Fonctions hyperboliques : Exercices et définitions

fR R
x
f(−x) = f(x)
fR R
x
f(−x) = −f(x)
x7→ xnn∈N∗
f:R→RP
(x,f(x))
Cf={M∈P| ∃x∈R, M (x,f(x))}
Cff
f:R→Ra∈R
Ra
−af(t) dt
f:R→R
h:R→Rh:R→R
∀x∈R, f(x) = g(x) + h(x)

x
sinh(x) = ex−e−x
2
sh
R
sin(x) = eix −e−ix
2i
sinh
sinh R+
sinh R
sinh [−4; 4]
sinh
x
cosh(x) = ex+ e−x
2
ch
R

cos(x) = eix + e−ix
2
cosh
cosh R+
cosh R
cosh [−4; 4]
cosh
∀x∈R,cosh2(x)−sinh2(x) = 1
∀x∈R,cosh(x) + sinh(x) = ex
x
sinh(x+y) =
sinh(x−y) =
cosh(x+y) =
cosh(x−y) =
sinh(2x) =
cosh(2x) =

x
[cosh(t) + sinh(t)]n= cosh(nt) + sinh(nt)
x(t) = εcosh(t)
y(t) = sinh(t), ε ∈ {−1; 1}