Hyperbolic functions

  • Hyperbolic functions are analogues of trigonometric functions that are defined in terms of the exponential function.
  • The hyperbolic functions are denoted by sinh, cosh, tanh, csch, sech, and coth.
    Hyperbolic functions have many of the same properties as trigonometric functions, such as being periodic and having certain symmetries and identities.
  • Hyperbolic functions are commonly used in areas of mathematics such as calculus, differential equations, and complex analysis.
  • The hyperbolic functions can be used to solve problems involving hyperbolic geometry and hyperbolic trigonometry.

Important Formulas to Remember in these Hyperbolic functions

  • \( \sinh x=\frac{1}{2}(e^x-e^{-x}) \)
  • \( \cosh x=\frac{1}{2}(e^x+e^{-x}) \)
  • \( \tanh x=\frac{\sinh x}{\cosh x}=\frac{e^x-e^{-x}}{e^x+e^{-x}} \)