Difference between revisions of "Cosecant"

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The cosecant function is defined by
 
The cosecant function is defined by
$$\csc(z)=\dfrac{1}{\sin(z)}.$$
+
$$\csc(z)=\dfrac{1}{\sin(z)},$$
 +
where $\sin$ denotes the [[sine]] function.
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Cosecant.png|Graph of $\csc$ on $\mathbb{R}$.
+
File:Cosecantplot.png|Graph of $\csc$ on $[-2\pi,2\pi]$.
File:Complex Csc.jpg|[[Domain coloring]] of [[analytic continuation]] of $\csc$.
+
File:Complexcosecantplot.png|[[Domain coloring]] of $\csc$.
 +
File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle.
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
 
=Properties=
 
=Properties=
{{:Derivative of cosecant}}
+
[[Derivative of cosecant]] <br />
{{:Relationship between csc, Gudermannian, and coth}}
+
[[Derivative of cotangent]]<br />
{{:Relationship between coth, inverse Gudermannian, and csc}}
+
[[Relationship between csch and csc]]<br />
 +
[[Relationship between csc, Gudermannian, and coth]] <br />
 +
[[Relationship between coth, inverse Gudermannian, and csc]]<br />
 +
[[Derivative of Bessel Y with respect to its order]]<br />
 +
[[Hankel H (1) in terms of csc and Bessel J]]<br />
 +
[[Hankel H (2) in terms of csc and Bessel J]]<br />
  
<center>{{:Trigonometric functions footer}}</center>
+
=See Also=
 +
[[Arccsc]]<br />
 +
[[Arccsch]] <br />
 +
[[Csch]] <br />
 +
[[Sine]]<br />
 +
 
 +
=References=
 +
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Tangent|next=Secant}}: 4.3.4
 +
 
 +
{{:Trigonometric functions footer}}
 +
 
 +
[[Category:SpecialFunction]]
 +
[[Category:Definition]]

Latest revision as of 15:39, 10 July 2017

The cosecant function is defined by $$\csc(z)=\dfrac{1}{\sin(z)},$$ where $\sin$ denotes the sine function.

Properties

Derivative of cosecant
Derivative of cotangent
Relationship between csch and csc
Relationship between csc, Gudermannian, and coth
Relationship between coth, inverse Gudermannian, and csc
Derivative of Bessel Y with respect to its order
Hankel H (1) in terms of csc and Bessel J
Hankel H (2) in terms of csc and Bessel J

See Also

Arccsc
Arccsch
Csch
Sine

References

Trigonometric functions