Sine (sin) comes from “sinus” in Latin meaning bend fold or curve. This is so named because the sin math function comes to us through Arabic scholars who called it “jaib”, which is Arabic for “bosom”. They called it that because that Arabic word sounded like the Sanskrit word “jiva”. Jiva is Sanskrit for chord. The ancient Indians called it a chord.
@@timkoehlerecause English is the unholy child of the Germanic, Romance and Celtic languages. .😋🤪 There is a possibility that some aristocratic mathematicians during the Victorian era in the British empire and the USA made the change, less out of reason and more out of academic prestige, and posibly money from their aristocrat patrons(which was the norm at the time)
tan comes from tangent, whose value you get when you draw a line with that angle to the line that is tangent to the circle in the video, the y value is the value of tangent
@@egemen157ify Nice of you to be helpful, but I think it was a comment about how the video ends abruptly before all of the topics introduced have been covered.
Sinus is Latin, it means gulf and wave but it also means female breast. “Tangens” means “touching”. Trig can easily be made so much more interesting to teens...
@@thanhvinhnguyento7069 I have always found that the history of Sciences and Math, and the personalities involved, makes it more interesting. Other subjects, languages and history for example, tell a lot about the people involved.
Your teaching is so inspiring! It breaths in practical way of thinking! You remind us that math makes sense, and that there is no point in learning on heart!
Very interesting. Having been born in 1970, I remember at school having a book that contained tables for sin and cosine values. When we did geometry we had to use these tables. We were banned from using calculators for the first five years of doing maths.
actually there is a small addition to the sine theory . the reall word was "jaya" and it was invented by aryabhatta who was an indian mathematician . "jaya " meant "half chord " and was hence used in astronomy . also the jaya was then came to be known as "bosom " which is how the arabians called it but then the europeans mistook the word as chord and then they named it as "sinus" which is an latin word . then it was came to be known as sine by the english . i hope this is informative :) :)
You are wrong. Sine's etymology dates back from the ancient Indian word in Sanskrit which is jyā. Then in 10th century mathematics took off in the middle east and this term was adopted by the Islamic scholars which then has been translated from ancient Indian texts from Sanskrit to Arabic as jība. When mathetmatics took off in western Europe (around 1200s), the European scholars went to Madrid (which was islamic at that time) and copied texts from Arabic to Latin which then they made a CURIOUS mistake. When they came across the word jība, they couldn't find any word jība in the Arabic language and they thought that jība is a grammar mistake for the word jaib, which in Latin is 'sinus' (english - 'sin') and it means 'harbor'. Then for the cosine people gave it the name as the companion length of the sine thus cosine.
He's not wrong at all. The word 'sine' does indeed come from Latin. The fact the *concept* of sine is from another culture doesn't change the etymology of the word. I think you're concerned about history/culture rather than etymology. Either way, he's not wrong to say the word 'sine' comes from Latin because it does. I've studied Latin and Maths to a high level, and Eddie is correct.
Sine is an English translation of the word sinus which in Latin means 'harbor, port'. Why would anyone in the world would call sine a harbor? It dates back from a bad translation mistake. My source is very reliable because it comes from a professor James Tanton who has a Ph.D. in mathematics from Princeton University and who's also a scholar at the Mathematical Association of America and Eddie is wrong on this one. Greetings
What's his video title? Why are sine & cosine given their names? Right? Well, they were given their names because of a bad translation. That's the correct answer. End of story.
I don't get how you translate 'sinus' as 'harbor' when I've always known it to mean either 'wave' or 'curve'. I've since discovered it can also mean 'bosom'. So, in a sense, it's serendipitous that the mistake has resulted in a word whose meaning has a slight relevance to the subject matter (i.e. 'curve' isn't a million miles away from what a sine wave looks like). Also, harbor in Latin is 'portus' (hence the English 'port'). I've honestly never used 'sinus' to mean harbor in the 7 years of Latin I did in school. Anyway, I think all that matters is that Eddie's students are learning mathematics. He should have just skipped the (incorrect or ambiguous) history lesson on the word 'sine' because it adds nothing to the maths comprehension.
Sine has been derived Sinus. Aryabhatt described Ardha-jya in Sanskrit for the angle (which we call sine today). Ardha-jya > jya > jiba > jb > jaib > sinus > sine
@Prashant I can't tell if you are trolling or if you were lied to by Indian instructors who tried to pretend that everybody copied you.....when in reality your culture copied the hard work done in babylonia and greece and western europe. Meanwhile, in reality, since much mathematical work had been transmitted to the east before the dark ages and then rediscovered in Arabic forms of writing.....they needed a word in Latin that would properly describe the shape they had in mind. And there was already a latin word which means "fold" or "bay" or "bosom" ....namely the word "Sinus". So they applied that already existing word to the trigonometric shape of Sine that they were talking about in the mathematics.
