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. Also, similarly to how the derivatives of sin (t) and cos (t) are cos (t) and –sin (t) …

The two basic hyperbolic functions are sinh and cosh: sinh (x) = ex - e-x2. (pronounced shine or sinch). cosh (x) = ex + e-x2.

So for some suitable t, cosh t and sinh t are the coordinates of a typical point on the hyperbola. In fact, it turns out that t is twice the area shown in the first graph of figure 4.11.2.

There are six hyperbolic functions are sinh x, cosh x, tanh x, coth x, sech x, csch x. In this article, we will define these hyperbolic functions and their properties, graphs, identities, derivatives, etc. along with …

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Dec 22, 2025 · The notation is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the shape of a hanging cable, known as the catenary. It is implemented in the …

Cosh, short for hyperbolic cosine, is a mathematical function that is part of the family of hyperbolic functions. It is closely related to the hyperbolic sine function and is used extensively in the study of …