How to use the TANH function
What is the TANH function?
The TANH function calculatesĀ the hyperbolic tangent of a number.
What is the hyperbolic tangent?
The hyperbolic tangent is analogous to the regular tangent function but for hyperbolas rather than circles.
sinh(x) = (e2x -1) / (e2x + 1)
or
tanh(x) = sinh(x) / cosh(x)
Where sinh and cosh are the hyperbolic sine and cosine.
What is e?
The number e is an irrational constant that is approximately equal to 2.71828. It is the base of the natural logarithm function, which is denoted by ln. The natural logarithm function is the inverse of the natural exponential function, which is denoted by ex. This means that if y = ex, then x = ln y.
What is hyperbolic?
Hyperbolic functions are similar to ordinary trigonometric functions, but they use a different shape to define them.
Trigonometric functions use a circle, while hyperbolic functions use hyperbolas. The chart above shows a hyperbola and two asymptotes (dashed lines) where the intersection is at the center of the hyperbola.
The unit hyperbola looks like this:
It shows x2Ā -y2=1 and x2Ā -y2=-1
What are asymptotes?
Asymptotes are straight lines that the function curves towards but never intersects.
What are the domain, range and asymptotes of all the main hyperbolic functions?
This table displays the key properties of the main hyperbolic functions:
Hyperbolic Function | Domain | Asymptotes | Range |
sinh(x) | All real numbers | Vertical asymptotes at multiples of Ā±Ļi/2 | (-ā, ā) |
cosh(x) | All real numbers | Horizontal asymptotes at y=0 | (1, ā) |
tanh(x) | All real numbers | Horizontal asymptotes at y=Ā±1 | (-1, 1) |
sech(x) | All real numbers | Horizontal asymptotes at y=0 | (0, 1) |
csch(x) | All real x ā 0 | Vertical asymptotes at x=0 | (0, ā) |
coth(x) | All real numbers | Horizontal asymptotes at y=Ā±1 | (1, ā) |
The asymptotes shows the exponential nature and infinite limits of hyperbolic functions.
What is the hyperbolic domain?
The domain of a hyperbolic function refers to the set of input values it is defined and valid for.
What is the hyperbolic range?
The range of a hyperbolic function refers to the set of possible output values it returns.
What are the domain, range and asymptotes of all the main inverse hyperbolic functions?
This table displays the key properties of the inverse hyperbolic functions:
Inverse Hyperbolic Function | Domain | Asymptotes | Range |
arcsinh(x) | All real numbers | Horizontal asymptote at y=0 | (-ā, ā) |
arccosh(x) | x>=1 | None | (0, ā) |
arctanh(x) | -1<x<1 | Vertical asymptotes at x=Ā±1 | (-ā, ā) |
arcsech(x) | 0<x<1 | None | (0, ā) |
arccsch(x) | All real x ā 0 | Vertical asymptote at x=0 | (-ā, ā) |
arccoth(x) | All real numbers | None | (0, ā) |
TANH function Syntax
TANH(number)
TANH function Arguments
number | Ā Required. Any real number. |
TANH function example
Formula in cell C3:
Functions in 'Math and trigonometry' category
The TANH function function is one of 73 functions in the 'Math and trigonometry' category.
How to comment
How to add a formula to your comment
<code>Insert your formula here.</code>
Convert less than and larger than signs
Use html character entities instead of less than and larger than signs.
< becomes < and > becomes >
How to add VBA code to your comment
[vb 1="vbnet" language=","]
Put your VBA code here.
[/vb]
How to add a picture to your comment:
Upload picture to postimage.org or imgur
Paste image link to your comment.
Contact Oscar
You can contact me through this contact form