Talk:Sine and cosine/Archive 1

Archive 1

Is this a content fork?

Most of the content here seems to be duplicated from trigonometric functions. I'm inclined to think that this should just be a redirect to that article. That would unify all these closely related functions and avoid having separate articles for sine, cosine tan and maybe secant, cosec and cotan . What are other peoples opinions? Dingo1729 (talk) 05:30, 23 December 2010 (UTC)

What benefit is there to the reader, interested in the sine function, in having the two articles combined? The trigonometric functions article contains much information which is irrelevant to someone interested only in the sine function, and the sine article contains plenty of information which is absent from the Trig functions article and could not be reasonably squeezed into it. There is no policy against having overlapping content in articles. Over 20 other language wikipedias have articles on the sine function; Over 400+ internal links are specifically to Sine; and the page gets approx 1,051 hits a day. I see no issue in having cosine and tan articles if someone wishes to start them. —Pengo 06:36, 23 December 2010 (UTC)

My deepest apologies if I'm doing something wrong

The bit about the graphs and waves seems quite confusing. Isn't the sin x=1 when x is 90 degrees because then the objective side=hypotenuse? And why, in the animation does the triangle become a line at 90 degrees? At the 90 degrees point does x not become 90 degrees? And sine is a ratio of the objective side to the hypotenuse; but what of the objective side to the hypotenuse? The side lengths? Their shared angle? I'm really just wondering i you could make is slightly more clear in the first paragraph of the page? Kirikizan Kirikzan (talk) 16:38, 1 September 2011 (UTC)

Definition of Sine of an Angle Theta

I personally believe the best definition, and the one that should be most prominent in this article, ought to be the one as the y-coordinate of the point on the unit circle which makes an angle theta with the positive real axis. This has the advantage of being unambiguous, defined for all angles, and the most useful. I personally believe, the relation to right angled triangles should come afterwards. (My motives are slightly pedagogical. Many people only remember the first definition they encounter. I would prefer this to the correct definition.) I want to change it, but maybe it's worth having a discussion first.--345Kai (talk) 15:58, 15 October 2011 (UTC)

Hi Kai. I have no objections to you changing it. I haven't really been happy with the opening definition myself (and I started the article). Be bold, this is a relatively young article. That said, the "ratio of right angle sides" definition should probably stay near the top too, as it's a common one. —Pengo 22:17, 15 October 2011 (UTC)

Hi all, I've thought of a complex angle system that has three trigonometric identities (to make matters worse for those who think two are enough).

• Cosine of an angle is the horizontal (x) displacement,
• Sine of an angle is the vertical (y) displacement, and
• Just so your heads hurt, hypersine (not to be confused with hyperbolic sine) is the axial (z) displacement.

The real part of an angle is the counterclockwise rotation of a ray on the xy plane, and the imaginary part is the rotation of that plane about the x-axis (towards the positive side of the z-axis).

Is this similar to the generalization of trig identities to complex values given within the article? Cheers, The Doctahedron, 03:11, 17 December 2011 (UTC)

If you don't get a response here you might want to try Wikipedia:Reference desk/Mathematics. —Pengo 02:53, 18 December 2011 (UTC)

Domain and co-domain is for real numbers only

The domain and co-domain are given only for real numbers at basic features table. But sine is defined for complex numbers as well, and has different co-domain in that case (all complex numbers). I guess this should be mentioned in on the table. Such partial information might lead to further prolifilation of stupid jokes that assume that sine could not be equal 3 or 4. It obviously could, but on the complex numbers. — Preceding unsigned comment added by 178.130.5.204 (talk) 06:48, 27 February 2012 (UTC)

Agreed. I came to the talk page because I noted that issue too. I'm not certain if $(-\infty ,\infty )\in \mathbb {R}$ would be appropriate syntax for the infobox. Perhaps a footnote is needed? Thelema418 (talk) 19:39, 3 September 2012 (UTC)

Memory aid that includes 15° and 75°

I have found a memory aid that includes 15° and 75°. It goes as follows:

sin(0°) = sqrt(2 - 2)/2

sin(15°) = sqrt(2 - sqrt(3))/2

sin(30°) = sqrt(2 - 1)/2

sin(45°) = sqrt(2)/2

sin(60°) = sqrt(2 + 1)/2

sin(75°) = sqrt(2 + sqrt(3))/2

sin(90°) = sqrt(2 + 2)/2

I can insert it in the article. Any objections?

sqrt(2 - sqrt(3))/2 equals (sqrt6) - sqrt(2))/4. The latter is frequently mentioned as an exact value for sin(15°). It is, however, less easier to memorize. VandenheedeJanGJ (talk) 14:16, 10 April 2013 (UTC)

A better proposal is maybe to improve the traditional memory aid (called 1st memory aid below) and add a second one.

