pdf (it, 2.898,97 KB, 25/01/13)

x 2 + y 2 = 1
x 2 − y 2 = 1
R 2 Γ (±1, 0)
x 2 − y 2 = 1 γ
P = (x, y)
x (x, y) = (cosh θ, sinh θ)
θ/2 θ ≥ 0
θ/2 θ < 0
|θ|/2 cosh : R → [1, +∞[
sinh : R → R tanh : R → ] − 1, 1[
coth : R \ {0} → R\] − 1, 1[
tanh(x) = sinh(x)
cosh(x)
coth(x) = cosh(x)
sinh(x)
sech : R → [0, 1] csc : R \ {0} → R
sec(x) = 1
1
cosh(x) csc(x) = sinh(x)
arcsinh(x) = sinh −1
(x) = log x + x2
+ 1
arccosh(x) = cosh −1
(x) = log x + x2
− 1 , x ≥ 1
arctanh(x) = tanh −1 √
1 − x2 (x) = log
=
1 − x
1
2 ln
1 + x
, |x| < 1
1 − x
arcoth(x) = coth −1 √
x2 − 1
(x) = log
=
x − 1
1
2 ln
x + 1
, |x| > 1
x − 1
arcsech(x) = sech −1
1 ±
(x) = log
√ 1 − x2
, 0 < x ≤ 1
x
arccsch(x) = csch −1
1 ±
(x) = log
√ 1 + x2
.
x
d
sinh(x) = cosh(x)
dx
d
cosh(x) = sinh(x)
dx
d
dx tanh(x) = 1 − tanh2 (x) = sech 2 (x) = 1/ cosh 2 (x)
d
dx coth(x) = 1 − coth2 (x) = −csch 2 (x) = −1/ sinh 2 (x)
d
csch(x) = − coth(x)csch(x)
dx
d
sech(x) = − tanh(x)sech(x)
dx