Talk:Versine

I think that https://de.wikipedia.org/wiki/Sinus_versus_und_Kosinus_versus should be marked as the German version of this article, but I have no idea how to do that myself. Maybe someone more experienced than me could do that. Kriegaex (talk) 08:18, 31 October 2021 (UTC)

I think Haversine should redirect to Haversine_formula rather than here.

It is really always non-negative, as stated in the "History and applications" section, if it is defined as 2sin²(θ/2), but not, if it is defined as 1-cosθ. Are the definitions missing a pair of || somewhere? --Pt 23:33, 6 Oct 2004 (UTC)

:Sorry, my fault. --Pt 15:39, 7 Oct 2004 (UTC)

• Would it make sense to have a vertangent or versecant function? Or an exsine or extangent function? —Preceding unsigned comment added by Celtic Minstrel (talk • contribs) 22:53, 18 October 2007 (UTC)

:For a function $\backslash operatorname\{f\}$:

::$\backslash operatorname\{verf\}(x):=2\backslash left(\backslash operatorname\{f\}\backslash left(\backslash frac\{x\}\{2\}\backslash right)\backslash right)^2$

::$\backslash operatorname\{cof\}:=\backslash operatorname\{f\}\backslash left(\backslash frac\{\backslash pi\}\{2\}-x\backslash right)$

::$\backslash operatorname\{haf\}(x):=\backslash frac\{\backslash operatorname\{f\}(x)\}\{2\}$

:So it would make perfect sense to define a vertangent, a hacoversecant and what not. The reason we don't mention them in the article is that their use is not historically attested (as far as the authors of this article know). Barsamin (talk) 11:55, 11 October 2009 (UTC)

::Judging by the exsecant article, a hypothetical extangent or exsine would be defined as one less than the tangent or sine. Whether that's useful for anything, though? Probably not. Still, $\backslash operatorname\{exf\}(x):=\backslash operatorname\{f\}(x)\; -\; 1$ could be added to the list. (But don't do it just because I suggested it. That would be pointless and silly.) —Celtic Minstrel (talk • contribs) 03:36, 29 October 2009 (UTC)

Math notation, of course, is naturally ambiguous, like all natural languages. This case of ambiguity has to do with the use of exponents in math.

Consider this from the article:

:$\backslash textrm\{versin\}\; (\backslash theta)\; =\; 1\; -\; \backslash cos\; (\backslash theta)\; =\; 2\; \backslash sin^2\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)\; \backslash ,$

$\backslash sin$ is a function, and some mathematicians write, $f^2\backslash left(x\backslash right)$ when they mean

to say $f\backslash left(f\backslash left(x\backslash right)\backslash right)$. Therefore, it is not immediately apparent that the author of this

article really meant to say $\backslash sin\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)^2$ when s/he wrote

$\backslash sin^2\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)$. It was necessary for me to verify the identity with a

calculator before I could be sure. A more complex equation can be rendered totally unreadable by the proliferation of such ambiguity.

98.31.14.215 (talk) 13:29, 30 July 2008 (UTC)

:This mathematical notation for powers of sin and cos functions is totally standard and widespread. I'm sorry you're not familiar with it, but it's used all over mathematics/science/engineering and all over Wikipedia and this is not the place to fight against it. Go to Talk:Trigonometric functions and Wikipedia talk:WikiProject Mathematics if you want to try to convince editors to avoid this notation on Wikipedia, but it seems fruitless to me. —Steven G. Johnson (talk) 17:04, 30 July 2008 (UTC)

:The alternative you propose is, if anything, worse than the notation you criticize. $\backslash sin\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)^2$ can be misinterpreted as $\backslash sin\backslash left(\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)^2\backslash right)$, rather than the intended $\backslash left(\backslash sin\backslash left(\backslash frac\{\backslash theta\}\; \{2\}\backslash right)\backslash right)^2$.--Srleffler (talk) 05:12, 28 September 2008 (UTC)