1st memory aid (for natural multiples of 30° and 45° in quadrant I):

angle sine

0° 0° sqrt(0)/2

--- 30° sqrt(1)/2

45° --- sqrt(2)/2

--- 60° sqrt(3)/2

90° 90° sqrt(4)/2

2nd memory aid (for natural multiples of 15° and 22°30' in quadrant I):

angle sine

0° 0° sqrt(2 - sqrt(4))/2

--- 15° sqrt(2 - sqrt(3))/2

22°30' --- sqrt(2 - sqrt(2))/2

--- 30° sqrt(2 - sqrt(1))/2

45° 45° sqrt(2)/2

--- 60° sqrt(2 + sqrt(1))/2

67°30' --- sqrt(2 + sqrt(2))/2

--- 75° sqrt(2 + sqrt(3))/2

90° 90° sqrt(2 + sqrt(4))/2 VandenheedeJanGJ (talk) 18:31, 10 April 2013 (UTC)

VandenheedeJanGJ

A possible 3rd memory aid deals with natural multiples of 7°30' and 11°15':

angle sine

0° 0° sqrt(2 - sqrt(2 + sqrt(4))) / 2

--- 7°30' sqrt(2 - sqrt(2 + sqrt(3))) / 2

11°15' --- sqrt(2 - sqrt(2 + sqrt(2))) / 2

--- 15° sqrt(2 - sqrt(2 + sqrt(1))) / 2

22°30' 22°30' sqrt(2 - sqrt(2 + sqrt(0))) / 2

--- 30° sqrt(2 - sqrt(2 - sqrt(1))) / 2

etc.

Further memory aids each time halve the 2 smallest non zero angles and each time a square root is added in the nested radical.

VandenheedeJanGJ (talk) 19:54, 10 April 2013 (UTC)

The 1st memory aid looks like this:

x in degrees	0°		45°		90°
"	0°	30°		60°	90°
x in radians	0		π/4		π/2
"	0	π/6		π/3	π/2
$\mathrm {sin} \,x$	${\frac {\sqrt {0}}{2}}$	${\frac {\sqrt {1}}{2}}$	${\frac {\sqrt {2}}{2}}$	${\frac {\sqrt {3}}{2}}$	${\frac {\sqrt {4}}{2}}$

The 2nd, more refined memory aid, containing 15° and 75°, looks like this:

x in degrees	0°		22°30'		45°		67°30'		90°
"	0°	15°		30°	45°	60°		75°	90°
x in radians	0		π/8		π/4		3π/8		π/2
"	0	π/12		π/6	π/4	π/3		5π/12	π/2
$\mathrm {sin} \,x$	${\frac {\sqrt {2-{\sqrt {4}}}}{2}}$	${\frac {\sqrt {2-{\sqrt {3}}}}{2}}$	${\frac {\sqrt {2-{\sqrt {2}}}}{2}}$	${\frac {\sqrt {2-{\sqrt {1}}}}{2}}$	${\frac {\sqrt {2\pm {\sqrt {0}}}}{2}}$	${\frac {\sqrt {2+{\sqrt {1}}}}{2}}$	${\frac {\sqrt {2+{\sqrt {2}}}}{2}}$	${\frac {\sqrt {2+{\sqrt {3}}}}{2}}$	${\frac {\sqrt {2+{\sqrt {4}}}}{2}}$

VandenheedeJanGJ (talk) 13:38, 12 April 2013 (UTC)

actual definition of sine.

hi, can we get an actual definition of sine at the top please. It's clear to me, as a mathematics novice of little or no standing that this "article" does not actually define sine.

The sine of something definition does not really cut it. Sorry.

ie. The sine of an angle is... The sine of an arc is...

Yes I get that you can use "sine" to do things but that is not explaining what "sine" actually is.

So can we get some help on this?

Robert. Anglepoiselamp (talk) 08:18, 5 July 2013 (UTC)

Sine.

Greetings! Maths lovers, of smaller, medium or larger ability, I salute you!

The sine description has me rather at a loss, this pains me.

A constant problem I see is the propensity for people to define something by what is does OR how it interacts with others. Whittling a perfectly enthralling description to a few lines. Or less.

As far as I can tell sine is an actual thing, so it can be defined. And should be so done. The sine function would then dove tail into that and even lay people after some braining would quickly pick up the basic gist.

