Cosine: complement of sine. Thank you.

Wait! Come back! What is TanX?! Wow, what a cliffhanger!

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.

*Casually draws a pretty good sinusoid*

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!

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...

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!

I wish I had a teacher like u . U just inspire

The way of approach is very fundamental and original; Clarity of thought and enthusiastic to Teach with complete didactics! Thanks a lot !

Extremely articulate voice! Very easy to listen to. Great teacher!

I truly respect your teaching attitude. I wish I can teach as good as you teach.

That circle is so circle 👀

Great videos! Lucky students that have you as their teacher 💯

Sine: Hi Cosine! How ya doin? Cosine: Oh Hi Sine, Nice Haircut!

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.

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.

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 :) :)

SOH CAH TOA - remember that from high school 40 years ago. Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse etc. Useful acronym.

"I talk with a funny accent." "No, you listen funny!"

Watch Video : अब गणित के बिहारी मास्टर साहब भी वायरल... kzfaq.info/get/bejne/nrCDgpB_zZq2noU.html

That is so interesting, those are little terms and explanations that help a lot along the way

oh my god, so many pieces are lining up now.. hope you got many cos's for this!

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

doing an amazing job thanks sir

Just realized Woo's videos are perfect on new iPhones when you enlarge it

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.

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.

2:13 "comple(or i)ment as in hey nice haircut" i love you eddie!

2:14 compliment as in "I like your cut, G"

Best teacher I've ever seen being wasted on disrespectful students that don't appreciate the knowledge they're being given.

I know I'm high-on-pothenous

Hello sir your trigonometry videos gives me a lot of clues 👍👍

a really great teacher 😍😍👏👏👏👌👌👍👍

Never thought I’d be watching a math video for fun XD

Everyone else: "Oh yes. Math stuffs." Me: "lol. secx."

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!

Leaving me hanging on tangent

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)

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

Eddie I love you are the man.

Why did the video end abruptly??? oh man, the flow was good and nice.

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.

So a sine curve is "curved curve"?

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)

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 level are these lessons? great teacher!

Asslam o alikum. Thank you for video. I enjoyed it. Have a good day.

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^^

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

Cant believe I am watching this out of boredom

2:03 he came back just to say that joke 🙂

i can smell the markers he's using

Damn cliff hangers

Wow I just learned something, thanks man.

Beautiful! To think that I studied Mathematics for five years and I just got to know this😂

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

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

I was not expecting him to be Australian

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.

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.

Amazing ... nicely Explain .

Tangent comes from word Tangible, something that Touches.

Lol, yesterday I thought abour Sine and Cosine names and today I found this :v

excellent!

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

you are amazing sir

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.

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.

Wow! You're very good!

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."

How did I get through school trig without knowing cos is the complement of sin ?! Thank you Eddie !

Great teaching. One small suggestion, please write a little larger as it is not visible in our mobile screen.

What camera did you use to record this?

I'im in engineering and I didn't know that the "CO" in cosign standed for compliment. Crazy

IIRC sine comes from the Latin for fold (sinus) as in the sinuses we have in our heads.

I wish I had a teacher like this

great explaining

i wish you were my math teacher.. *tears*

Aw man, I really wanted to see TAN!!!

There are exercises for homework on the board, what textbooks exercises are the homework from? 🏆

It’s nice to know this. It’s machine shop math otherwise. Oh, and Eddie Woo wears a nice tie.

KZfaq in 2019 suggest this on my maths exam. Google is spying on us.

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

Hi Sir, Can you make Little Longer Videos ...

I have a degree in engineering, and minor in math. I just learned that the co in cosine is the abbreviation of compliment.

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

thank you, your student from Algeria

I think eddio whoo sir is the best way for teaching

Thank you.

"Sine" came before the term "sinusoidal"

RIP the joke at 1:59

is there another part to this video?

i wish i had been your student

WHERE DOES TANGENT COME FROMNZNANSNSBJS

Cosine= sin of the complementary angle

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.

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Good work Thanks...

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).