Introduction to radians | Unit circle definition of trig functions | Trigonometry | Khan Academy

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Understanding the definition and motivation for radians and the relationship between radians and degrees
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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
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Опубликовано:

12 сен 2024

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Комментарии : 307

@stevedl3150 9 лет назад

I think radians should be taught from Primary School, rather than degrees. Radians are obviously intrinsic to the circle, whereas degrees are not. Alas, I still find it difficult to think in terms of radians.

@lakshmipraba220 4 года назад

Same!

@kalaiselvanrajasekaran8352 4 года назад

The concept is so easy yet it is still being a great task to understand the radians.

@PenandPaperScience 2 года назад

This is the core argument I make in my video covering Radians! It's a measure that incorporates only intrinsic properties of the circle!

@isavenewspapers8890 5 месяцев назад

Have you heard of the number tau? It's represented with the Greek letter tau, which looks like this: τ τ is the ratio of a circle's circumference to its radius. This makes it 2 times π, or about 6.28. Using τ, one full rotation is τ radians. One-half of a full rotation is τ/2 radians. One-third of a full rotation is τ/3 radians. Whatever fraction of a full rotation you do, its measurement in radians is that same fraction of τ. If it helps, you can think of radians in terms of τ.

@vsatrawada 4 месяца назад

⁠

@arjunsogarwal6099 9 лет назад

RAIDUSESESESESESESESESESESES, wow what a word

@The_Pariah 6 лет назад

That was a very good way of explaining this. I've been out of high school long enough to have forgotten a lot of trig. Now that I'm doing programming, this stuff is needed and these refresher videos really help (especially when they're well done like this one).

@pboytrif1 6 лет назад

2:46 The moment I decided I liked the video... "I'm gonna attempt to draw a circle here....... *wobbly circle*...... not baaaaaad"

@raithigovender195 8 лет назад

aw. I was so excited to comment RAAAADIUSSSES then I saw the comments section and was like...yeah nvm

@slowloris2996 6 лет назад

I’m in the exact same situation.

@lcveiris 6 лет назад

Ikr😂

@ruguoserliegise2716 5 лет назад

same

@Jam-nh5wb 6 лет назад

U saying radiuseseseseseseseses drove me insane, I literally couldn’t pay attention to the video 😂

@Faith._.M 3 года назад

I was abt to say that

@sarahkenza3883 3 года назад

he literally wrote down the plural, it radians... IT'S RADIANS

@Ferdinaand 2 года назад

same and i was playing at 1.25 so it made it worse

@BobBob-uv9fq 2 года назад

Lol you’re correct ,but he’s explaining it well

@furqaanilahi8078 Год назад

@@sarahkenza3883 radii?

@tejasbinu5025 8 лет назад

What are RADIUESESESESE?

@fantasaicproductions7612 7 лет назад

listen to that part at video speed x2 and you'll find out what it means... its means hes part snake or should i say slytherin....

@LittleWhole 4 года назад

Radii

@saifullahrahman 7 лет назад

98% comments = radiuseseseses

@olivermiller8943 3 года назад

More like 60

@sirwaffle4006 7 лет назад

i never appreciate your circle drawing skills until i have to draw a circle myself

@alimuhammed9173 8 лет назад

RADIUESESESESE

@feelgood_cinematic1919 7 лет назад

i thought i was the only one!!! lol

@user-rf4vc7mt4d 7 лет назад

micheal jordan It's been a week, but... You don't have to watch it to understand, but it would definitely help

@Neel-ff4mn 7 лет назад

2:23 To sum DEGREE! Lol!

@ultrainstinctx6135 6 лет назад

Ali Muhammed I

@roblox_pandagameryt8612 6 лет назад

Sub to me and i sub to u~

@ellipszia 10 лет назад

radiuseseseseseseseseses

@sunnylefabulous6736 5 лет назад

i knew from the moment our teacher started explaining this in class there'd be our lord and saviour, Sal Khan, who would explain this much, much better

@user-ip9xi4ty9p 10 лет назад

very helpful! cracked me up every time he said radiuseseseses =)

@timothycarney2951 8 лет назад

Radiuseseses?!? Radii! Radii! Radieye! RADI👁!

@KaushalKumar-vq8kb 5 лет назад

Absolutely!

@CreationTribe 5 лет назад

Yup - which is weird since I've heard him say "radii" multiple times in other videos. Is he just being funny? I don't get it.

@Cesariono 11 лет назад

The definition of the radian suddenly makes so much sense. I used radians in my calculations but I never really understood why they even bothered. Now my mind has been blown.

@callumsimpson1278 8 лет назад

What program do they use for the drawing?

@XtremeKillah101 10 лет назад

radiuseseseseseses

@sourabhuwusingh 7 лет назад

A great explanation! Khan Academy is a great place to learn.

@amrsaleh1342 7 лет назад

"just to show u this isn't voodo" 😂😂😂😂

@ruguoserliegise2716 5 лет назад

Had me rolling

@mischief9499 3 года назад

hahahah

@poochihuku3701 2 года назад

The kinds of things that make me a stickler to learn from these videos

@benzonex 9 лет назад

radiuseseses...

