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

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

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11 жыл бұрын

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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Пікірлер: 306

@arjunsogarwal6099 9 жыл бұрын

RAIDUSESESESESESESESESESESES, wow what a word

@stevedl3150 9 жыл бұрын

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 жыл бұрын

Same!

@kalaiselvanrajasekaran8352 4 жыл бұрын

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

@PenandPaperScience 2 жыл бұрын

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 2 ай бұрын

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 2 ай бұрын

⁠

@raithigovender195 8 жыл бұрын

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

@slowloris2996 6 жыл бұрын

I’m in the exact same situation.

@lcveiris 5 жыл бұрын

Ikr😂

@ruguoserliegise2716 5 жыл бұрын

same

@pboytrif1 5 жыл бұрын

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

@The_Pariah 6 жыл бұрын

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).

@saifullahrahman 7 жыл бұрын

98% comments = radiuseseseses

@olivermiller8943 3 жыл бұрын

More like 60

@sirwaffle4006 7 жыл бұрын

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

@Jam-nh5wb 6 жыл бұрын

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

@Faith._.M 3 жыл бұрын

I was abt to say that

@sarahkenza3883 2 жыл бұрын

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

@Ferdinaand 2 жыл бұрын

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

@BobBob-uv9fq 2 жыл бұрын

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

@furqaanilahi8078 Жыл бұрын

@@sarahkenza3883 radii?

@SomethinRofl 7 жыл бұрын

thanks for making these videos man you're better at teaching this than my professor.

@sunnylefabulous6736 5 жыл бұрын

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

@tejasbinu5025 7 жыл бұрын

What are RADIUESESESESE?

@fantasaicproductions7612 7 жыл бұрын

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 жыл бұрын

Radii

@ellipszia 9 жыл бұрын

radiuseseseseseseseseses

@user-ip9xi4ty9p 10 жыл бұрын

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

@alimuhammed9173 8 жыл бұрын

RADIUESESESESE

@feelgood_cinematic1919 7 жыл бұрын

i thought i was the only one!!! lol

@user-rf4vc7mt4d 7 жыл бұрын

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 жыл бұрын

2:23 To sum DEGREE! Lol!

@ultrainstinctx6135 6 жыл бұрын

Ali Muhammed I

@roblox_pandagameryt8612 6 жыл бұрын

Sub to me and i sub to u~

@timothycarney2951 8 жыл бұрын

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

@KaushalKumar-vq8kb 5 жыл бұрын

Absolutely!

@CreationTribe 4 жыл бұрын

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.

@XtremeKillah101 10 жыл бұрын

radiuseseseseseses

@Cesariono 11 жыл бұрын

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.

@herwin4946 9 жыл бұрын

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

@benzonex 9 жыл бұрын

radiuseseses...

@amrsaleh1342 7 жыл бұрын

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

@ruguoserliegise2716 5 жыл бұрын

Had me rolling

@mischief9499 3 жыл бұрын

hahahah

@poochihuku3701 2 жыл бұрын

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

@sourabhuwusingh 7 жыл бұрын

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

@tracker1312 10 жыл бұрын

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

@jar0bi 11 жыл бұрын

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

@angmori172 7 жыл бұрын

Awesome, thanks! Finally got radians!

@svengunther7653 3 жыл бұрын

Clear, easy, with background. Thanks :)

@laxmandesai573 7 жыл бұрын

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

@bluewolf8085 4 жыл бұрын

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

@namraaah271 2 жыл бұрын

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...

@yeo1913 2 жыл бұрын

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

@johnydove4402 6 жыл бұрын

this is great GOD BLESS

@meightyalliu5408 9 жыл бұрын

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

@Propapanda0213 4 жыл бұрын

Nice video! Straightforward and easy to understand

@TechnicalGarg 3 жыл бұрын

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

@MrWarmWeather 11 жыл бұрын

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

@saflanix 4 жыл бұрын

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

@MerlinZuni 2 жыл бұрын

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

@saintisraelmedi7686 5 жыл бұрын

This video very helpful. 👍🏻

@ThomasGardner12321 11 жыл бұрын

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

@DopeBoysClan 10 жыл бұрын

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 2 жыл бұрын

where u from?how u doin now

@valejandro1771 Жыл бұрын

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

@gottfriedwiggles3230 10 жыл бұрын

Very nice explanation! Thank you

@angelinoz5159 5 жыл бұрын

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

@yaronzaret9549 10 жыл бұрын

Great video Sal, keep them coming!

