Hyperbolic Formulas

Posted By on December 21, 2014


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Trigonometric Formulas
Limits Formulas

Definitions of hyperbolic functions

sinhx=exex2
coshx=ex+ex2
tanhx=exexex+ex=sinhxcoshx
cschx=2exex=1sinhx
sechx=2ex+ex=1coshx
cothx=ex+exexex=coshxsinhx

Derivatives

ddxsinhx=coshx
ddxcoshx=sinhx
ddxtanhx=sech2x
ddxcschx=cschxcothx
ddxsechx=sechxtanhx
ddxcothx=csch2x

Hyperbolic identities

cosh2xsinh2x=1
tanh2x+sech2x=1
coth2xcsch2x=1
sinh(x±y)=sinhxcoshy±coshxsinhy
cosh(x±y)=coshxcoshy±sinhxsinhy
sinh(2x)=2sinhxcoshx
cosh(2x)=cosh2x+sinh2x
sinh2x=1+cosh2x2
cosh2x=1+cosh2x2

Inverse Hyperbolic functions

sinh1x=ln(x+x2+1−−−−−√),  x(,)
cosh1x=ln(x+x21−−−−−√),  x[1,)
tanh1x=12ln(1+x1x),  x(1,1)
coth1x=12ln(x+1x1),  x(,1)(1,)
sech1x=ln(1+1x2−−−−−√x),  x(0,1]
csch1x=ln(1x+1x2−−−−−√|x|),  x(,0)(0,)

Derivatives of Inverse Hyperbolic functions

ddxsinh1x=1x2+1−−−−−√
ddxcosh1x=1x21−−−−−√
ddxtanh1x=11x2
ddxcsch1x=1|x|1+x2−−−−−√
ddxsech1x=1x1x2−−−−−√
ddxcoth1x=11x2
Trigonometric Formulas
Limits Formulas

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Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

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