Hyperbolic Functions Handwritten Notes for College Students


In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola.


The hyperbolic functions are analogs of the circular function or the trigonometric functions. The hyperbolic function occurs in the solutions of linear differential equations, calculation of distance and angles in the hyperbolic geometry, Laplace’s equations in the cartesian coordinates. Generally, the hyperbolic function takes place in the real argument called the hyperbolic angle. The basic hyperbolic functions are:

  • Hyperbolic sine (sinh)
  • Hyperbolic cosine (cosh)
  • Hyperbolic tangent (tanh)

From these three basic functions, the other functions such as hyperbolic cosecant (cosech), hyperbolic secant(sech) and hyperbolic cotangent (coth) functions are derived. Let us discuss the basic hyperbolic functions, graphs, properties, and inverse hyperbolic functions in detail.


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