1
Funkcje hiperboliczne
x
x
x
x
x
x
x
x
e
e
e
e
x
x
tghx
e
e
x
e
e
x
−
−
−
−
+
−
=
=
+
=
−
=
cosh
sinh
:
2
:
cosh
2
:
sinh
,
gdzie
{ }
0
\
cosh
sinh
R
D
R
D
D
D
ctgh
tgh
=
=
=
=
x
x
x
x
e
e
e
e
x
x
ctghx
−
−
−
+
=
=
sinh
cosh
:
,
0
≠
x
Jedynka hiperboliczna
1
sinh
cosh
2
2
=
−
x
x
Inne wzory
x
x
x
x
x
x
cosh
sinh
2
2
sinh
sinh
cosh
2
cosh
2
2
⋅
=
+
=
(
)
(
)
x
x
x
x
sinh
cosh
cosh
sinh
=
′
=
′
(
)
(
)
x
ctghx
x
tghx
2
2
sinh
1
cosh
1
−
=
′
=
′