@DopeBoysClan 10 лет назад

I just had a "I UNDERSTAND" moment. I would have not resorted to these videos, along with the rest of the people here had teachers derived the meaning to mathematical concepts, instead of saying "here it is, use it". The amount of stupidity evident in today's education is absolutely mind-blowing, unfathomable. I can only but barley understand the teachers motives for not deriving and explaining where particular principles come from, that of which is they don't care, they want the paychecks and to go home. Fuck society man.

@namraaah271 3 года назад

where u from?how u doin now

@valejandro1771 Год назад

@@namraaah271 HOPE he's ok. It's been a lot of time :0

@jar0bi 11 лет назад

I'm taking a trigonometry class right now and this explains so much thank you

@saflanix 4 года назад

My teacher recorded a few videos during quarantine and I never watched them cuz these are so much better☺️

@yeo1913 2 года назад

You haven't lost yet and you have more to achieve

@rishab5501 4 года назад

Nobody: Sal: I think it's intuitive, cause in an intuitive response I'll intuitively intuitive. Me: A video on what intuitive means?

@herwin4946 10 лет назад

Thank you! I was so confused with the radian, but now I understand much more now.

@TechnicalGarg 3 года назад

That was really nice. Many teachers just tell to remember this without informing about proper concept. But u r gr8.. Thank you a lot❤

@meightyalliu5408 9 лет назад

this video is clear! save my life from digging into textbook:P

@bluewolf8085 4 года назад

I learned alot today, Radiuseseseses are very important...😂😂😂😂

@namraaah271 3 года назад

if u still don't get it don't worry just read the textbook or whatever and keep trying to understand and then watch the video...i swear you'll get it.I have been spending the whole day trying to understand this and now i finally get it.time taken-approx 6 hours.dude...

@areeb9781 8 лет назад

amazingly explained. just wondering what radian is ? read some books but didn't get the satisfied answer and you really solved my problem. thanks for sharing :)

@abdosalah4337 5 лет назад

So what is radian cuz i dont understand

@EmpowerQuest1 10 месяцев назад

❤I know, the video was uploaded ten years ago but it had something that made me keep watching it till the end. ❤

@johnydove4402 6 лет назад

this is great GOD BLESS

@tracker1312 10 лет назад

This was explained amazingly well. I don't think any of my teachers ever explained this, neither in grade school or college.

@PenandPaperScience 2 года назад

I wanted to plug my own video attempt where I explain this concept, but I have nothing to add. Great video! :D

@minameehan617 2 дня назад

Thank you so much your video made so much more sense than my teacher 🙏

@HuckleberryHim 11 лет назад

I got ~57.2957795131 degrees per radian using a calculator and pi as far as it would go (3.141592653589793).

@laxmandesai573 7 лет назад

I love the way u teach!! wish all the teachers were just like u

@ThomasGardner12321 11 лет назад

Thanks this is going to help me with my Core 2 A-level exams alot! :)

@svengunther7653 4 года назад

Clear, easy, with background. Thanks :)

@angelinoz5159 6 лет назад

Fantastic explanation. I study as well as teach physics. I couldn't have done it better myself. Congratulations.

@Achw3l 11 лет назад

Very well explained!! Logical and easy to follow :)

@MrWarmWeather 11 лет назад

great video. best I've seen on the subject so far. thanks!

@lemonrev 11 лет назад

radians something i dont think everyone is associated with the term and i like it how your thinking out side the box with the alien thing, with looking at circles, Do you think this actually should be the model for looking at degreese in general in stead of useing our term the degreese of ?

@chissstardestroyer 4 года назад

On the topic of using Pi in division; that in and of itself is usually why people round it to 3.14, to the hundredths place, otherwise it takes literally forever, or almost, to reach the termination point/end point, of the formula. As you pointed out, Mr. Khan, a very interesting way to convert them; actually you have a better time dividing by zero than dividing by pi to the final digit.

@Medi-Nor 6 лет назад

This video very helpful. 👍🏻

@Propapanda0213 4 года назад

Nice video! Straightforward and easy to understand

@nitinchawla8854 4 года назад

You made a good video...👍 Made me understand the radian concept.

@vsatrawada 4 месяца назад

I was so focused in much in math that I forgot you teach like everything in the world.

@drtoro 11 лет назад

how successfull are you to make things easier to understand..

@MerlinZuni 2 года назад

Thanks for this explanation. I'm taking a coding class and this was very helpful.

@lucy2459 3 года назад

thank you so much for making this so clear and being so friendly :) this really helped me. my maths teacher just gets angry when i don't understand things so stuff like this is a godsend :D

@TheAmazingFocus 11 лет назад

He already did a video on Tau versus Pi. He probably doesn't want to introduce too much at once when introducing the concept of radians. Though an aside about it in a future angular measure would be nice!

@krishshah3974 4 года назад

Having motivation behind ideas (rather than just memorizing them) makes Khan Academy amazing!

@GuruprakashAcademy 11 лет назад

hey sal what microphone u are using. I am also making videos. Please let me know. Thans in advance

@SoundPeaks 4 года назад

thanks, what tools allows you to make video like that? How do you draw and move mouse so precisely?

