What does atanh mean in Matlab?

What does atanh mean in Matlab?

the inverse hyperbolic tangent of
Y = atanh( X ) returns the inverse hyperbolic tangent of the elements of X . The function accepts both real and complex inputs. All angles are in radians.

What is ArcTanh equal to?

The following definition for the inverse hyperbolic tangent determines the range and branch cuts: arctanh z = (log (1+z) – log (1-z))/2.

What does sinh 1 mean?

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.

Is tanh an Arctan?

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 natural log in Matlab?

Y = log( X ) returns the natural logarithm ln(x) of each element in array X . The log function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally.

What is 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 ArcSinh infinity?

The arcsine is the inverse sine function. Since x can be in the range of [-1,1], arcsin(x) is undefined outside the range of [-1,1]. So the limit of arcsine of x when x is approaching infinity is undefined: Arcsin function ►

Why is there no C in Arsinh?

It’s because arcsin gives the arc length on the unit circle for a given y-coordinate, whereas arsinh gives an area enclosed by a hyperbola and two rays from the origin for a given y-coordinate. The red shaded area below is equal to arsinh(a), where a is the length of the blue line segment.

What is Coshx?

cosh x. Key Point. The hyperbolic function f(x) = cosh x is defined by the formula. cosh x = ex + e−x 2 . The function satisfies the conditions cosh 0 = 1 and coshx = cosh(−x).

What is sin and sinh?

Sinh is the hyperbolic sine function, which is the hyperbolic analogue of the Sin circular function used throughout trigonometry. It is defined for real numbers by letting be twice the area between the axis and a ray through the origin intersecting the unit hyperbola .

What is the value of Sinhx?

sinh x = ex − e−x 2 . sinh 0 = e0 − e−0 2 = 1 − 1 2 = 0 .