As it seems to be a pivotal (polar pun) function maybe by firmly locating it in physical sense it would be easier for people to understand? yes?

i.e OK chaps, this is Sine, if you rotate the triangle around the pole then Sine changes and the ratio of Sine to coSine changes too etc etc... and if you plot the change in Sine on a Cartesian graph. x being angular dimension y being Sine then you get a "Sine wave".

Being a bit of a critic of introductory maths education I generally I see the same lack of understanding of "fundamental" or "elementary" maths time and time again. The most common tactic to avoid any solid ground work in these areas is to move past them into deeper water as soon as possible. And I see this in the article on sine.

Never underestimate a clear and concise description, not matter how short or terse.

Sine is this: ( insert great description of sine here).

Kind regards to you all,

Robert. Anglepoiselamp (talk) 15:07, 9 July 2013 (UTC)

Was this page designed to confuse dyslexics?

In the diagram of the triangle I would have thought it would be better to call the adjacent side a and the opposite o. — Preceding unsigned comment added by 64.203.137.12 (talk) 08:16, 17 July 2013 (UTC)

Inverse

The Inverse sub-section has problems imho. "As sine is non-injective, it is not an exact inverse function but a partial inverse function." → I have NEVER heard of a "partial inverse function". Which function is this sentence referring to sine or arcsine?? The inverse sine function is a partial function - NOT a partial inverse function. (or a partial function on the Real numbers?)

"For example, sin(0) = 0, but also sin(π) = 0, sin(2π) = 0 etc. It follows that the arcsine function is multivalued: arcsin(0) = 0, but also arcsin(0) = π, arcsin(0) = 2π, etc."→ OMG! this is claiming that functions can be multivalued! THIS IS WRONG. They are single valued BY DEFINITION. As the wikipedia article on multivalued functions points out, a mvf, despite its name, is NOT a function. This goes on to claim that arcsin(0) = π, 2π, etc. !!! THIS IS also WRONG!! We need to limit the range to -½π to +½π inorder to have a function at all. Using arcsin() as a multivalued function to explain why it can not be a multivalue function is crazy-talk. This has been explained in many places in much better ways than the attempt here. "When only one value is desired, the function may be restricted to its principal branch." → The FUNCTION MUST be restricted. I am not enough of a mathematician to know how the multivalued function issue should be handled (in a single article, or in each article that encounters it?). Multivalued functions are NOT functions. Utilization of the terminology ought to be linked or explained each time it is used AND the terminology should be exact: a multivalued function is NOT a function with multiple values. (The Whitehouse is NOT a house that is white.) The problem of the inverse for any many-to-one function is the same, in general, isn't it?Abitslow (talk) 00:03, 2 November 2013 (UTC)

Animation

• Old animation
• New animation

A recent edit introduced the new animation in Sine#Relation to the unit circle. The new animation is far too fast—I would guess about 30% of its current speed might be right. As a guide, the old animation was very good as far as speed goes (it is much slower, although the delay before restarting is perhaps too long). Any opinions? I'm wondering if the new animation is unnecessarily busy. Johnuniq (talk) 07:02, 27 May 2014 (UTC)

Fixed Points of the Sine

Can we get some expansion here? Certainly there is one boring real fixed point of the sine, sin(0) = 0, but should there be something about the infinite number of complex fixed points such as sin(20.238517707+3.7167676797i ) = 20.238517707+3.7167676797i? — Preceding unsigned comment added by 165.214.14.22 (talk) 19:02, 22 May 2012 (UTC)

Does "Fixed Points" even need a section? Most functions don't have a section about their fixed points, I don't see how the sine function's fixed points are terribly important/interesting. Ze49899 (talk) 03:18, 22 June 2014 (UTC)

mistranslation?

I'm not into Arabic languages nor Sanskrit :( Anyway, read this (http://www.billcasselman.com/unpublished_works/sinus_origin.htm) : "Here I’m interested to point out that Latin sinus which became English sine was used as a translation of a similar metaphor in the Arabic original where the trigonometric function was compared using the Arabic noun jaib ‘inner fold of a garment,’ (Arabic jaib equalling Latin sinus in meaning)" Are these two different arabic words or the same just differently written? As the word sinus was already present in latin and its meaning is fitting for the sine curve; and it's not improbable that the arabic scholars also named it similarly - or so the latin translators believed? Hoemaco (talk) 09:07, 31 August 2011 (UTC)

The Latin word sinus alludes to the winding nature of the sine curve. The chord tables in Ptolemy's Almagest were needed for his epicycle theory which was probably due to Hipparchus. The word may also be used in the sense of a meandering river like the Meander near Miletus on the Ionian GreeK coast, the home of Hipparchus and Pythagoras. --Jbergquist (talk) 21:52, 29 September 2014 (UTC)