:I agree that there is an annoying ambiguity arising from the use of exponents on trig functions, but it is standardized, and your alternative is even worse, as Srleffler explains. If we were to write it out in the full, unambiguous manner, we would have an annoying proliferation of parentheses. I prefer the ambiguity, personally. —Celtic Minstrel (talk • contribs) 03:32, 29 October 2009 (UTC)

This article should have a diagram showing the versine function plotted vs. angle.--Srleffler (talk) 05:15, 28 September 2008 (UTC)

:Done. Lytir (talk) 05:26, 28 October 2009 (UTC)

Refering to wikipedia's diagram http://en.wikipedia.org/wiki/File:Circle-trig6.svg which is used on the Trigonometric functions page, the Versed Sine and Coversed Sine are both shown, however the corresponding COsine functions (versed cosine and coversed cosine) are not. Since the diagram is (there) claimed to show "all of the trigonometric functions" that this is an omission.

I was trying to clarify in my mind the distinction between coversed cosine and versed sine (and failed!), but as a "visual learner" inclusion of a completed diagram would be rather helpful!

188.221.150.127 (talk) 18:51, 24 April 2010 (UTC)

:Done (back in 2015 already). --Matthiaspaul (talk) 16:56, 31 July 2017 (UTC)

Article says:

:In fact, the earliest surviving trigonometric table, from the fourth–fifth century Siddhantas from India, was a table of values for the sine and versed sine only (in 3.75° increments from 0 to 90°).

Checking Indian astronomy, it appears that this is indeed fourth–fifth century A.D.. In which case, Ptolemy's table of chords is a trig table, found in the Almagest, still extant, and at least 150 years older. (The oldest known trig table is by Hipparchus, 3 centuries older still, but no known copies survive.) -- 203.20.101.203 (talk) 08:30, 19 July 2011 (UTC)

::You are right. According to Boyer (A History of Mathematics), the Siddhantas is the earliest surviving table of the modern sine function (half chords), whereas Ptolemy's table is the earliest surviving table of chords. — Steven G. Johnson (talk) 16:42, 19 July 2011 (UTC)

It appears to me that between 0 and PI(180 degrees), does the result of sin(angle) - versine (angle) always equals zero (?) But what about angles

between PI rad or 180 degrees - and 2 PI rad or 360 degrees ? I would like the article to show sine, versine and haversine curves for one entire lap, if possible. I think that would be helpfull for readers as well. Boeing720 (talk) 02:36, 4 January 2017 (UTC)

: No. The article does show versine and haversine curves from -360° (-2*pi) to +360° (+2*pi), that is for two full turns.

: However, what might be confusing (and should be improved in the images) is the scale in radians given as decimal numbers (e.g. 0, 2, 4, 6) instead of a radian scale given in fractions of pi (e.g. 0, 2/3*pi, 4/3*pi, 2*pi).

: --Matthiaspaul (talk) 18:04, 17 March 2018 (UTC)

:: Actually, a scale (0, 1/2*pi, pi, 3/2*pi, 2*pi) would be more useful.

:: --Matthiaspaul (talk) 18:13, 17 March 2018 (UTC)

{{Talk:Versine/GA1}}

I've noticed that the overview has a ridiculous amount of citations. Some have up to 10 citations, just to show that something is a synonym! This seems a little unnecessary.Eridian314 (talk) 18:01, 3 February 2021 (UTC)

You can see how to convert a function $f(x)$ into $verf(x)$ up there but what about $arcverf(x)$? I think it should be included along with how to convert a function $f(x)$ into $verf(x)$. — Preceding unsigned comment added by 50.39.195.196 (talk) 17:04, 15 March 2021 (UTC)

Mathworld doesn't cut it here. All of the several historical sources I can find which mention it call $1\; +\; \backslash cos\backslash theta$ the "suversed sine" (short for "versed sine of the supplement"). @Matthiaspaul? –jacobolus (t) 15:51, 3 May 2025 (UTC)

I also can't find any source for "covercosine" or "hacovercosine" which predates Wikipedia and Mathworld. They seem like nonsense made up by Eric W. Weisstein. –jacobolus (t) 16:08, 3 May 2025 (UTC)