What does ArcTanh mean?

the inverse hyperbolic tangent function
ArcTanh is the inverse hyperbolic tangent function. For a real number x, ArcTanh[x] represents the hyperbolic angle measure such that . ArcTanh automatically threads over lists. For certain special arguments, ArcTanh automatically evaluates to exact values.

What is sinh1?

The hyperbolic sine function, sinhx, is one-to-one, and therefore has a well-defined inverse, sinh−1x, shown in blue in the figure. In order to invert the hyperbolic cosine function, however, we need (as with square root) to restrict its domain.

What is the inverse of Coshx?

So for y = cosh ( x ) y=\cosh{(x)} y=cosh(x), the inverse function would be x = cosh ( y ) x=\cosh{(y)} x=cosh(y).

Is arctan and tanh same?

This shows that the asymptotic behavior of the two functions is completely different. As indicated in other answers, tan and tanh are related to the function exp whereas arctan and artanh are related to the function log, whereby the transition from trigonometric functions to hyperbolic ones lives in the complex domain.

What is the difference between Tan and tanh?

Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. Tanh[α] is defined as the ratio of the corresponding hyperbolic sine and hyperbolic cosine functions via . Tanh may also be defined as , where is the base of the natural logarithm Log.

What is Coshx Sinhx?

Definition 4.11.1 The hyperbolic cosine is the function coshx=ex+e−x2, and the hyperbolic sine is the function sinhx=ex−e−x2.

Can hyperbolic functions be negative?

Again, the graph of coshx will always stay above the graph of e−x/2 when x is negative. This is because, even though ex/2 (the first part of the sum) gets very small, it is always greater than zero. But as x gets more and more negative the difference between the two graphs gets smaller and smaller.