The annual motion of the Sun north and south of the Equator may have suggested the legend of Apollo's chariot and epicycles. The sine curve is produced by the spinning motion of a wheel along with translation. The fact that sinus was used to translate an Arabic word indicates that it may have had a similar usage at the time. It cannot be taken as evidence of priority for the Arabic meaning. --Jbergquist (talk) 00:38, 30 September 2014 (UTC)

The motion of a point on a rolling wheel is known as a roulette and that on the rim is a cycloid. The parametric equations for a cycloid are,

${\begin{aligned}&x=vt+r\sin \left({{\phi }_{0}}-{\frac {v}{r}}t\right)\\&y=r-r\cos \left({{\phi }_{0}}-{\frac {v}{r}}t\right)\\\end{aligned}}$

where r is the radius of the wheel, v its horizontal velocity and φ₀ indicates an initial angular position on the rim. The horizontal and vertical positions of the point are x and y respectively. The horizontal motion is similar to that of an epicycle and if the circular track rotated the speed of the hub could be changed. This suggests the unsteady motion of an epicycle. --Jbergquist (talk) 22:48, 1 October 2014 (UTC)

sin(pi*x^1/2)

No where on Wikipedia have I found mention of the interesting fact the equation sin(pi*x^(1/a)) crosses the x-axis at only the integers where n^(1/a) is an integer, ie all the perfect powers. I think this belongs somewhere, whether on the perfect square page, the sine page, or the sine wave page, but I can't find any mathematical sources that describe this other than my own graph. Can somebody either correct me if I'm wrong, find a source, or let me know that the graph is enough and hand me a medal for discovering a new mathematical property? Thank you. Skylord a52 (talk) 01:13, 17 April 2015 (UTC)

codomain

The template confuses the codomain (which is the set R) with the image (which is [-1,1]). JDiala (talk) 15:36, 14 August 2015 (UTC)

Combine

Should this page be combined into Trigonometric Functions as the content is already covered in that page? Wetit🐷 0 03:03, 1 October 2016 (UTC)

The Domain Colouring Picture

This seems inaccurate. Examining the real line, that is the the x azis, it should move from brightness (absolute magnitude) 0 to 1 and the saturation (complex argument) should be zero, pi, or undefined. I think the hue is actually being used for argument, not saturation. But it still seems wrong.--Mongreilf (talk) 14:18, 28 December 2016 (UTC)

Derivative in calculus with scalar in radius sine

Why isn't a scalar included with the calculus chapter? E.g.

For the sine function in radians:

$f(x)=\sin(\alpha x)\,$

The derivative is:

$f'(x)=\alpha \cos(\alpha x)\,$

— Preceding unsigned comment added by JHBonarius (talk • contribs)

Because that is a straightforward application of the chain rule and has nothing to do with the sine function per se. --JBL (talk) 12:59, 1 June 2017 (UTC)

Recent edits

Laurdecl, to answer the questions in your edit summary: first, the sentence belongs in brackets because it is an aside (this is the article about sine, the other trig functions are incidental). Second, the section on relation to slope has several major issues: its title is wrong (it does not relate sine to slope), none of the key words are defined, it is uncited, and the definition it offers cannot actually be made correct without fully transforming it into the unit circle definition because of issues about which angle and which way to measure the angle (consider the case of a segment with negative slope). I spent some time thinking about resolving these issues, but I don't think that there is any better way than simply removing the section. If you feel there is some important idea in that section not in the unit circle section, I invite you to introduce it there, preferably with a source.

Separately, there is some issue of "angles" versus "measures of angles" -- it is my belief that the input to sine is the measure of an angle, not an angle itself. Do you agree? (This confusion precedes your edits and is present in both yours and mine, but it would be easy to sort out.) --JBL (talk) 12:57, 1 June 2017 (UTC)

I removed the section again because it is very confusing. Normally we think of slope as rise over run, not rise per unit hypotenuse. The concept in the section is not common; hence no citation. I have removed it for now and I do not think it should be reinserted without a reputable citation from a textbook or journal article, indicating that it is in standard use.—Anita5192 (talk) 16:11, 1 June 2017 (UTC)

If you want to format the stuff about related functions as an aside, you could use {{efn}} to do it. It looks bad to have multiple sentences in brackets. I left the slope section in there because I think that it's worth mentioning to the reader as a possible definition of sine. I agree it is poorly worded and doesn't really have anything to do with gradient in a strict sense (unless you substitute run in ⁠rise/run⁠ with hyp. length). If there really isn't a way to merge it into the section above, then I'm fine with leaving it out, although I think that if it helps one reader then it's worth having. About the angle measure, I see that as purely semantic. Is there a practical difference between 30° and the measure of 30°? Laurdecl ^talk 09:36, 2 June 2017 (UTC)

