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.
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.
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.
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 :) :)
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.
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.
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.
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.
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'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.
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).
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.
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.
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."
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
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.
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.
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.
I disagree! 1) Sine means curve, agreed, however, the curve in question is not the value of sine plotted against the angle. 2) The definition of sine does not come from triangles. It is a circular function. If you mark the angle on a unit circle and draw in the radius at that angle, the length of the arc from the x-axis to the end of the radius effectively the angle. Its length is numerically equal to the angle in radians. The height of that line above the x-axis is the sine. It is the "curve height". The cosine, that accompanies (co) the sine is the distance between the end of the radius and the y-axis. A tangent can be made to touch the circle where the radius ends. That gives tan and cot lengths as distances to the x and y axes respectively. The secant cuts (think secateurs) the circle etc.
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
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^^
@@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.
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
@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.
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.
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
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
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
@@rgudduu Jyaa (ज्या) means bowstring, like from a bow and arrow. When you draw out how sine is represented on the unit circle, and draw it with the symmetric part on the negative side of the y-axis, the arc along the circle, and the altitude line of the triangle together, look like a bow and arrow. Kojyaa (कोज्या) was the Sanskrit name for cosine. Interesting how the prefix still sounds the same.
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.
Cosine: complement of sine.
Thank you.
Similarly Cot= compliment of Tan!!!
Nerd humour? Nerd humour..
@@Shadow77999 Not humor at all - it's the construction of the word.
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.
👏👏👏👏👍
okay, but why is it, that in English they called it sine and did not stick with sinus like in other european languages ?
Chords, when played, produce sine waves. Crazy
@@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)
@@timkoehler because European only knows how to FK up things.
Wait! Come back! What is TanX?! Wow, what a cliffhanger!
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
tangent from to touch, secant from to cut,
I cant sleep now!
@@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.
Tan = Tangent
A line or plane which touches a given curve or solid at a single point.
Watch Video : अब गणित के बिहारी मास्टर साहब भी वायरल... ruclips.net/video/hJSO-Nh4RnQ/видео.html
Mate, your teaching is absolutely outstanding! The approach is the way it is supposed to be, really! You are a legend! Thank you so much!
I wish I had a teacher like u . U just inspire
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...
Yeah sine and breast are the same exact word in Spanish
So... touch and breast together. Sounds good. I wondered why I liked math.
Let's leave out the cutting part, however.
Ben Heideveld if i knew that maths would’ve appealed to me
This should be mainstream in textbooks
@@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.
couldn't you just approximate with Taylor series? would have taken longer for arcsin/arccos/arctan tho
yes sure DuDono, let's teach high schoolers taylor series while they can't even do basic trig yet
@@eddielienert8171 highschool any% speedrun tricks brah
Did someone explain to you what those values were?
@@eduardokuri1983 those values were the ratios between the sides of a triangle.
Extremely articulate voice! Very easy to listen to. Great teacher!
The way of approach is very fundamental and original;
Clarity of thought and enthusiastic to Teach with complete didactics!
Thanks a lot !
*Casually draws a pretty good sinusoid*
Petru Stefanescu Hahahahahahahahahahahahahaha
its not hard to do so
The slope is too steep
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.
SOH CAH TOA - remember that from high school 40 years ago. Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse etc. Useful acronym.
I too remember Soh Cah Toa from 1980s while I was in school. I am back to relearning maths for programming.
Wow y’all are old, I learned that last year.
This is the shit that keeps me going through the trig portions of papers.
Incidentally, it's also a powerful thum used by dragonborn.
FUS ROH DAH
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.
I don't think anyone really cares about the history of the word.
It's the definition and use that's more important.
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.
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 :) :)
A latin word* no offense
@Zeus Pater he corrected his 'an latin word' to a latin word*
Cosine was called ardha-jya.
In Bulgaria its still sinus
Yes. This is what is also documented in the interesting book "Trigonometric Pearls". Proud to belong to the country of great mathematician Aryabhatta.
I truly respect your teaching attitude. I wish I can teach as good as you teach.
Sine: Hi Cosine! How ya doin?
Cosine: Oh Hi Sine, Nice Haircut!
Not bad
I'm stupid I don't get it
Oh its a joke from the video, I thought it had something to do with their properties lol
more like
cosine: "I like your cut, G"
*slaps the back of the head of sine*
That circle is so circle 👀
Your eyes just need adjusting
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.
Great videos! Lucky students that have you as their teacher 💯
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
That's quite a far fetched etymological derivation.
@@radun.stingaciu711 that's how it is.
@@Prashantchauhansmail How can you arrive from jaib to sinus ? :))
Nonsense.
@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.
2:13
"comple(or i)ment as in hey nice haircut"
i love you eddie!
"I talk with a funny accent." "No, you listen funny!"
Lol
Best teacher I've ever seen being wasted on disrespectful students that don't appreciate the knowledge they're being given.
Seriously, what the hell is up with all the talking? Why is he not telling them to shut up and listen?
2:14 compliment as in
"I like your cut, G"
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.
I know I'm high-on-pothenous
Key's visible disappointment
yoni2356 I said that
That is so interesting, those are little terms and explanations that help a lot along the way
They are actually wrong 😏
oh my god, so many pieces are lining up now.. hope you got many cos's for this!