@Sadin15 11 лет назад

It is more commonly known as Arc Length. It is represented with an S and can be found using S = theta * radius

@justTryin 4 года назад

Why not just figure the angles based on the diameter so only 1 ×pi per circle

@noobtrader454 3 года назад

how neatly u write on this is mind blown

@RaharijaoDavid 8 лет назад

Just wanted to ask , why did you remove the r from "2(pie)×r"? , if you could or anybody could answer me , I'd be grateful

@atanaspetkov9298 8 лет назад

because r=1 and 2(pi)x1=2(pi)

@RaharijaoDavid 8 лет назад

ok thx

@frannylissetrodriguez4066 3 месяца назад

Thank you so MUCH !

@angmori172 7 лет назад

Awesome, thanks! Finally got radians!

@exceptionalchris 6 лет назад

"This isnt some voodoo" classic.

@teenatkhan1695 6 лет назад

Chris Btw what is it😂

@Sitara04 11 лет назад

do you have a video where you explain "complex" roots?

@chithienle9790 2 года назад

your lectures are very easy to understan

@teenatkhan1695 6 лет назад

Thank Gosh this exists

@yaronzaret9549 10 лет назад

Great video Sal, keep them coming!

@AndewMole 5 лет назад

On average he said "ses" 3.333 times. 4:32, 5:09, 5:50, 6:22, 6:44, 6:46, 7:07, 7:13, 8:36 4, 1, 5, 4, 3, 3, 5, 2, 3

@gottfriedwiggles3230 10 лет назад

Very nice explanation! Thank you

@imyasharya 5 лет назад

Hey Mr Sal Khan, would you tell me how can we draw 1 radian on paper?

@samcaddy8544 6 лет назад

Explained brilliantly

@pranjalpandey7020 7 лет назад

Great video really informative.Great Easter egg

@charlieromeo7663 2 года назад

Thanks for the explanation.

@Kenneth_H_Olsen 8 лет назад

yeah. the interesting thing is that the formula for radians is 2* pi * r. Making it seem that one needs 2 pi then multiply with the radius. but actually it is not 2 of Pi, but 2 radiuses that make one diameter. Diameter * pi = 360 degrees. and r * pi = 180 degrees . the formula should be 2r* pi. If the radius is 0.5 units then one can wrap 6.28 radiuses around the circumference (or 2Pi), but 3.14 diameters around the circumference (or Pi, diameter being 2r or 2*0.5 = 1) . Just being picky but I think it is important . why would one need 2 rotations of pi, and a radius, when it is the double radius or diameter that is defining the circumference with pi ? would it be correct to say this : 1. Radius is the number of times a radius is wrapped around the circumference . 2. find the radian of 3 degrees. 180 / 3 = 60 Pi radian = 180 Pi radian / 60 = 180 / 60 0.05 rad = 3 degrees .

@tfalaschini 8 лет назад

The order of the factors doesn't affect the product ;)

@tfalaschini 8 лет назад

The order of the factors doesn't affect the product. ;)

@aminmoafi5148 Год назад

Thank you!

@yplayergames7934 7 месяцев назад

Even though it's a 11 years vídeo, this explained radians very well that I understand very clearly

@theflash9735 5 лет назад

THIS IS SOOOOO GOOD !.... AND IT'S 7 YEARS AGO !!!!

@vihaansinghhh3034 4 года назад

6:23 RADIUSESESESESESESESESESESESESESEES..".... till 1 min 😂😂😂🤣

@271skippy 6 лет назад

I swear, I could never have gotten anywhere in math were it not for Khan Academy and Teaching Textbooks

@primaryaccount1410 3 года назад

7:34 degrees-es-es

@Ash-ec4ip 2 года назад

I respect u a lot.... Thank u❤️

@footage6402 6 лет назад

I have a question if the unit circle is only 1 radius unit then why is 30 degrees or 60 or 90 written as square root 1/2. Squ2 / 2... etc over 2. Isn't a radian equal to arc length over radius ?? How is denominator 2 when the unit circle radius is always 1?

@lemon23 5 лет назад

7:34 degreeeseseses... man's got crazy xd

@abdosalah4337 5 лет назад

Hey dude can u just tell me what is the meaning of radians cuz i dont rly understand

@chissstardestroyer 4 года назад

If you divide by pi you'll be dividing forever, unless you abrieviate pi at some point, because pi is a non-terminating, non-repeating decimal, so it goes on and on forever. In fact, for many decades they've had computers just trying to calculate the termination of pi.

@poweruser64 3 года назад

thanks for all the -radiuseses- radii

@JowieSterken 11 лет назад

Thanx mate, this is really helpful! =D

@chissstardestroyer 4 года назад

But, Mr. Khan, a radian in theory could be frankly any size measurement compared to the circle that regards any angle that regards half or less of a straight angle, or even greater, as it only deals with the radius of said circle compared to the angle. Isn't that overall a rather poor quality measurement, considering the need for precision?

@chissstardestroyer 4 года назад

The Babylonians appear to have used a Base 12 numerical system, but 60 is equally easy to divide by the dozen as by the half-score, or by the full score.