I will think about the question of the aside more. 30° is a measure -- it tells you how big something is. By contrast, an angle is a geometric thing determined by some points and lines in the plane; it has a measure, but it is not itself one. --JBL (talk) 12:20, 2 June 2017 (UTC)

Etymology

The section currently reads - "Etymologically, the word sine derives from the Sanskrit word for chord, jiva*(jya being its more popular synonym)." - I think this is plainly misleading by conflating proximate and ultimate origins and by confusing the origin of the word with the presumed origin of the concept. Etymology and history need to be clarified. As far as the etymology goes, the immediate word sine is from Latin rather than from the Sanskrit word. I think this section needs to be reworded. Also someone has transcribed the Arabic intermediate but the Sanskrit is not even phonetically transcribed right (it is ज्या in the original - see for example this; jiva seems to be a typo or a misinterpretation - it is usually written as IAST jyā IPA /ɟjɑː/ as given in most reliable sources on Indian trigonometry - example this. In the history section there is a mention of "The chord function" - the link is unhelpful and does not explain what a "chord function" is supposed to mean? It seems that Hipparchus' ideas were based on isosceles triangles - See Carthy, Daniel P. Mc; Byrne, John G. "Al-Khwārizmī's Sine Tables and a Western Table with the Hindu Norm of R = 150". Archive for History of Exact Sciences. 57 (3): 243–266. doi:10.1007/s00407-002-0058-6. ISSN 0003-9519.. Since my own attempts at improvement are reverted, I leave my suggestions here for anyone interested in improving accuracy, referencing and structuring. Shyamal (talk) 18:21, 3 March 2017 (UTC)

There's an inconsistency here with regards to the scholar responsible for the mistranslation anecdote. This page claims it was Gerard of Cremona, however his page makes no mention of the fact, while that of Robert of Chester claims that he did it, with the referance given on the Robert of Chester page quoting two different accounts, one naming Gerard, and the other Robert. Basically it's a mess, and has the smell of an uncheckable legend. I don't have the time to keep digging for an answer, so I'll just throw that out there that all 3 pages need to be brought in line. Fearghalj (talk) 20:53, 24 April 2018 (UTC)

While it may be uncheckable, it is not a legend. There is a priority dispute as to who first translated "jaib" as "sinus". According to D.E. Smith, History of Mathematics (1925), "When Gherardo of Cremona (ca. 1150) made his translation from the Arabic he used sinus for jaib, ..." (Vol. II, p. 616). Some authors (Eves and Maor, in particular) have repeated this and Eves makes it sound like Gherardo originated the translation. However, in a footnote in the same book, Smith says, "The term was probably first used in Robert of Chester's revision of ..." (Vol. I, p. 202), and this is repeated by Boyer. However, Smith is getting his information from A. Braunmühl's Geschichte der Trigonometrie, I (Leipzig, 1900), which discusses this priority issue and brings up the prior use of the term by Plato of Tivoli. Cajori (1906) also mentions Plato of Tivoli as the originator, probably using the same source. It is doubtful that this matter will ever be cleared up and I am not quite sure how we should proceed without giving undue weight to a very trivial dispute. --Bill Cherowitzo (talk) 18:59, 25 April 2018 (UTC)

I have attempted to provide some clarification with a reference. --Bill Cherowitzo (talk) 20:25, 26 April 2018 (UTC)

