Hyperbolické  
Funkce	
MB202
Jaro 2015
433670
433418
sinh(x) =
ex
− e−x
2
=
e2x
−1
2ex
D(sinh) = R
H(sinh) = R
sinh(x)	
argsinh(x) = ln(x + x2
+1)
D(argsinh) = R
H(argsinh) = R
argsinh(x)	
cosh(x)	
cosh(x) =
ex
+e−x
2
=
e2x
+1
2ex
D(cosh) = R
H(cosh) = 1,∞
argcosh(x)	
argcosh(x) = ln(x + x2
−1)
D(argcosh) = 1,∞
H(argcosh) = 0,∞
argsinh(sinh(x))	
argcosh(cosh(x))	
tgh(x)	
tgh(x)	
      argtgh(x)	
argtgh(tgh(x))	
coth(x)	
coth(x)    argcoth(x)	
argcoth(coth(x))	
vzorečky	
sinh(x ± y) = sinh(x)cosh(y)±cosh(x)sinh(y)
cosh(x ± y) = cosh(x)cosh(y)±sinh(x)sinh(y)
sinh(2x) = 2sinh(x)cosh(x)
cosh(2x) = cosh2
(x)+sinh2
(x)
sinh2
(x) =
1
2
(cosh(2x)−1)
cosh2
(x) =
1
2
(cosh(2x)+1)
cosh2
(x)−sinh2
(x) =1
tgh(x ± y) =
tgh(x)±tgh(y)
1±tgh(x)tgh(y)
tgh(2x) =
2tgh(x)
1+tgh2
(x)
vztah  k  sin/cos	
sinh(x) = −isin(ix)
cosh(x) = cos(ix)
tgh(x) = −itg(ix)
coth(x) = icot(ix)
užití	
•  řetězovka
•  fyzika
•  tractrix