Difference between revisions of "Arccosh"
From specialfunctionswiki
(→Properties) |
|||
| (8 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| + | The inverse hyperbolic cosine function $\mathrm{arccosh}$ is the [[inverse function]] of the [[hyperbolic cosine]] function. It may be defined by | ||
| + | $$\mathrm{arccosh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$ | ||
| + | where $\log$ denotes the [[logarithm]]. | ||
| + | |||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Arccoshplot.png|Graph of $\mathrm{arccos}$ on $[1,10]$. |
| − | File: | + | File:Complexarccoshplot.png|[[Domain coloring]] of $\mathrm{arccosh}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| − | < | + | =Properties= |
| + | [[Derivative of arccosh]] <br /> | ||
| + | [[Antiderivative of arccosh]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Arccos]] <br /> | ||
| + | [[Cosh]] <br /> | ||
| + | [[Cosine]] <br /> | ||
| + | |||
| + | {{:Inverse hyperbolic trigonometric functions footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 23:42, 11 December 2016
The inverse hyperbolic cosine function $\mathrm{arccosh}$ is the inverse function of the hyperbolic cosine function. It may be defined by $$\mathrm{arccosh}(z)=\log \left(z + \sqrt{1+z^2} \right),$$ where $\log$ denotes the logarithm.
Graph of $\mathrm{arccos}$ on $[1,10]$.
Domain coloring of $\mathrm{arccosh}$.
Properties
Derivative of arccosh
Antiderivative of arccosh
