Introduction to radians | Unit circle definition of trig functions | Trigonometry | Khan Academy
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- Опубліковано 15 вер 2024
- Understanding the definition and motivation for radians and the relationship between radians and degrees
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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.
Same!
The concept is so easy yet it is still being a great task to understand the radians.
This is the core argument I make in my video covering Radians! It's a measure that incorporates only intrinsic properties of the circle!
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.
RAIDUSESESESESESESESESESESES, wow what a word
2:46 The moment I decided I liked the video... "I'm gonna attempt to draw a circle here....... *wobbly circle*...... not baaaaaad"
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).
aw. I was so excited to comment RAAAADIUSSSES then I saw the comments section and was like...yeah nvm
I’m in the exact same situation.
Ikr😂
same
U saying radiuseseseseseseseses drove me insane, I literally couldn’t pay attention to the video 😂
I was abt to say that
he literally wrote down the plural, it radians... IT'S RADIANS
same and i was playing at 1.25 so it made it worse
Lol you’re correct ,but he’s explaining it well
@@sarahkenza3883 radii?
i never appreciate your circle drawing skills until i have to draw a circle myself
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
What are RADIUESESESESE?
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....
Radii
98% comments = radiuseseseses
More like 60
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.
very helpful! cracked me up every time he said radiuseseseses =)
RADIUESESESESE
i thought i was the only one!!! lol
micheal jordan It's been a week, but... You don't have to watch it to understand, but it would definitely help
2:23 To sum DEGREE! Lol!
Ali Muhammed I
Sub to me and i sub to u~
radiuseseseseseseseseses
Radiuseseses?!? Radii! Radii! Radieye! RADI👁!
Absolutely!
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.
A great explanation!
Khan Academy is a great place to learn.
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...
I'm taking a trigonometry class right now and this explains so much thank you
My teacher recorded a few videos during quarantine and I never watched them cuz these are so much better☺️
"just to show u this isn't voodo" 😂😂😂😂
Had me rolling
hahahah
The kinds of things that make me a stickler to learn from these videos
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.
where u from?how u doin now
@@namraaah271 HOPE he's ok. It's been a lot of time :0
this is great GOD BLESS
radiuseseseseseses
radiuseseses...
This was explained amazingly well. I don't think any of my teachers ever explained this, neither in grade school or college.
That was really nice. Many teachers just tell to remember this without informing about proper concept. But u r gr8.. Thank you a lot❤
You haven't lost yet and you have more to achieve
I wanted to plug my own video attempt where I explain this concept, but I have nothing to add. Great video! :D
❤I know, the video was uploaded ten years ago but it had something that made me keep watching it till the end. ❤
Clear, easy, with background. Thanks :)
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 :)
So what is radian cuz i dont understand
What program do they use for the drawing?
I learned alot today, Radiuseseseses are very important...😂😂😂😂
this video is clear!
save my life from digging into textbook:P
Thank you! I was so confused with the radian, but now I understand much more now.
Fantastic explanation. I study as well as teach physics. I couldn't have done it better myself. Congratulations.
I got ~57.2957795131 degrees per radian using a calculator and pi as far as it would go (3.141592653589793).
Thanks for this explanation. I'm taking a coding class and this was very helpful.
Thank you so much your video made so much more sense than my teacher 🙏
This video very helpful. 👍🏻
Thanks this is going to help me with my Core 2 A-level exams alot! :)
Nobody:
Sal: I think it's intuitive, cause in an intuitive response I'll intuitively intuitive.
Me: A video on what intuitive means?
I was so focused in much in math that I forgot you teach like everything in the world.
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
I love the way u teach!! wish all the teachers were just like u
You made a good video...👍 Made me understand the radian concept.
Having motivation behind ideas (rather than just memorizing them) makes Khan Academy amazing!
how successfull are you to make things easier to understand..
Nice video! Straightforward and easy to understand
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.
Awesome, thanks! Finally got radians!
your lectures are very easy to understan
how neatly u write on this is mind blown
I swear, I could never have gotten anywhere in math were it not for Khan Academy and Teaching Textbooks
great video. best I've seen on the subject so far. thanks!
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!
Thank Gosh this exists
Why not just figure the angles based on the diameter so only 1 ×pi per circle
Even though it's a 11 years vídeo, this explained radians very well that I understand very clearly
Very well explained!! Logical and easy to follow :)
Thank you so MUCH !
Thanks for the explanation.
It is more commonly known as Arc Length. It is represented with an S and can be found using S = theta * radius
Thank you!
Great video really informative.Great Easter egg
Explained brilliantly
THIS IS SOOOOO GOOD !.... AND IT'S 7 YEARS AGO !!!!
Very nice explanation! Thank you
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 ?
Great video Sal, keep them coming!
He is good in explaining really
Much better than me😫😂
I respect u a lot.... Thank u❤️
thanks for all the -radiuseses- radii
"This isnt some voodoo" classic.
Chris
Btw what is it😂
7:34 degrees-es-es
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
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.
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.
Radii!!
Hey Mr Sal Khan, would you tell me how can we draw 1 radian on paper?
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 .
The order of the factors doesn't affect the product ;)
The order of the factors doesn't affect the product. ;)
Nice.
THANKS
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
because r=1 and 2(pi)x1=2(pi)
ok thx
thanks, what tools allows you to make video like that? How do you draw and move mouse so precisely?
6:23 RADIUSESESESESESESESESESESESESESEES..".... till 1 min 😂😂😂🤣
7:34 degreeeseseses... man's got crazy xd
Hey dude can u just tell me what is the meaning of radians cuz i dont rly understand
do you have a video where you explain "complex" roots?
yay i understand it much better
Wow nice video keep it up .
Great video
Thank you!!!!!!!!!!!!!
"let's cut to the chase: 2:43"
Thanks
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?
We want more videos like tz
u r great bro
god bless you guys
ur awesome!!!
hey sal what microphone u are using. I am also making videos. Please let me know. Thans in advance