x	Sh 2 x = 2 ch x sh x
En fonction de t = tan(x/2) ou t =th(x/2)
Tan x =	Th x =
Sin x =	Sh x =
Cos x =	Ch x =
Produit → somme
Cos^2 x =	Ch^2 x =
Sin^2 x =	Sh^2 x =
sin a cos b = [ sin (a+b) + sin (a–b)]	sh a ch b = [ sh (a+b) + sh (a–b)]
sin a sin b = [ cos (a–b) – cos (a+b)]	sh a sh b = [ ch (a+b) – ch (a-b)]
cos a cos b = [ cos (a+b) + cos (a–b)]	ch a ch b = [ ch (a+b) + ch (a–b)]