Why Radians?

[wreckim]

Math is like a beautiful, truthful story. However, you need a real story teller, that has passion and loves the story he's telling you to at least grasp the moral of the story, to make you say: tell me another one! Tell it again! Eddie Woo....you do that. Thank you.

[tranquilious]

10 years later, and this video is still a masterpiece. I applaud for his teaching skills 👏🏻👏🏻.
Keep it up!

[xniyana]

Wow. I've been wondering for years why anyone would use radians instead of degrees and finally I get a sensible explanation for it. Very good video.

[clionekimura]

Brilliant teaching. Story telling style, easily digestible. Thank you Mr. Woo!

[CervezaDeGaraje]

Math would have been so much easier with a teacher like you! Amazing!! Thanks!

[canadiannuclearman]

radians are great they are handy in physics. a car with a wheel of 1 foot and rotating at 100 radians per second the car will be moving at 100 feet per second
V=Rc
R is radius
c is radions per second
V= (radius units) metres or ft per second

[jessicalv]

I always learned what radian is, and months later I forget about it. Then I watch again, forget, watch, forget... But thanks for your video to help me catch up in just a couple minutes :)

[dendriloquist]

absolutely the best math-teacher I've ever had, , thank you Eddie

[onlyfams]

Man whenever eddie lies to me and tells me I'm smart, for some reason it really does help me grasp the concepts a little bit better. :)

[krishtygupta]

OMG i had been so confused like WHY RADIAN?? STICK WITH DEGREES. but your explaination cleared EVERYTHING.

[lianchundong]

quite clear. But could you show me some mathematical history about the introduction of radians, such as what problems drove the mathematician to look for another way of angle measurement, and what kinds things directed the mathematician to the idea of measuring the arc length? Thanks a lot.

[SoloPro]

As a mathematics tutor your videos are very nice and give that extra insight which makes you a very good teacher. Please make a playlist of all these cool videos of understanding as I really enjoy the simplicity in the understanding especially when its linked the basic concepts.
Keep up the great work!

[manojbaishya_]

the area of the segment formula intuitively leads to the conclusion that theta ~= sin(theta) for small angles (expressed in radians) where the segment area seems to approach limit zero

PS: appreciation of this fundamental topic grows manifold after studying applied rotational dynamics

[RealSlopeDude]

I love the way he says "here." He says he-ah.

[lawrencedoliveiro]

This is also an issue in computer graphics APIs. It is true that humans find angles in degrees easier to interpret and specify, even though the underlying calculations are usually easier to perform in radians. I think the simplest approach is to specify all angles in radians, and convert from degrees for user input and back to degrees for user output.

Sometimes it can be convenient for the user to work in other angle units as well, for example units of a whole circle, where 1 circle = 360° = 2π radians.

It is common for maths libraries to provide functions to perform the necessary conversions. But then you need two functions for each angle unit, one to convert to radians and one to convert from radians. It is simpler to provide a single conversion factor for each unit, for example for degrees you could provide the constant “deg” defined as follows:

deg = 2 * math.pi / 180

Then if a value “theta” is in degrees, it can be converted easily to radians, for example to compute the sine, thus:

s = math.sin(theta * deg)

and conversely a value in radians can be easily converted to degrees by dividing by the same factor:

theta = math.asin(s) / deg

[mischief]

arc length at 1 radians = r
arc length at θ radians (θ = 180°) = θ * r
arc length = s = θ * r
also arc length of semi circle is = π * r, hence >> π * r = 180° * r >> π = 180°

[ghousepasha]

No one would ask this question, thank you eddie

[chip.rollinson]

Radians exist for one reason - the make the slope of the function y=sin(x) equal to 1 at x=0. This makes the derivative of the sine the cosine and, in turn, the derivative of cosine equal to negative sine. The rest of the trig derivatives follow. When the period of y=sin(x) is 360, the slope at x=0 is pi/180 which is not very convenient.

[kamyarphysicsschool]

This video is great. I appreciate having your valuable opinion about my video in the same topic.

[HDDude]

When I was taking HS mathematics radians was never explained to me like this. We were given the unit circle and told to memorize it. It never made sense at the time.