Difference between revisions of "Arctan"

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The $\mathrm{arctan}$ function is the inverse function of the [[tangent]] function.<br />
 
The $\mathrm{arctan}$ function is the inverse function of the [[tangent]] function.<br />
  
[[File:Arctan.png|500px]]
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<div align="center">
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<gallery>
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File:Arctanplot.png|Graph of $\mathrm{arctan}$ on $[-20,20]$.
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File:Complexarctanplot.png|[[Domain coloring]] of $\mathrm{arctan}$.
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</gallery>
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</div>
  
[[File:Complex arctan.jpg|500px]]
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=Properties=
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[[Derivative of arctan]]<br />
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[[Antiderivative of arctan]]<br />
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[[Relationship between arctan and arccot]]<br />
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[[2F1(1/2,1;3/2;-z^2)=arctan(z)/z]]<br />
  
=Properties=
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=References=
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[http://mathworld.wolfram.com/InverseTangent.html Weisstein, Eric W. "Inverse Tangent." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseTangent.html]
<strong>Proposition:</strong>
 
$$\dfrac{d}{dz} \mathrm{arctan}(z) = \dfrac{1}{z^2+1}$$
 
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<strong>Proof:</strong> █
 
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=See Also=
<strong>Proposition:</strong>
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[[Tangent]] <br />
$$\int \mathrm{arctan}(z) = z\mathrm{arctan}(z) - \dfrac{1}{2}\log(1+z^2)+C$$
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[[Tanh]] <br />
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[[Arctanh]]
<strong>Proof:</strong>
 
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{{:Inverse trigonometric functions footer}}
<strong>Proposition:</strong>
 
$$\mathrm{arctan}(z) = \mathrm{arccot}\left( \dfrac{1}{z} \right)$$
 
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<strong>Proof:</strong> █
 
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=References=
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[[Category:SpecialFunction]]
[http://mathworld.wolfram.com/InverseTangent.html Weisstein, Eric W. "Inverse Tangent." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseTangent.html]
 

Latest revision as of 02:46, 16 September 2016

The $\mathrm{arctan}$ function is the inverse function of the tangent function.

Properties

Derivative of arctan
Antiderivative of arctan
Relationship between arctan and arccot
2F1(1/2,1;3/2;-z^2)=arctan(z)/z

References

Weisstein, Eric W. "Inverse Tangent." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseTangent.html

See Also

Tangent
Tanh
Arctanh

Inverse trigonometric functions