I'm in 2nd year college studying for civil engineering and idk why we weren't taught this when i was in middle school, we just had to memorize the SOH CAH TOA without knowing what they meant and why they existed.
I get it now. I freaken get it now! 28 years old and no one in my life was ever able to explain it to me until now! Jeez... Thank you very much Mr. Woo
It is teacher's like Ed Woo that keeps Math alive and well in the world. We need to have much more teacher's like Ed who inspire and get people interested in this exceedingly important subject.
from wiki Etymologically, the word sine derives from the Sanskrit word for chord, jiva*(jya being its more popular synonym). This was transliterated in Arabic as jiba جيب, which however is meaningless in that language and abbreviated jb جب . Since Arabic is written without short vowels, "jb" was interpreted as the word jaib جيب, which means "bosom". When the Arabic texts were translated in the 12th century into Latin by Gerard of Cremona, he used the Latin equivalent for "bosom", sinus (which means "bosom" or "bay" or "fold").[12][13] Gerard was probably not the first scholar to use this translation; Robert of Chester appears to have preceded him and there is evidence of even earlier usage.[14] The English form sine was introduced in the 1590s.
What a great explanation. So sine takes its name from a sine curve. Cool. Just like the word 'car' takes its name from the vehicle with 4 wheels. It's a car so that's where the word car comes from. My God this was so helpful.
Sine means wavy thing....and cosine is the complement (90) of sine. It's 90 degrees rotation to the left and begins on the top instead of on the bottom of the curve.
From Wikipedia: "The word sine (Latin sinus) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, itself a transliteration of the Sanskrit word for half of a chord, jya-ardha. The word cosine derives from a contraction of the medieval Latin complementi sinus."
Here is the crazy thing. I learned all this in high school and stressed over exams on it. 20 years later I don’t remember a single thing about it. What a damn waste of time. Time is the only thing we have in life and I was robbed of it. The educational system needs major changes.
Better to use a point rotating on a circle to trace out the curves. This also shows why and when sine and cosine are positive or negative... and is the easiest way to use Pythagoras to derive the identity Sin^2(x) + cas^2(x) = 1 Tan is derived from sin/cos, and this is also seen in the rotating point explanation. Etc Judging by the comments, there's some pretty dull teaching going on
I always distinguish sinus and cosinus graph with this trick: sine means "without" in latin. Thus, I recall that it starts at 0. (Whereas cos start at 1)
I use the trick of thinking of the unit circle. If you take the point on the circle at angle theta from the x axis in the counter-clockwise direction, the coordinates are (cos theta, sin theta). You start at (1, 0), go around to (0, 1), then (-1, 0), and last (0, -1). And in this way of thinking, the tangent of the circle at that point gives us the tan and cotan values. The length going to the x axis is the tan, and the length going to the y axis is the cotan.
At tan 90 the tangent vanishes to become an infinity convergence as equivalent to sine90/cos 90 interference as point of tangent becomes an infinity at a distance of nonlinearity oscillate between +and -infinity.
Etymology: Sine (English) noun from Latin sinus, meaning cavity, ex. the nasal sinus or facial cavities (sinus in French , seno in Spanish/Portuguese ). Sine (Latin) adjective meaning concave, empty, without, ex. sine qua non: a condition "without which no" other things are possible (sans French, sin Spanish, sem Portuguese ). In math the term was originally referred to the concavity formed by a circular sector, i.e. the side b of a right triangle, defined as the base (side a) divided by the radius of the circular sector or hypotenuse (side c).
Cotrig(x) = trig(90 - x) works well for standard trig functions. Where we run into a problem, is with hyperbolic trig functions. cosh(x) has nothing to do with sinh(90 degrees - x) or sinh(pi/2 - x).
In Latin "sinus" means "pocket" (two small entities in our noses are named in the same way because of their shape). In Arabic, they only write consonants and "jb" meant "jeba" (pocket), but was also used for "jiba", which was the Arabic transcript of Sanskrit "jiva" (or "jiya hava" in full) which meant "semi bow" where "bow" was actually used for a chorde in a circle. So, first came a transcript from Sanskrit to Arabic with one sound changed (Arabic uses B, but has no V), then came "homographic" representation of 2 different words (jiba and jeba), then came the wrong translation to Latin. Why the translation was wrong ? Because the first translator to Latin knew very well the word "jeba" for "pocket", but did not know anything about "jiba", because at that time this was a neologism in Arabic. This is like a person in 1950s who knows that in English "computer" is a name of profession, and then he suddenly learns that a new machine is named that way.
