Introduction to radians | Unit circle definition of trig functions | Trigonometry | Khan Academy
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- เผยแพร่เมื่อ 14 ต.ค. 2024
- 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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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
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
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).
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?
98% comments = radiuseseseses
More like 60
i never appreciate your circle drawing skills until i have to draw a circle myself
radiuseseseseseseseseses
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
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.
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~
radiuseseseseseses
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...
"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
A great explanation!
Khan Academy is a great place to learn.
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☺️
radiuseseses...
this video is clear!
save my life from digging into textbook:P
You haven't lost yet and you have more to achieve
What program do they use for the drawing?
❤I know, the video was uploaded ten years ago but it had something that made me keep watching it till the end. ❤
I wanted to plug my own video attempt where I explain this concept, but I have nothing to add. Great video! :D
this is great GOD BLESS
Clear, easy, with background. Thanks :)
That was really nice. Many teachers just tell to remember this without informing about proper concept. But u r gr8.. Thank you a lot❤
I learned alot today, Radiuseseseses are very important...😂😂😂😂
This was explained amazingly well. I don't think any of my teachers ever explained this, neither in grade school or college.
Thank you so much your video made so much more sense than my teacher 🙏
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
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.
your lectures are very easy to understan
This video very helpful. 👍🏻
Thank you! I was so confused with the radian, but now I understand much more now.
Thanks for this explanation. I'm taking a coding class and this was very helpful.
Thanks for the explanation.
how successfull are you to make things easier to understand..
I got ~57.2957795131 degrees per radian using a calculator and pi as far as it would go (3.141592653589793).
Fantastic explanation. I study as well as teach physics. I couldn't have done it better myself. Congratulations.
Thanks this is going to help me with my Core 2 A-level exams alot! :)
Thank you so MUCH !
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!
I swear, I could never have gotten anywhere in math were it not for Khan Academy and Teaching Textbooks
Even though it's a 11 years vídeo, this explained radians very well that I understand very clearly
You made a good video...👍 Made me understand the radian concept.
Nice video! Straightforward and easy to understand
Having motivation behind ideas (rather than just memorizing them) makes Khan Academy amazing!
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!
how neatly u write on this is mind blown
Thank Gosh this exists
I love the way u teach!! wish all the teachers were just like u
Thank you!
thanks for all the -radiuseses- radii
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
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
I respect u a lot.... Thank u❤️
Explained brilliantly
Very well explained!! Logical and easy to follow :)
THIS IS SOOOOO GOOD !.... AND IT'S 7 YEARS AGO !!!!
great video. best I've seen on the subject so far. thanks!
Very nice explanation! Thank you
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.
7:34 degrees-es-es
Great video really informative.Great Easter egg
It is more commonly known as Arc Length. It is represented with an S and can be found using S = theta * radius
He is good in explaining really
Much better than me😫😂
"This isnt some voodoo" classic.
Chris
Btw what is it😂
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.
6:23 RADIUSESESESESESESESESESESESESESEES..".... till 1 min 😂😂😂🤣
Radii!!
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 ?
thanks, what tools allows you to make video like that? How do you draw and move mouse so precisely?
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. ;)
Great video Sal, keep them coming!
Whenever he said sixty symbols I couldn't stop thinking about Brady's Channel.
yay i understand it much better
this guy really has some sense of humour 😀😀
Nice.
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?
Great video
Wow nice video keep it up .
Thanks
hey sal what microphone u are using. I am also making videos. Please let me know. Thans in advance
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?
Thank you!!!!!!!!!!!!!
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
We want more videos like tz
u r great bro
god bless you guys
ur awesome!!!
Spent my whole life thinking this was in fact some voodoo stuff and now I finally understand
Hey Mr Sal Khan, would you tell me how can we draw 1 radian on paper?