Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" and the hyperbolic cosine "cosh" from which are derived the hyperbolic tangent "tanh" and so on, corresponding to the derived trigonometric functions.

Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.

Hyperbolic sine and cosine
satisfy the identity cosh

Select the check box in the following applet to view graph of function.

Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.

The hyperbolic
functions cosh x and sinh x are deļ¬ned using the exponential function
e

^{x}. Following are the definitions of cosh x , sinh x and tanh x.
cosh x = (e

^{x}+ e^{-x})/2
sinh x = (e

^{x}- e^{-x})/2
tanh x = (e

^{x}- e^{-x})/(e^{x}+ e^{-x})^{2}- sinh^{2}=1Select the check box in the following applet to view graph of function.

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