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.

The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh(x) = e x − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh(x) = e x + e-x 2 (pronounced "cosh") They use the natural exponential function e x. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary

If x = sinh y, then y = sinh-1 a is called the inverse hyperbolic sine of x. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as in the case of inverse trigonometric functions we restrict ourselves to principal values for which they can be considered as single-valued.

Calculate and plot the values of sinh(x), exp(x), and exp(-x). As expected, the sinh curve is positive where exp(x) is large, and negative where exp(-x) is large. Input angles in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

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The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure.

Nov 25, 2024 · Learn the different hyperbolic trigonometric functions, including sine, cosine, and tangent, with their formulas, examples, and diagrams. Also, learn their identities.

Sinh (pronounced as “shine”) represents the hyperbolic sine function. While the trigonometric function sine is defined as a circle , sinh is related to measurements from a hyperbola. It involves the natural exponential term e$^x$:

We’ll show you how the rules for $\dfrac{d}{dx} \sinh x$ and $\dfrac{d}{dx} \cosh x$ were established and the rest of the derivative rules will be summarized in a table. Since $\sinh x = \dfrac{e^x – e^{-x}}{2}$ and $\cosh x = \dfrac{e^x + e^{-x}}{2}$, we can use these to establish the derivative rules for $\sinh x$ and $\cosh x$.

The two basic hyperbolic functions are sinh and cosh. sinh(x) = (e x − e −x)/2 cosh(x) = (e x + e −x)/2 (From those two we also get the tanh, coth, sech and csch functions.) Here you see how sinh compares to the sine function and cosh compares to the cosine function: