Why use Radians?

In this video, we explore the concept of radians and why they are a useful unit for measuring angles. We start with an introduction of degrees, explaining the way we're all used to measuring angles. Then, we dive into the mathematical properties of radians, including the relationship between the circumference of a circle and its radius. We also explain why radians are a more useful unit for measuring angles.

[basedonprinciple]

Makes so much sense. Defining the circle's dimensions by its radius! We already have 2*pi*r to guide us there, so just keep using r. So now the angle becomes defined as how many r lengths the arc is. It's not another unit, it's a way of looking at the circle's angles in terms of how many wraps r makes around it. This kind of thing was definitely not taught when I learned about radians and made the concept confusing. Derivation helps understand the why!

[demonicdrn]

Fantastic explanation and wonderful motivation! I'm sure this will be a great resource for confused Algebra 2 students!

[isazisempi]

Why does everbody that doed math videos explain the trival part slow and rush past the important details

[AchtungBaby]

Another convenient benefit of radians that is often overlooked is the fact that they are dimensionless and don't usually require a unit or annoying superscript like degrees do.
If an angle is expressed as π/6, it's implicitly known to be in radians, whereas the corresponding angle in degrees needs to be expressed 30°.

[mikehipparchusnewton]

It's interesting what percentage of the world's population who says they're "good at math" doesn't really understand this phenomenon. This video is an excellent explanation but most math really just begins with a definition and then having faith in the subsequent calculations after that.

So 1 radian angle is when L=r By Definition. Therefore when theta is in radians (only), theta = L/r.

From that a multitude of calculations can be made if the basic circle formulas like c=2pi*r are remembered, ect. But it's important to remember that radian angle is arc length over radius by definition first. Thus, theta= L/r. It helps when drawing a circle and then going on from there and it shows how it's an actual measurement of a part of the circle that can be used for calculations in circular functions.

[orangeapple]

I wasn't paying attention in class and this actually made my day

[MirlitronOne]

Another simplification is that, when using radians, the slope of sin(x) at the origin (and at intervals of 2*pi thereafter) is equal to one.

[LesIsMoreFilms]

Awesome video! What program did you use to animate?

[WhiteEvileyes]

Clearly and so nice animation! Thank u

[KrasBadan]

I'm actually surprised no one uses a full rotation as a unit.

Like the right angle is 1/4, 30° is 1/12.

It's the same as radians with tau but divided by tau.

[israairshad]

How 2pi/360 came over dy/dx= 2pi/360 *cos(theta)

[mndtr]

Another reason why we use radians to measure angles is linearity. You see that if we measure angles with a circle we can add or subtract angles together and measure of their sum would be equal to the sum of measures

[ekoi]

The only drawback is that they want to represent the entire circumference as a whole unit, but in reality, π (pi) only covers half the pie (circumference). That’s why τ (tau), which equals 2π, was introduced. However, π sounds cool. It would be more consistent if the whole circumference were represented by π, hence 1 whole pie. I wonder if a system based on the diameter, perhaps called 'diameterian, ' might offer a more intuitive approach.

[Differentsinformations]

please why radian disappeared on L (m) = r (m) . θ(rad) , why L unite her (m.rad) please answer my question

[imnobody]

Dunno if this is a right place to ask, but, can someone explain to me why 2.5π radians are 143.2°? I mean, i understand the equation but why 2.5π are less degrees than 2π?

[meharsamba]

He should visualise tge equations as he talks about them

[billythenarwhal]

Shoulda just stuck to degrees, I'd rather have more complex equations than 2 units that mean the same thing and rely on memorization rather than calculation.

[bernaridho]

Even better: use radian, not rad; use radius, not r.