Introduction to Radians (3 of 3: Definition + Why Radians Aren't Units)

[@Manticore_007]

Mr. Woo is so insπring! I'm addicted to his enthusiasm, it's so important when teaching.

[@Satishoz]

“That’s so awesome” - living the dream Eddie of seeing beauty of maths dropping into a persons head.

[@JeremyHoffman]

10:00 is the timestamp 🙂

[@yumnuska]

I already know this, but Eddie is so good at teaching that I’m watching his videos to find good nuggets for my kid. I had the exact same reaction at that moment. Eddie. You are a phenomenon.

[@reik2006]

It seems to me, that the amazement in the end was based implicitly in the realization, that for any circle the ratio of circumference to diameter is a constant, namely pie. Then again I've not been explicitly aware, that one radian is one radius of length on the arc. Feels like two insights for one mathematical truth :)

[@asadfarraj]

This person, in what seems like 3 videos totalling around 30 minutes, taught me that thing, which over 3 YEARS and 7 different teachers later I still couldn't understand. Why? All of them basically just repeated the definition and were done with the explaining. This man went into much more detail than I could have expected. Thank you.

[@schenzur]

I got what radian was as a definition but it was extremely hard for me to visualize it and see it like degrees but after watching this video I have been enlightened. I can't thank you enough sir.

[@omikronsigma2446]

Ligit best KZbin channel ever, period.

[@shivrajchandel4342]

Sir your videos gives my mind magical touch to clear all my doubts .... You are awesome sir

[@stuartsandskill270]

India mein aise tecaher nhi hai na apne... wo exam ke liye bas padhate hai

[@shneebzzz487]

just coming up to my year 11 exams and this really helped me! thanks so much man your an inspiration

[@Hythloday71]

Good little series ... it is now apparent why the series definitions of sine and cosine would naturally be in radians - it is all talking about ratios !

[@weflic]

I have studied the concept before but this video was whole new to me. You're the best maths teacher.

[@imnimbusy2885]

I only just found you recently but all this high level trigonometric learning that my class hasn’t done really helps! Thanks so much - I really enjoy maths and understanding it, which you are great at stimulating.

[@bunpeishiratori5849]

It's three in the morning and I'm watching a guy teaching math.

[@pyrodon333]

Same

[@sfgfgfgfg]

Same tho

[@philipprevost2982]

This is first KZbin math teacher I've seen explain what the essence of a radian really is: a radian angle measurement is merely the RATIO between the length of the radius of the circle and the length of the arc traced out by that angle on the circle. If the two lengths are equal then we have a 1:1 ratio and the angle between the starting point of the arc and it's end point is 1 radian. If the ratio between the arc length and the radius length is 3.14:1 then the angle is 3.14 radians or pi radians or 180 degrees. We're using the radius length as our UNIT OF MEASUREMENT. If the radius is 7 inches or 627 miles we're mentally making it a 1 on our unit of measurement for simplicity's sake. At the end we can multiply our radian result times the 7 inches of radius or the 627 miles of radius to get our real world measurements of the length of the arc in tape measures or on our odometers respectively. The milky way is 100,000 light years across and therefore has a radius of 50,000 light years. If we drive a starship a quarter ways around the rim of our galaxy the angle between the two points will be pi/2 or 1.57 radians. The arc traversed will be 1.57x50,000 light years in length.

[@pavelkoprivec8840]

Simply brialiant. Similarity and Ratios not just right triangles but also circles.

[@satishgoda]

Satish Goda Outstanding teaching. My knowledge of radians has come a full two*pi. Thank you Sir

[@theMagos]

You mean you're back where you started? :)

[@abirroy1333]

You're an absolute inspiration! There is no better way to explain this topic of circle.

[@williambolton4698]

I hope that any kid watching this also realises how incredibly annoying the constant background chatter and late arrivals can be for other students.

[@rilijn]

And NOW it finally makes sense. This was the missing piece I needed to understand the concept! Thank you!

[@stellamariefanboy.6768]

Can you explain to me? I’m still a little lost and I need to explain this to a class for a project 😂

[@aryyaa217]

you are such a great teacher. thank you for posting these on youtube!!

[@simonandrews6160]

I think an explanation of the origin of pi would help a lot with clarity here. As in, the distance around the circumference of the unit circle, anti-clockwise from 0π to π ( 0˚ to 180˚ degrees), is 3.14 radians, which is of course, the numerical value of pi.

[@ac17dollars]

pi are circumference by diameter which is always constant. They just made a symbol for it, or we could have it as k and write C=2kr and of course since k is constant found experimently by drawing circles and taking ratios k=3.14 just replace k with pi and there you go.

[@carultch]

@@ac17dollars It is very difficult to get pi measured accurately, when do it by experiment. An ancient idea for how to calculate pi is to develop an equation of a regular n-gon (as in a polygon with n equal sides and n equal angles), and calculate the ratio of its perimeter to its diameter. Take n as high as practical to calculate, and you can determine how to calculate pi. The n-gon has an area that can be derived from breaking it into triangles. This is what Archimedes did, with the 96-gon. Newton came up with a much more computationally efficient method for calculating pi, based on integrating sqrt(1-x^2) as an infinite series.