Arc length

Just an extension of the discussion on Talk:Ellipse
The following discussion has been closed. Please do not modify it.
I repost here what was twice vandalized for all editors to see. Both vandals have violated the rules by removing my edits without discussing them on this Talk page. The arc length of the sine curve between $a$ and $b$ is $\int _{a}^{b}\!{\sqrt {1+\cos ^{2}(x)}}\,dx$ This integral is an elliptic integral of the second kind. The arc length for a full period is ${\frac {4{\sqrt {2\pi ^{3}}}}{\Gamma (1/4)^{2}}}+{\frac {\Gamma (1/4)^{2}}{\sqrt {2\pi }}}=7.640395578\ldots$ where $\Gamma$ is the Gamma function. Alternatively, (See footnote 7 at the bottom of page 1097 of the referenced Notices of the AMS article) it is efiiciently calculated as $2\left(M+{\frac {\pi }{M}}\right)$, where $M=1.19814\ldots$ is the arithmetic-geometric mean of $1$ and ${\sqrt {2}}$. The reciprocal of $M$ is known as Gauss constant. The graph of the sine function might be viewed as a "degenerate" graph of the elliptic function graph. Generally, the length of a period of the graph of an elliptic function is expressed via the modified arithmetic-geometric mean which was apparently introduced for efficiently calculating the length of a thread in a linear parallel force field. Cocorrector (talk) 08:21, 12 November 2018 (UTC) References The contexts, including for the above, are extensively dealt with at Talk:Ellipse. The sophistic claim without discussing does now not hold anymore for this page, too. Purgy (talk) 10:55, 12 November 2018 (UTC) Four comments: There's no need to provide an alternative to the expression in terms of the gamma function. This function is among the most well known of the special functions. The alternative expression in terms of the AGM is just a reflection of the special value of $\Gamma ({\tfrac {1}{4}})$. Reference 1 is a dubious reference. Its main claim, that it provides the first efficient method of computing the complete elliptic function of the second kind, is false. Equivalent methods have been around since the 19th century (see Talk:Ellipse). The business about the sine function being a degenerate elliptic function is off-topic (references 2 and 3). Reference 3 is published by LAP Lambert Academic Publishing which is a subsidiary of OmniScriptum; the Wikipedia article describes several problematic practices of this outfit. cffk (talk) 14:24, 12 November 2018 (UTC) Ок cffk u seem quite bitter and “a bit we todd did” or is it the other way around? Is that the reason your candidacy will never be considered for any publication at the “AMS Notices”? All your four arguments are dubiously false since not only u're incapable of valuably contributing but u'ant even capable of appreciating valuable contribution of others who stand head and shoulders above you in the math and physics food chain. We all see that 83.149.239.125 had already explained to u the MAGM to a much greater extent than u'll ever care to know, so adding a formula here from that source with “several problematic practices of this outfit” would suffice for your little head. Do not dismiss it since nobody can make it any simpler than this $l=N(k,1/k),$ where this time $l$ is a length of a thread in linear parallel force field and $k$ is the Jacobi elliptic modulus. With this simple formula and its quite physical interpretation, as I've most recently confirmed from both secondary and primary source, the MAGM was born. Anyone smarter than you from all over the world would easily see that the MAGM appears here without the AGM. Then we all as easily see that you were repeatedly told by the same 83.149.239.125 on Talk:Ellipse that the MAGM can be calculated in two equivalent ways allowing us to appreciate the beautiful formula which was published in An eloquent formula for the perimeter of an ellipse for all of us, including those with mathematical abilities not exceeding mine or even yours, to see. A glimpse at the paper suffices to tell that the author was aware of the equivalence before publishing the paper. Certainly, the equivalence was not discovered by you after the Adlaj publising his paper as you suggest. You comparison is dubious and the Python code you wrote isn't worthy to be included anywhere. U don't even seem to understand yourself since you admitted that Adlaj presented Gauss' method in another way bu you failed to understand the significance of this "other way". What a crippled pitiful soul one would have to attempt hiding or dismissing the formula $C={\frac {2\pi N(a^{2},b^{2})}{M(a,b)}},$ and what delusion would lead one to “discover” an error in that awesome beauty and what repeated bout would lead the same one to “double” on that “rediscovery”, in another article, of the same “error” which you u'ant capable of articulating. The formula is beautiful and one has to be quite stupid to argue otherwise. And it is a new 21-st century formula and no one deserves a credit for it aside from its author and Gauss. One has to be quite obnoxious to intervene. Unlike you, the author while fully capable of appreciating the main contribution of Gauss, was capable of appreciating the beauty which u're blind to. Although he did, the author did not need to reference anyone else other than Euler and Gauss. Richard Brent was not as gracious to give Euler and Gauss the credit which they deserved but the truth can’t forever be concealed. The idiot Tom Van Baak thought that Gauss formula of May 30, 1799 was recently discovered as he claimed in his truly dubious article A New and Wonderful Pendulum Period Equation citing Adlaj’s paper as a “Good introduction to elliptic integrals, AGM, and pendulums” without ever reading there that full and all credit was given to Gauss alone. So consistently, u are so oblivious to all this and all the rest of that deviant discussions which are propagated by people as ugly as u. Luckily, there is no permanent place for the ugliness which people like u strive to preserve in mathematics. Your lowest quality followers such as User:Wcherowi and User:Joel B. Lewis are not even able to repeat your arguments since they do not understand them. They just feel and stick to your sick attitude. Most likely they support your pettiness and envy but nothing more. One of them User:Joel B. Lewis has already threatened me with an arranged consensus which seems to unfold here before my eyes. Quite a disgusting environment which can’t permanently last as that beautiful formula would, while exposing lowlifes along its way. So stop wasting your life, the sooner’s the better for u and everyone else. Cocorrector (talk) 19:34, 13 November 2018 (UTC) @Cocorrector: Your comments are a continuation of the discussion on Talk:Ellipse; please move them there. You should limit the comments on this page to a discussion of Sine. cffk (talk) 20:36, 13 November 2018 (UTC) Cocorrector, it is deeply shocking that someone as pleasant and charming as yourself is unable to convince other people of the value of your suggestions. Luckily, this mystery is problematic for you alone. --JBL (talk) 22:28, 13 November 2018 (UTC)

