What is meant by hyperbolic functions?

noun Mathematics. a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions.

What is the hyperbolic formula?

The hyperbolic sine and cosine are given by the following: cosh ⁡ a = e a + e − a 2 , sinh ⁡ a = e a − e − a 2 .

What is hyperbolic cosine mean?

Definition of hyperbolic cosine : the hyperbolic function that is analogous to the cosine and defined by the equation cosh x = (ex + e-x)/2 —abbreviation cosh.

Are hyperbolic functions in JEE?

Hyperbolic Functions Chapter 1 Hyperbolic Functions is the vital part of the IIT JEE syllabus. It is, in fact, an indispensable part of the human race. Physics, Chemistry and Mathematics have equal weightage in the IIT JEE but Maths 30.

Is hyperbolic sine the same as inverse sine?

(Beyer 1987, p. 481), sometimes called the area hyperbolic sine (Harris and Stocker 1998, p. 264) is the multivalued function that is the inverse function of the hyperbolic sine.

Why do we need hyperbolic functions?

Hyperbolic functions also satisfy identities analogous to those of the ordinary trigonometric functions and have important physical applications. For example, the hyperbolic cosine function may be used to describe the shape of the curve formed by a high-voltage line suspended between two towers (see catenary).

Are hyperbolic functions periodic?

The functions are called the hyperbolic cosine and the hyperbolic sine, respectively, and we write x(v) = cosh v and y(v) = sinh v. Obviously, the hyperbolic functions cannot be used to model periodic behaviors, since both cosh v and sinh v will just grow and grow as v increases.

Why are hyperbolic functions called hyperbolic?

Just as the ordinary sine and cosine functions trace (or parameterize) a circle, so the sinh and cosh parameterize a hyperbola—hence the hyperbolic appellation. Hyperbolic functions also satisfy identities analogous to those of the ordinary trigonometric functions and have important physical applications.

What is the difference between trigonometric functions and hyperbolic function?

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. 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 unit hyperbola.

Why do we learn hyperbolic functions?

Hyperbolic functions also satisfy identities analogous to those of the ordinary trigonometric functions and have important physical applications. Hyperbolic functions may also be used to define a measure of distance in certain kinds of non-Euclidean geometry.