When I think of tangent I think of the slope of a tangential line, or rise over run. If you look at the unit circle on the left, opposite over adjacent, or dy/dx. But where does it come from? Tangent means touch. For a unit circle, a right triangle formed by a base as a radius of the circle from its center and an angle will have the side opposite that angle touching the circle with a length equal to the tangent of that angle.
Same reason you and I have names!! 🤷🏻♂️ Just imagine calling sine 'THE FUNCTION WHICH HAS NO NAME' and calling cosine 'THE OTHER FUNCTION WHICH HAS NO NAME' 🤣
The question is not why they are given names in general, but why they are given those specific names of all other possible names. We could call them rise wave for sine and coast wave for cosine.
Yeah, which was a direct translation from the Sanskrit word Jiva, meaning sinus, that Indian mathematicians were using for the trigonometric function. The Sanskrit word had two meanings, and the other one made more obvious sense for it, but the translators translated it into sinus and it just stayed.
Ethimologically, sine comes from "sinus" (cavity in latin) because of some translation mistake done by roman scribes and the fact that arabic mathematicians shortened their words without a way to know for certain what they meant
My TB says "the idea of sine days back to Aryabhatta who called it jya or Ardha-jya that literally means half-chord". This is quite apparent in a unit circle.
well i guess that sine is a translation for jib in arabic that not accuratly translated jib جيب in arabic means the place or location of entering in trigeometry that means the ratio between the entere of the angle to its hypo
Meeeh... I enjoy most of those videos, but here what is said is just false! "Sin" comes from the latin "sinus" (curve, cavity) and was a translation from "jaib" (same meaning) which was was how Gerard de Cremone (XIIth century) had mistakenly read "jiba", an arabic transcription for the indian word "jiva" (string) like the string of a bow. Then in cosinus, cotangent, cosecant, "co" comes from the latin word "cum" (with") as in "coworker", "companion". NOT complementary!!!
All this is cool, but also completely wrong - cosine is indeed from sine, but sine is a mistranslation from ancient Arabic "half-chord" via Sanskrit into Latin (IIRC).
Yeah, it comes from the Sanskrit word Jiva that means life, but also sinus and a bowstring/half chord. While the last one was probably the reason Indian mathematicians used it to call the trigonometric function, the translators chose the wrong meaning and it just stuck
I am afraid it is wrong, because the word sinus exists before graphics representation in cartesian axes; even before the concept of function. This video's explanation has the most common mistake about the origin of Trigonometric Function names. The Arabic word Jaib was translated into Latim as Sinus. But the word that should have been translated was Jiba, which means something like a "bowstring". In Arabic is common use just consonants to wright a word. Both words (Jaib and Jiba) have the same consonants, but Jiba was as less common word, specially because it came from Sanskrit
@@kashis3357 not Arabic, Sanskrit. The Sanskrit word for sinus is Jiva, and Indian and Arabic mathematicians used it for sin and it was translated directly into Greek or Latin
@@tentathesane8032 but when they translated it from Sanskrit(jiva) to Arabic(jiba) they abbreviated the word as they do in Arabic to 'Jb' and when the Europeans found the texts all the confusion began.
@benzot It does derive from sinus. There is some kind of very strange nationalistic bigotry being taught in certain eastern schools where they feel the need to lie to maintain a false pride.
nice job man. YOu manage to even teach an old bear like me something new. i kinda thought it have something to do with nose as the bone in the nose is called sinus something (forgot it) and the curve kinda looks like looking onto that bone^^ and come on we nkwo Cosine is called sine cause he´s always flirting with sine^^
Apparently he does not know the Latin word ’sinus’, which means basically ’bay’, hence the relation to ’curved coastline’ or ’curve’ referring to the curved form of the sine function ...
Hiya....I have a mathematics problem which I've been trying to solve for quite some time now but haven't gone far. It goes like this. A deer stands at the origin of the coordinate system and a tiger is on the positive y axis at a distance d from the deer. At time t=0, the deer starts with a velocity u along the x axis and also, the tiger starts with a velocity v with the velocity vector being directed to the deer at every instant. What is the equation of the path traced by the tiger in terms of x,y,u,v and d? And at what time would the tiger intercept the deer given that v>u? I suppose the curve would resemble a logarithmic spiral but I'm not so sure. I really hope you could chalk out the solution and come up with an illustrative video for it
I'm a fan of sin, sec and tan as the basic functions and 1/sin, sec, tan as cos versions. Its just more consistent to have cos mean one divided by that trig function