@frannylissetrodriguez4066 Ай бұрын

Thank you so MUCH !

@aminmoafi5148 Жыл бұрын

Thank you!

@samcaddy8544 6 жыл бұрын

Explained brilliantly

@nitinchawla8854 4 жыл бұрын

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

@charlieromeo7663 Жыл бұрын

Thanks for the explanation.

@teenatkhan1695 6 жыл бұрын

Thank Gosh this exists

@drtoro 11 жыл бұрын

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

@lucy2459 3 жыл бұрын

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

@chithienle9790 Жыл бұрын

your lectures are very easy to understan

@Ash-ec4ip 2 жыл бұрын

I respect u a lot.... Thank u❤️

@pranjalpandey7020 6 жыл бұрын

Great video really informative.Great Easter egg

@HuckleberryHim 11 жыл бұрын

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

@poweruser64 3 жыл бұрын

thanks for all the -radiuseses- radii

@theflash9735 5 жыл бұрын

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

@waterwaterwa 7 жыл бұрын

Thank you!!!!!!!!!!!!!

@noobtrader454 2 жыл бұрын

how neatly u write on this is mind blown

@EmpowerQuest1 8 ай бұрын

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

@PenandPaperScience 2 жыл бұрын

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

@vsatrawada 2 ай бұрын

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

@harrisonriley16 5 жыл бұрын

Great video

@chissstardestroyer 4 жыл бұрын

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.

@paras2901 11 жыл бұрын

ur awesome!!!

@Theiftanlazx 11 жыл бұрын

yay i understand it much better

@Cryztaliser 11 жыл бұрын

excellent video

@callumsimpson1278 8 жыл бұрын

What program do they use for the drawing?

@ramillax5478 3 жыл бұрын

THANKS

@nabarungathiri6835 6 жыл бұрын

u r great bro

@mmohan692 6 жыл бұрын

Wow nice video keep it up .

@hazleenazlee506 3 жыл бұрын

Thanks

@6xsnspsychotik963 5 жыл бұрын

god bless you guys

@yplayergames7934 5 ай бұрын

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

@271skippy 6 жыл бұрын

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

@fromexoplanet21 2 жыл бұрын

Amazing👏👌

@calcul8er205 9 жыл бұрын

Radii!!

@TheAmazingFocus 11 жыл бұрын

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!

@JowieSterken 11 жыл бұрын

Thanx mate, this is really helpful! =D

@f4nte 11 жыл бұрын

Nice.

@rishab5501 3 жыл бұрын

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

@mmohan692 6 жыл бұрын

We want more videos like tz

@areeb9781 8 жыл бұрын

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 жыл бұрын

So what is radian cuz i dont understand

@Sadin15 10 жыл бұрын

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

@primaryaccount1410 3 жыл бұрын

7:34 degrees-es-es

@krishshah3974 4 жыл бұрын

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

@exceptionalchris 6 жыл бұрын

"This isnt some voodoo" classic.

@teenatkhan1695 6 жыл бұрын

Chris Btw what is it😂

@bilal2k1 11 жыл бұрын

Genius

@nikhilparaggarapinhilik4733 5 жыл бұрын

He is good in explaining really Much better than me😫😂

@Achw3l 11 жыл бұрын

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

@AndewMole 5 жыл бұрын

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

@Sitara04 11 жыл бұрын

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

@Ze0nite 7 жыл бұрын

Spent my whole life thinking this was in fact some voodoo stuff and now I finally understand

@lemonrev 11 жыл бұрын

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 жыл бұрын

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.

@BareClause 11 жыл бұрын

I thought u did this alreadyyy

@SoundPeaks 4 жыл бұрын

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

@rashedalam3450 3 жыл бұрын

That's a better circle than i've ever drawn

@chissstardestroyer 4 жыл бұрын

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.