ABSTRACT
The hyperbolic sine, cosine and tangent functions, written sinh x , cosh x and
tanh x , are defined in terms of the exponential function as follows:
sinh x ex ex
2 (hyperbolic sine function),
cosh x ex ex
2 (hyperbolic cosine function),
tanh x sinh x
cosh x (hyperbolic tangent function):
By analogy with trigonometric functions the hyperbolic cosecant, secant
and cotangent functions written cosech x , sech x and coth x , are defined as
cosech x 1
sinh x (x"0) (hyperbolic cosecant function),
sech x 1
cosh x (hyperbolic secant function),
coth x
tanh x (x"0) (hyperbolic cotangent function):
Their graphs, which are not periodic, are shown in Fig. 64. It can be seen
from the definitions, and also from the graphs, that sinh x , tanh x , cosech x and coth x are odd functions, while cosh x and sech x are even functions.
