hyperbole

\sinh x:=÷{exp(x)-\exp(-x)}{2}
\cosh x:=÷{exp(x)+\exp(-x)}{2}
\tanh x:=÷{\sinh x}{\cosh x}

Properties

  • \sinh(x+y)=\sinh(x)⋅\cosh(y)+\cosh(x)⋅\sinh(y)
  • \cosh(x+y)=\cosh(x)⋅\cosh(y)+\sinh(x)⋅\sinh(y)
  • \sinh(-x)=-\sinh(x)
  • (\cosh(x))²-(\sinh(x))²=1
  • ÷{d}{dx}(\sinh x)=\cosh x
  • ÷{d}{dx}(\cosh x)=\sinh x

Author: Danny (remove the ".nospam" to send)

Last modification on: Sat, 04 May 2024 .