[@Julian-sy5pp]

Got all my doubts cleared in 11 minutes!

[@AlessioTanzi]

Unbelievably clear! Greetings from Italy

[@hoang-anhvu3920]

wow he got so much better at explaining the concept, compared to his video of 2013. Excellent job

[@philipprevost2982]

Yeah. The best way to learn something is to teach it.

[@afrini]

Thank you so much Mr. Woo

[@ahnafazizict7684]

pi radian= 180 degrees. now taking 180 on the other side, we have pi/180 radians = 1 degree. now radian is a unitless quantity, so any number attached to it must be a unitless number. thus pi/180 radian is a unitless number. so following the above equation , 1 degree is a unitless number. now if degree were not a unitless quantity, it would mean that 1 degree is not a unitless number. (contradiction) thus, degree is a unitless quantity as well. is my argument accurate?

[@tgooda4672]

No

[@JohnSmith-rf1tx]

No. The problem with it is saying that pi = 180 degrees. In truth these aren't equal in the mathematical sense. They are two different ways to express the same idea, but that doesn't make them mathematically equal. Therefore you can't really do things like divide both sides by 180. Writing it that way is shorthand to allow new students to convert from the degree system to radians, but it's inaccurate. The most you can say is that 180 degrees corresponds to pi radians, but they aren't equal.

[@carultch]

By this logic, if you coined a hypothetical angle unit called the diadian (1*pi diadians = 1 revolution), that was defined such that it would be the arc length of 1 diameter wrapped around the circle per unit diameter, it would also "not be a unit" just like the radian. Yet if both these concepts coexisted, we'd still have to call at least one of them a unit.

[@studyplusmathematics562]

I m a teacher from India thank bro

[@ShaheenHaider-nb9fc]

These students belong to which standard/class? anybody can answer ....?

[@joshuaabimanyu6115]

" thє вєѕt tєαchєr " 💙

[@Julian-sy5pp]

I love this teacher !!!!

[@NeeldeepXI]

which country

[@TheGamingWattsit]

What does he mean by: "Radians are the ratio between the arc length and the radius of the circle"

[@shneebzzz487]

arc length (divided by) radius = radien

[@philipprevost2982]

The length of the arc between the starting point and ending point of the angle divided by the length of the radius. If the length of the arc is 56.4 centimeters and the radius of the circle is 56.4 centimeters then WE SAY that the ANGLE (not the length) between the starting point and the end point of that arc is 1 radian. If the arc length is 6452 miles and the radius length of this great big circle is also 6452 miles then the ANGLE between the two points of the arc is also 1 radian. A radian is thus a RATIO and not so much a real world measurement. We multiply our resulting radians times the real world length of the radius to get the real world length of our arc.

[@ThePreparedMuslim]

I'm always amazed at the rudeness of the Western students who are talking and making such noise in the backgrounds - the etiquettes with the teacher are very poor, interrupting him, talking to each other while he's talking... He even is so patient with them, but they don't appreciate it.

[@allanr1771]

"a dimensionless quantity" student in background "WHAT!?" me "lolololololololol" in case you are in the same place a radian is the radius of the given circle which can increase or decrease in size, using the unit circle in fact makes this a constant when you really think about it.

[@jacklloyd2735]

Just Wow🔥🔥

[@farvardinmainyu1961]

If τ is used instead of π , all this will become easier , I think...

[@KevinGnanaraj]

Why the heck did we learn degrees in the first place if radians are this fundamental to trig??

[@paulgiaccone6115]

Because they're easier to understand and because they are used in everyday life.

[@philipprevost2982]

Because the ancient Babylonians didn't know trigonometry.

[@carultch]

Because everyone else who forgot half their high school math, still thinks in degrees for angles. Plus, most tools for angles are calibrated in degrees. If you want to communicate with people who will build what you design, you specify your angles in degrees. Tell a machinist or a carpenter to build a pi/4 angle between two lines in your design, and that is Greek to them in more ways than one. You can find radian protractors, but good luck finding a radian miter gauge. Radians exist to make Calculus and Physics as elegant as they can be, degrees exist to communicate with everyone who isn't familiar with radians.

[@ck0024]

Salute man

[@mahishrivastava15]

Whole time i was having epiphany....

[@vikrantattri0163]

Great

[@TheFarmanimalfriend]

Rotation is 'always' counter clockwise. pi/2 should be on the upper side, not the lower side.

[@samrudhp8519]

TheFarmanimalfriend I guess you didn't see what he did there? He measured the 90° beneath and put an arrow mark towards the x axis of the circle

[@virtual500]

He didn't want to draw over where he already drew something.

[@lydie6702]

SOoooOOooooo GooOOOoooOd