Talk:Versine

Versine was nominated as a Mathematics good article, but it did not meet the good article criteria at the time (April 24, 2020). There are suggestions on the review page for improving the article. If you can improve it, please do; it may then be renominated.

Mathematics B‑class Low‑priority

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Redirect

I think Haversine should redirect to Haversine_formula rather than here.

Non-negative

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)

vertangent etc.

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)[reply]

For a function

\operatorname {f}

:

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

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

\operatorname {haf} (x):={\frac {\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)[reply]

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,

\operatorname {exf} (x):=\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)[reply]

Ambiguous math notation

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:

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

$\sin$ is a function, and some mathematicians write, $f^{2}\left(x\right)$ when they mean to say $f\left(f\left(x\right)\right)$ . Therefore, it is not immediately apparent that the author of this article really meant to say $\sin \left({\frac {\theta }{2}}\right)^{2}$ when s/he wrote $\sin ^{2}\left({\frac {\theta }{2}}\right)$ . 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)[reply]

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)[reply]

The alternative you propose is, if anything, worse than the notation you criticize.

\sin \left({\frac {\theta }{2}}\right)^{2}

can be misinterpreted as

\sin \left(\left({\frac {\theta }{2}}\right)^{2}\right)

, rather than the intended

\left(\sin \left({\frac {\theta }{2}}\right)\right)^{2}

.--Srleffler (talk) 05:12, 28 September 2008 (UTC)[reply]

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)[reply]

Diagram needed

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

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

Graphical clarification needed

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)[reply]

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

Ptolemy's is older

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)[reply]

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)[reply]

versine - sin

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)[reply]

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)[reply]

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)[reply]

GA Review

This review is transcluded from Talk:Versine/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: David Eppstein (talk · contribs) 05:32, 24 April 2020 (UTC)[reply]

The nominator has neither edited the article nor discussed the nomination on the talk page. In fact, the nominator appears to have made only one edit to a computer science article, no edits to any mathematics article, and no other edits to articles of a technical nature before this nomination. The lead does not adequately summarize the article. The first section, "Overview", is an unreadable mass of boldfaced synonyms and citation overkill. The next section, "History and applications", has multiple unsourced paragraphs, and appears to be a collection of random facts thrown together in a random order rather than having any logical structure. The "Definitions" section has no text at all, as do several subsequent sections. The "Circular rotations" section has no references at all. The references section includes an excessively long quotation (although not a copyvio as the source is public domain by now). Many of the references are to the dubiously-reliable MathWorld. Several references are to publications with unknown titles that the person using the reference obviously has not read, because they go on to say "according to [someone else], this reference says [something vague about the subject]". The Stávek reference is to an unreliable predatory journal, as is the Stávek entry in "further reading". There is a year-old and still-valid "citation needed" tag on the supposed and unlikely Indian etymology of the Latin word for an arrow. If one wishes to find applications of this function, they are scattered in multiple sections, none of them with section headings identifying them as applications. Given that the versin is such a trivial variation of the cos, there is no indication why the article on it needs to go into such intricate detail about many many other trigonometric functions that are also trivial variations on cos; this is supposed to be an article on versin, not a catalog of all other trigonometric functions. This is very far in many ways from being a Good Article; I think it should be an immediate fail, per WP:GAFAIL. —David Eppstein (talk) 05:45, 24 April 2020 (UTC)[reply]

Is the overview over-cited?

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)[reply]

Inverse

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 $verf(x)$ .