What is the difference between trigonometric and hyperbolic functions?

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.

What is hyperbolic trigonometry used for?

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).

How are hyperbolic trig functions similar to circular trig functions How are they different?

Unlike the ordinary (“circular”) trig functions, the hyperbolic trig functions don’t oscillate. Rather, both grow like et/2 as t → ∞, and ±e−t/2 as t → −∞. The derivatives of the hyperbolic trig functions are d dt sinh(t) = cosh(t), d dt cosh(t) = sinh(t). Their integrals are just as easy.

What is being hyperbolic?

Definition of hyperbolic (Entry 1 of 2) : of, relating to, or marked by language that exaggerates or overstates the truth : of, relating to, or marked by hyperbole hyperbolic claims. hyperbolic. adjective (2)

What are the six hyperbolic functions?

The six well‐known hyperbolic functions are the hyperbolic sine , hyperbolic cosine , hyperbolic tangent , hyperbolic cotangent , hyperbolic cosecant , and hyperbolic secant .

What is another word for hyperbolic?

What is another word for hyperbolic?