Etymology again

An IP has recently been trying to insert a statement to the effect that the OED claims that there is no Sanskrit origin to the word (or concept if you like) sine. The link provided to justify this leads to a paywall, and I have objected to its use more than once. The IP has failed to understand the intent of my edit summaries and has acted as if I had claimed that the OED was in some sense wrong with this entry. I have just checked the OED and the statement there says that sine comes from the Latin sinus which in turn is how the Arabic jaib (or sometimes written jiba) was translated in the middle ages. The OED makes no claims about the origins of the word jaib. The IP seems to think that this means that this Arabic term did not have Sanskrit origins, but the OED does not say this, so this is just WP:SYNTH. On the other hand, Webster's Unabridged International Dictionary does trace jaib back to the Sanskrit jyā. Together with the fact that all mathematical historians who have weighed in on the subject agree, it strikes me that the IP is just pushing a POV and does not have a real case. --Bill Cherowitzo (talk) 23:03, 14 February 2019 (UTC)

I agree, this is silly, the claim is totally reasonable for inclusion. --JBL (talk) 16:02, 15 February 2019 (UTC)

Bill is completely missing the point. The point of inserting OED reference is to give multiple viewpoints in a scholarly fashion. For the sake of academic diversity of opinions and honesty, one must present different viewpoints rather than make believe a certain authority. There are several stories about the origins of sine and cosine. More detailed version can be found in The Words of Mathematics by Schwartzman. It is quoted here "sine (noun): most immediately from Latin sinus "a curved surface," with subsidiary meanings such as "fold of a toga" and hence the "bosom" beneath the toga; "bay" or "cove." How that word came to represent a trigonometric function is quite a circuitous-and, depending on the authority you believe, contradictory-story. Howard Eves, in his An Introduction to the History of Mathematics, explains the origin of the word in the following way. The Hindu mathematician Aryabhata used the tenn jya, literally "chord," to represent the value of the equivalent of the sine function. When the Arabs translated Indian mathematical works, they transliterated jya as jfba, which actually meant nothing in Arabic. Now Arabic, like Hebrew, is often written with consonants only (pt n th vwls fr yrslf), so jfba became simply jb. Later readers, seeing jb, pronounced it as jaib, which was a real Arabic word meaning "cove, bay." When European mathematicians translated Arabic writings to Latin, they replaced jaib with the Latin word for "cove," which happened to be sinus. The American Heritage Dictionary claims that Arabic jayb (Eves's jaib) did have a meaning, namely "chord of an are," but that Europeans confused the word with the homonym jayb meaning "fold of a gannent," which happened to correspond to Latin sinus. The Oxford Dictionary of English Etymology claims that Arabic jaib meant "bosom," again translated by Latin sinus. For an equally intricate tale of Arabic-Latin translation" Farooq — Preceding unsigned comment added by 12.70.165.255 (talk) 01:15, 16 February 2019 (UTC)

The source you are quoting supports that the word comes from Arabic via Latin, which is what the article says. The source emphatically does not support the claim that "the word sine is not traced to any Sanskrit word" -- it says nothing one way or the other about where the Arabic word comes from. In particular, this is 100% consistent with the (referenced) claim in the article that the chain is Sanskrit -> Arabic -> Latin. --JBL (talk) 01:36, 16 February 2019 (UTC)

Merge proposal: Sine wave into Sine

I propose to merge the content of Sine wave into Sine as the former article can be adequately expressed within the context of the latter. Jamgoodman (talk) 16:57, 1 July 2019 (UTC)

Deletion of Sine Squared section

User @Comfr: wants to have a section about the function sin(x)^2; I say this section is redundant as the relationships between sin(x)^2 and the other trigonometric functions are detailed elsewhere, but also the section focuses too specifically on a topic not general enough for the whole article. It would not be appropriate to have a section for sin(2*x), sin(x/2) not sin(x)+1 but they are equally notable as sin(x)^2. I support the redirect and some content in the article referring to sin(x)^2 but an entire section is gratuitous. If Comfr can clarify their position why they think the section should stay, it would be appreciated. Also, please remember that having a redirect does not constitute notability. Plenty of redirects remain on the site despite their articles' deletion. Thanks. Jamgoodman (talk) 08:38, 13 August 2019 (UTC)

