Difference between revisions of "Versine"

From specialfunctionswiki
Jump to: navigation, search
 
(7 intermediate revisions by the same user not shown)
Line 2: Line 2:
 
$$\mathrm{versin}(z)=1-\cos(z),$$
 
$$\mathrm{versin}(z)=1-\cos(z),$$
 
where $ \cos$ denotes the [[cosine]] function.
 
where $ \cos$ denotes the [[cosine]] function.
 +
 +
<div align="center">
 +
<gallery>
 +
File:Versinplot.png|Plot of $\mathrm{versin}$ on $[-10,10]$.
 +
File:Complexversinplot.png|[[Domain coloring]] of $\mathrm{versin}$.
 +
File:Trig Functions Diagram.svg|Trig functions diagram using the unit circle.
 +
</gallery>
 +
</div>
  
 
=Properties=
 
=Properties=
 +
[[Derivative of versine]]<br />
 +
[[Antiderivative of versine]]<br />
  
 
=References=
 
=References=
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Integral from 0 to infinity of cos(mt)/(1+t^2)dt equals (pi/2)e^(-m)|next=Coversine}}: 4.3.147
+
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Coversine}}: $4.3.147$
 +
 
 +
[[Category:SpecialFunction]]
 +
[[Category:Definition]]

Latest revision as of 02:33, 5 January 2017

The versine function $\mathrm{versin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula $$\mathrm{versin}(z)=1-\cos(z),$$ where $ \cos$ denotes the cosine function.

Properties

Derivative of versine
Antiderivative of versine

References