Difference between revisions of "Arccot"

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There are two functions commonly called $\mathrm{arccot}$, which refers to inverse functions of the [[cotangent | $\mathrm{cot}$]] function. First is the function $\mathrm{arccot_1}\colon \mathbb{R} \rightarrow (0,\pi)$ which results from restricting cotangent to $(0,\pi)$ and second is the function $\mathrm{arccot_2} \colon \mathbb{R} \rightarrow \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \setminus \{0\}$ which results from restricting cotangent to $\left( -\frac{\pi}{2}, \frac{\pi}{2} \right)$.  
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The [[function]] $\mathrm{arccot} \colon \mathbb{R} \rightarrow \left( - \dfrac{\pi}{2}, \dfrac{\pi}{2} \right] \setminus \{0\}$ is the [[inverse function]] of the [[cotangent]] function.  
  
 
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File:Arccots.png|Graph of $\mathrm{arccot}_1$ and $\mathrm{arccot}_2$ on $\mathbb{R}$.
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File:Arccotplot.png|Graph of $\mathrm{arccot}$ on $\mathbb{R}$.
File:Complex ArcCot.jpg|[[Domain coloring]] of [[analytic continuation]] $\mathrm{arccot}$.
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File:Complexarccotplot.png|[[Domain coloring]] of $\mathrm{arccot}$.
 
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=Properties=
 
=Properties=
{{:Derivative of arccot}}
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[[Derivative of arccot]]
  
 
=References=
 
=References=
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[[Arccoth]]  
 
[[Arccoth]]  
  
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[[Category:SpecialFunction]]

Latest revision as of 03:44, 6 July 2016

The function $\mathrm{arccot} \colon \mathbb{R} \rightarrow \left( - \dfrac{\pi}{2}, \dfrac{\pi}{2} \right] \setminus \{0\}$ is the inverse function of the cotangent function.

Properties

Derivative of arccot

References

Which is the correct graph of arccot x?

See Also

Cotangent
Coth
Arccoth

Inverse trigonometric functions