I agree that the function $sin(x)^{2}$ does not merit its own section for the reasons listed above and because it is a sinusoid of a different frequency from $sin(x),$ translated from the origin, which is not significantly different. I think this alone should be mentioned.—Anita5192 (talk) 15:43, 13 August 2019 (UTC)

Sines and squares of sines ofter appear in alternating current equations. As I was attempting to understand an anomalous power factor reading, I began wondering about how squaring affected the shape of a sine function. I assumed that part of a period would be compressed, while another would be stretched. That is all I knew.

I searched for sine squared in Wikipedia, and a redirect took me to the page Trigonometry. Unfortunately, I could not find anything about sine squared on the trigonometry page. I also looked at List of trigonometric identities, Trigonometric functions, and many other searches, without ever finding anything about what a sine squared function might look like.

The breakthrough came when I made a graph of sine and sine squared. I was surprised to see that sine squared was actually a rescaled sine function.

I wish I could have better integrated sine squared into the article, but that was beyond my mathematical ability, so I did the best I could. Perhaps user @Jamgoodman: could identify the specific places where the redundant information already exists, and make those places come up in a Wikipedia search.

Please remember Wikipedia articles should be written so they can be understood by general readers to at least an introductory level WP:TECHNICAL. Many of my colleagues can look at an equation, and immediately see various transformations. I can't.

I thank Jamgoodman for his careful review of my edits. He/she is helping to improve the quality of Wikipedia. Comfr (talk) 03:02, 14 August 2019 (UTC)

I think it would be reasonable to include, in some form (probably not what Comfr originally produced), the double- and half-angle formulas for sine (with an appropriate reference), including the (surprising!) fact that $\sin ^{2}(x)$ is again a sinusoid. It would be much better to include a proper source, say, a standard textbook on trigonometry or precalculus. One or another version of the formula in question does appear in the (incredibly terrible) article List_of_trigonometric_identities -- check out the section List_of_trigonometric_identities#Half-angle_formulae -- but I don't know how a person who didn't already know what they were looking for would be able to find it. --JBL (talk) 23:16, 14 August 2019 (UTC)

I created the new section sine squared only after I failed to find the information anywhere in Wikipedia. I am not a mathematician, but Wikipedia is a work in progress, so I put what I had discovered into a new section, and expected that eventually more experienced editors would replace it with something better. When I could not find a reference meeting Wikipedia's standards, I supplied this derivation in my original revision. I created the new section to save other readers from the pain I went through. — Preceding unsigned comment added by Comfr (talk • contribs)

Yes, you already made this clear (though the information is already in WP, as I noted). --JBL (talk) 11:16, 15 August 2019 (UTC)

Weighing in a little late, but I'm glad to see this section made it back in despite being "redundant". Practically the entire Sine article is "redundant", most of it was copy-pasted by me from Trigonometric functions and articles like List of trigonometric identities, where apparently some smart folk might know to look for information on sine squared. No harm having some redundancy if it means the information can be more easily found and understood. Clearly there are properties of sine squared are not trivial or obvious, and I can't imagine a better place to have it. —Pengo 09:12, 4 July 2020 (UTC)

Confusing labels of triangle sides

In one of the figures, why is the opposite side labelled a and the adjacent side labelled b? This is confusing. An editor just tried to "fix" one of the equations by changing a to o, which is more intuitive, and it was reverted because that does not match the diagram. Why not label the opposite side o and the adjacent side a?—Anita5192 (talk) 18:04, 29 January 2021 (UTC)

In the section Sine#Right-angled triangle definition it says for the entire article: "* The opposite side is the side opposite to the angle of interest, in this case side a", and this change from a to o was done in just one single place. At the very least it should have been changed for all instances of a, but that would probably be a bad idea, as o looks like zero. I assume that this is the reason why originally a was chosen. - DVdm (talk) 18:49, 29 January 2021 (UTC)

Bug?

In the "Arc length" section, for some reason, "from $0$ to $x$" is displayed as "from to $x$". It is quite confusing. Is it just me, or is someone else experiencing this issue? A1E6 (talk) 13:51, 22 August 2021 (UTC)

Yep. It's the math-0 bug. See Wikipedia:Village_pump_(technical)#Math_0. I added a space to solve it. - DVdm (talk) 14:30, 22 August 2021 (UTC)