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)},$$ |
| + | where $\sin$ denotes the [[sine]] function. | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Cosecantplot.png|Graph of $\csc$ on $[-2\pi,2\pi]$. |
| − | File: | + | File:Complexcosecantplot.png|[[Domain coloring]] of $\csc$. |
| + | File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle. | ||
</gallery> | </gallery> | ||
</div> | </div> | ||
=Properties= | =Properties= | ||
| − | + | [[Derivative of cosecant]] <br /> | |
| − | + | [[Derivative of cotangent]]<br /> | |
| − | + | [[Relationship between csch and csc]]<br /> | |
| + | [[Relationship between csc, Gudermannian, and coth]] <br /> | ||
| + | [[Relationship between coth, inverse Gudermannian, and csc]]<br /> | ||
| + | [[Derivative of Bessel Y with respect to its order]]<br /> | ||
| + | [[Hankel H (1) in terms of csc and Bessel J]]<br /> | ||
| + | [[Hankel H (2) in terms of csc and Bessel J]]<br /> | ||
| − | < | + | =See Also= |
| + | [[Arccsc]]<br /> | ||
| + | [[Arccsch]] <br /> | ||
| + | [[Csch]] <br /> | ||
| + | [[Sine]]<br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Tangent|next=Secant}}: 4.3.4 | ||
| + | |||
| + | {{:Trigonometric functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
| + | [[Category:Definition]] | ||
Latest revision as of 15:39, 10 July 2017
The cosecant function is defined by $$\csc(z)=\dfrac{1}{\sin(z)},$$ where $\sin$ denotes the sine function.
Graph of $\csc$ on $[-2\pi,2\pi]$.
Domain coloring of $\csc$.
Trig functions diagram using the unit circle.
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
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.3.4
