Difference between revisions of "Cotangent"

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The cotangent function is defined by the formula
 
The cotangent function is defined by the formula
$$\cot(z)=\dfrac{1}{\tan z}=\dfrac{\cos(z)}{\sin(z)},$$
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$$\cot(z)=\dfrac{1}{\tan z} \equiv \dfrac{\cos(z)}{\sin(z)},$$
 
where $\tan$ denotes the [[tangent]] function.
 
where $\tan$ denotes the [[tangent]] function.
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Cotangent.png|Plot of cotangent function on $\mathbb{R}$.
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File:Cotangentplot.png|Plot of cotangent function over $[-2\pi,2\pi]$.
File:Complex Cot.jpg|[[Domain coloring]] of [[analytic continuation]] of $\cot$.
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File:Complexcotangentplot.png|[[Domain coloring]] of $\cot$.
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File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
 
=Properties=
 
=Properties=
{{:Derivative of cotangent}}
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[[Derivative of cotangent]]<br />
{{:Relationship between cot and coth}}
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[[Relationship between cot and coth]]<br />
{{:Relationship between coth and cot}}
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[[Relationship between coth and cot]]<br />
{{:Relationship between cot, Gudermannian, and csch}}
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[[Relationship between cot, Gudermannian, and csch]]<br />
{{:Relationship between csch, inverse Gudermannian, and cot}}
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[[Relationship between csch, inverse Gudermannian, and cot]]<br />
  
 
=See Also=
 
=See Also=
[[Arccot]]
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[[Arccot]] <br />
[[Coth]]
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[[Coth]] <br />
[[Arccoth]]
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[[Arccoth]] <br />
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=References=
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Secant|next=findme}}: 4.3.6
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{{:Trigonometric functions footer}}
  
<center>{{:Trigonometric functions footer}}</center>
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[[Category:SpecialFunction]]

Latest revision as of 03:38, 6 July 2016


The cotangent function is defined by the formula $$\cot(z)=\dfrac{1}{\tan z} \equiv \dfrac{\cos(z)}{\sin(z)},$$ where $\tan$ denotes the tangent function.

Properties

Derivative of cotangent
Relationship between cot and coth
Relationship between coth and cot
Relationship between cot, Gudermannian, and csch
Relationship between csch, inverse Gudermannian, and cot

See Also

Arccot
Coth
Arccoth

References

Trigonometric functions