Difference between revisions of "Cotangent"
From specialfunctionswiki
| (20 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| + | __NOTOC__ | ||
| + | |||
The cotangent function is defined by the formula | The cotangent function is defined by the formula | ||
| − | $$\cot(z)=\dfrac{1}{\tan z} | + | $$\cot(z)=\dfrac{1}{\tan z} \equiv \dfrac{\cos(z)}{\sin(z)},$$ |
where $\tan$ denotes the [[tangent]] function. | where $\tan$ denotes the [[tangent]] function. | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | File:Cotangentplot.png|Plot of cotangent function over $[-2\pi,2\pi]$. |
| − | File: | + | File:Complexcotangentplot.png|[[Domain coloring]] of $\cot$. |
| + | File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle. | ||
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Derivative of cotangent]]<br /> | ||
| + | [[Relationship between cot and coth]]<br /> | ||
| + | [[Relationship between coth and cot]]<br /> | ||
| + | [[Relationship between cot, Gudermannian, and csch]]<br /> | ||
| + | [[Relationship between csch, inverse Gudermannian, and cot]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Arccot]] <br /> | ||
| + | [[Coth]] <br /> | ||
| + | [[Arccoth]] <br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Secant|next=findme}}: 4.3.6 | ||
| + | |||
| + | {{:Trigonometric functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 03:38, 6 July 2016
The cotangent function is defined by the formula
$$\cot(z)=\dfrac{1}{\tan z} \equiv \dfrac{\cos(z)}{\sin(z)},$$
where $\tan$ denotes the tangent function.
Plot of cotangent function over $[-2\pi,2\pi]$.
Domain coloring of $\cot$.
Trig functions diagram using the unit circle.
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
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.3.6
