Dave's Math Tables: Hyperbolic Trigonometric Identities |
csch(x) = 1/sinh(x) = 2/( e x - e -x )
cosh(x) = ( e x + e -x )/2
sech(x) = 1/cosh(x) = 2/( e x + e -x )
tanh(x) = sinh(x)/cosh(x) = ( e x - e -x )/( e x + e -x )
coth(x) = 1/tanh(x) = ( e x + e -x)/( e x - e -x )
cosh 2(x) - sinh 2(x) = 1
tanh 2(x) + sech 2(x) = 1
coth 2(x) - csch 2(x) = 1
arccosh(z) = ln( z (z 2 - 1) )
arctanh(z) = 1/2 ln( (1+z)/(1-z) )
arccsch(z) = ln( (1+(1+z 2) )/z )
arcsech(z) = ln( (1(1-z 2) )/z )
arccoth(z) = 1/2 ln( (z+1)/(z-1) )
csch(z) = i csc(iz)
cosh(z) = cos(iz)
sech(z) = sec(iz)
tanh(z) = -i tan(iz)
coth(z) = cot(iz)