Asslam o alikum. Thank you for video. I enjoyed it. Have a good day.
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.
JNCressey That’s literally the origin of the sine and cosine. That’s not a “trick” that’s the definition lmao.
Great teaching. One small suggestion, please write a little larger as it is not visible in our mobile screen.
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.
Love your videos!
Sir, the graphical illustration is indeed insightful. I could visualise that at tan 90, the line can no longer become a tangent to the circle.
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'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 think eddio whoo sir is the best way for teaching
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).
it's the same for tanx and cotx; secx and cscx.
cotx(co-tangent x) = tan(90°-x)
cscx(co-secant x) = sec(90°-x)
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).
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.
He is teaching this from before they learnt how sine relates in terms of curves and only when they were learning about triangles.
IIRC sine comes from the Latin for fold (sinus) as in the sinuses we have in our heads.
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.
2:03 he came back just to say that joke 🙂
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."
Cant believe I am watching this out of boredom
Hello sir your trigonometry videos gives me a lot of clues 👍👍
If I had this guy as my Alevel maths teacher I wouldn't care how hard it was I'd have gotten an A instead of dropping the subject
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
Really? Until now? You just weren't listening in class.
AnteConfig - Trust me man, I’m the same way. I learn something new every time. That’s why I watch this stuff!
Never thought I’d be watching a math video for fun XD
Same
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.
i can smell the markers he's using
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.
RIP the joke at 1:59
Just realized Woo's videos are perfect on new iPhones when you enlarge it
Everyone else: "Oh yes. Math stuffs."
Me: "lol. secx."
Excellent math teacher. And 9 yrs ago.
Beautiful!
To think that I studied Mathematics for five years and I just got to know this😂
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.
Amazing ... nicely Explain .
Sir the vedio quality is not good. Im missing out. Also thre is noise. Its really intresting but I can't get enough
Tangent comes from word Tangible, something that Touches.
I disagree!
1) Sine means curve, agreed, however, the curve in question is not the value of sine plotted against the angle.
2) The definition of sine does not come from triangles. It is a circular function.
If you mark the angle on a unit circle and draw in the radius at that angle, the length of the arc from the x-axis to the end of the radius effectively the angle. Its length is numerically equal to the angle in radians. The height of that line above the x-axis is the sine. It is the "curve height". The cosine, that accompanies (co) the sine is the distance between the end of the radius and the y-axis.
A tangent can be made to touch the circle where the radius ends. That gives tan and cot lengths as distances to the x and y axes respectively. The secant cuts (think secateurs) the circle etc.
It’s nice to know this. It’s machine shop math otherwise. Oh, and Eddie Woo wears a nice tie.
Leaving me hanging on tangent
So a sine curve is "curved curve"?
Hi Sir, Can you make Little Longer Videos ...
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
what level are these lessons? great teacher!
I have a degree in engineering, and minor in math. I just learned that the co in cosine is the abbreviation of compliment.
Wow I just learned something, thanks man.
1:48 I love the Australian accent ... "I know some of you know what the cooeeuuaarrrrr in cosine means."
RUclips in 2019 suggest this on my maths exam. Google is spying on us.
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^^
doing an amazing job
thanks sir
"Sine" came before the term "sinusoidal"
lol
Sine doesn't mean anything, there was an error in translation from Arabic to Latin back then. The real term was "jiva".
@@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 i knew that
@@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.
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
Please, do you mind explaning the sec. Help!
@@elyseepasteur6163 Sec's education?
How did I get through school trig without knowing cos is the complement of sin ?! Thank you Eddie !
I'im in engineering and I didn't know that the "CO" in cosign standed for compliment. Crazy
With all due respect, I think that sin derives from latin sinus (gulf like a gulf in the sea) from the shape of the function
@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.
Sinus also means female breast. “Tangens” means “touching”. Trig can easily be made so much more interesting to teens...
i wish you were my math teacher.. *tears*
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.
a really great teacher 😍😍👏👏👏👌👌👍👍
Some People Have Curly Brown Hair Through Proper Brushing
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
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
Wow! You're very good!
I was not expecting him to be Australian
Thanks but will it help me in my daily life endeavours?
Depends on what your daily life endeavours are..
If your daily life endeavours are being a maths teacher, then yes
Good work Thanks...
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
Why people like are not available in Bangladesh ??
why man why!!
BTW one of the learner of you...
love from Bangladesh..
Jesus is available to all, he loves you so much and he saves, praise Jesus!!!
Sin & Cosine are just English translation of sanskrit word "ज्या" & "कोज्या"
An English translation of a Latin mistranslation of an Arabic translation of the Sanskrit words***
jyaa means?
@@rgudduu Jyaa (ज्या) means bowstring, like from a bow and arrow. When you draw out how sine is represented on the unit circle, and draw it with the symmetric part on the negative side of the y-axis, the arc along the circle, and the altitude line of the triangle together, look like a bow and arrow.
Kojyaa (कोज्या) was the Sanskrit name for cosine. Interesting how the prefix still sounds the same.
@@carultch , thanks. Wikipedia has a good article. Pretty clear now
I wish I had a teacher like this
thank you, your student from Algeria
sine you are so fine ! - cos complimenting sine
i wish i had been your student
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.
Cosine= sin of the complementary angle
SOH
CAH
TOA
That’s how I remember it!