Hyperbolische Functies
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)-½
d/dx acosh x/a = (x2 -
a2)-½
d/dx atanh x/a = a(a2 -
x2)-1
ò (sinh ax)
dx = (1/a) cosh ax
ò (cosh ax) dx = (1/a)
sinh ax
ò (tanh ax) dx = (1/a)
loge cosh ax
Voor |x| < 1
sinh x = x +
x3/3! + x5/5! + ...
cosh x = 1 + x2/2! +
x4/4! + ...
Labo
elektriciteit-elektronica