Hyperbolic Functions

Cuthbert Nyack
sinh x = (ex - e-x)/2
cosh x = (ex + e-x)/2
tanh x = sinh x/cosh x

ex = cosh x + sinh x
e-x = cosh x - sinh x

cosh2 x - sinh2 x = 1
cosh(x y) = cosh x cosh y sinh x sinh y
sinh(x y) = sinh x cosh y cosh x sinh y

d/dx sinh ax = a cosh ax
d/dx cosh ax = a sinh ax
d/dx tanh ax = a sech2 ax

d/dx asinh x/a = (x2 + a2)-
d/dx acosh x/a = (x2 - a2)-
d/dx atanh x/a = a(a2 - x2)-1

(sinh ax) dx = (1/a) cosh ax
(cosh ax) dx = (1/a) sinh ax
(tanh ax) dx = (1/a) loge cosh ax

for |x| < 1
sinh x = x + x3/3! + x5/5! + ...
cosh x = 1 + x2/2! + x4/4! + ...


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Copyright 1996 Cuthbert A. Nyack.