|
Hyperbolic functions
are analogs of the ordinary
trigonometric, or circular, functions.
The points (cosh t, sinh t)
define the right half of the equilateral
hyperbola
x² - y²
= 1,
in the same way that
the points (cos t, sin t) define a circle.
Furthermore,
cosh2t
- sinh2t = 1. The hyperbolic functions are periodic
with a complex period of 2πj.
The parameter t is not a circular angle, but rather a
hyperbolic angle.
The Hyperbolic Functions
sinh z =
(ez - e-z) / 2
where z is a complex number, i.e., z = x + jy
cosh z =
(ez + e-z) / 2
where z is a complex number, i.e., z = x + jy
tanh z =
sinh z / cosh z
csch z =
1 / sinh z
sech z =
1 / cosh z
coth z =
1 / tanh z
Hyperbolic Functions in Relation to Trigonometric Functions
sinh z =
-j
sin jz
cosh z =
cos jz
tanh z =
-j tan jz
csch z =
j csc jz
sech z =
sec jz
coth z =
j cot jz
See Also:
Trigonometric
Functions;
Math Used
in ECE
|
