Java Reference
In-Depth Information
Hyperbolic functions and arc-functions
Engineering problems often require the evaluation of hyperbolic functions.
These functions,called the hyperbolic tangent (tanh),hyperbolic sine
(sinh),and hyperbolic cosine (cosh),have properties similar to the circular
trigonometric functions,except that the hyperbolic functions are related to
the hyperbola rather than to the circle. However,the hyperbolic functions
cannot be readily derived from their trigonometric counterparts. Instead,
they are expressed by the following formulas
ee
x
−
−
x
sinh( )
x
=
2
x
−
x
ee
+
cosh( )
x
=
2
x
−
x
ee
x
ee
x
−
tanh( )
=
x
−
x
+
sinh( )
tanh( )
x
=
cosh( )
x
In evaluating the hyperbolic functions code can make use of the exp()
method in java.lang.Math previously discussed. The exp() method returns
a power of e,which allows estimating the numerator in the sinh and cosh.
Hyperbolic arc-tangent functions can be calculated according to the
following formulas:
−
1
2
sinh ( )
x
=++
ln(
x
x
1
−
1
2
cosh ( )
x
=+−
+
ln(
x
x
x
1
11
−
1
tanh ( )
x
=
l
21
−
x
Here again the input angle is in radians. The following program dem-
onstrates the calculation of hyperbolic functions and arc-functions.
