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[[Image:Exsecant and exosecant plot.png|frame|right|exsecant (blue) and excosecant (green)]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
[[Image:Circle-trig6.svg|right|thumb|320px|The trigonometric functions, including the exsecant, can be constructed geometrically in terms of a unit circle centered at ''O''.  The exsecant is the portion ''DE'' of the secant ''exterior'' to (''ex'') the circle.]]
The '''exsecant''', also abbreviated '''exsec''', is a [[trigonometric function]] defined in terms of the secant function sec(θ):


:<math>\operatorname{exsec}(\theta) = \sec(\theta) - 1. \,</math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


Once important in fields such as [[surveying]], [[astronomy]], and [[spherical trigonometry]], the exsecant function is now little-used.  Mainly, this is because the availability of [[calculator]]s and [[computer]]s has removed the need for trigonometric tables of specialized functions such as this one.
Registered users will be able to choose between the following three rendering modes:


A related function is the '''excosecant''' ('''excsc'''), the exsecant of the complementary angle:
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>\operatorname{excsc}(\theta) = \operatorname{exsec}(\pi/2 - \theta) = \csc(\theta) - 1. \!</math>
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


The reason to define a special function for the exsecant is similar to the rationale for the [[versine]]: for small [[angle]]s <var>θ</var>, the sec(<var>θ</var>) function approaches [[1 (number)|one]], and so using the above formula for the exsecant will involve the [[subtraction]] of two nearly equal quantities and exacerbate roundoff errors. Thus, a table of the secant function would need a very high accuracy to be used for the exsecant, making a specialized exsecant table useful.  Even with a computer, [[floating point]] errors can be problematic for exsecants of small angles.  A more accurate formula in this limit would be to use the identity:
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


:<math>\operatorname{exsec}(\theta) = \frac{1-\cos(\theta)}{\cos(\theta)}
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
= \frac{\operatorname{versin}(\theta)}{\cos(\theta)}
= 2 \sin^2(\theta/2) \sec(\theta).\ </math>


Prior to the availability of computers, this would require time-consuming multiplications.
==Demos==


The name ''exsecant'' can be understood from a graphical construction, at right, of the various trigonometric functions from a [[unit circle]], such as was used historically. sec(<var>θ</var>) is the [[secant line|secant]] <math>\overline{OE}</math>, and the exsecant is the portion <math>\overline{DE}</math> of this secant that lies ''exterior'' to the circle (''ex'' is [[Latin]] for ''out of'').
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


==See also==
* [[List of trigonometric identities#Historic shorthands|Trigonometric identities]]
* [[Versine|Versine and haversine]]


==References==
* accessibility:
* M. Abramowitz and I. A. Stegun, eds., ''Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables'' (Dover: New York, 1972), p.&nbsp;78.  (See [[Abramowitz and Stegun]].)
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
* James B. Calvert, [http://www.du.edu/~jcalvert/math/trig.htm Trigonometry] (2004). Retrieved 25 December 2004.
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


[[Category:Trigonometry]]
==Test pages ==
[[Category:Elementary special functions]]
 
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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