Why We Use Radians In Calculus?

Why do we use radians in calculus? What if we use degrees? Well, watch and find out!

blackpenredpen
math for fun

[blackpenredpen]

A better picture compares the graphs of sine in deg vs. in rad

[kostantinos]

I'd argue that the circumference of a circle is itself 2πR, but that's just circular logic.

[BigDBrian]

it's similar to the reason you use e as a base for exponents when it comes to differentiation, so that you don't get annoying constants.

[OonHan]

“Why do we use radians in calculus?”

_Because we are all adults now_

[neilgerace]

3:07 Be the change you want to see in the world: be a radian.

[VibingMath]

O man! U just explained what most students and teachers ask when we first study radian, thank you!

[almightyhydra]

The reason you need to use radians is that lim (h->0) (sin x) / x only approaches 1 if x is in radians. It's from this limit that one derives d/dx (sin x) = cos x.

[dhruvkumartiwari]

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[chirayu_jain]

The graph of y = sin(x degrees) was looking like the grah of y = 0

[angelmendez-rivera]

This is an extremely unconvincing argument, since objectively speaking, the criteria that the graph should have a y to x unit scale ratio of 1 is unreasonable, simply because it is ineffective both in theoretical study and practical application. A more convincing argument that is directly tied to the scale is the fact that degrees are unit, and transcendental functions, such as the trigonometric functions, cannot take units as inputs, only dimensionless constants. As such, we want to de-dimensionalize the angles into constants, and we want this procedure to be bijective. To do this, we naturalize the unit by choosing a constant intrinsic to circles, π. This naturalized angle degree measurement that uniquely characterizes the angle is what we then call a radian, and we use it because it is now dimensionless and natural, as opposed to being an artifical unit.

[muhe]

In fact, the reason for introducing the Radian system is to directly relate the angle to the length, because an angle can also be characterized directly by (arc length / radius).

[iradnuriel]

We use radians and not degrees because degrees have measurement units, and we don’t want x to be dependent on a measurement unit.
So we invented radians(radians aren’t measurement units but a ratio between an arch length and radius(cm/cm so it has no measurement units))

[chirayu_jain]

This was a question in my mind since I learned trignometry 🤔

[Arthur-xepu]

I remember that our physics professor told us that we use radians because we don't have a good enough reason to claim that a circle should be 360 degrees, so people tend to choose a more intuitive way, which is using radians.

[generalginger]

1:53 the subtitles were crazy lol🤣🤣😂🤣😂🤣

[benjaminbrady]

From a more advanced perspective too. The sine function (and indeed, alot of mathematical functions) does not meaningfully act on any quantity with units. As a quick example, imagine some angular unit r. The Taylor series of sine is the alternating sum of odd powers. Well, then we have a result in some quantity of r minus some quantity of r^3 plus some quantity of r^5 minus some quantity of r^7 and so on. As we know, no unit to a power can be expressed in terms of linear combinations of the unit alone so these terms cannot be combined and our answer is now meaningless

[Pete-Prolly]

Hey guys, does this sound familiar? You go to class, but your teacher can't explain anything, so you turn to YouTube & it helps... until you see commercials for Tutorguy & have to wait to hit "skip ad."

[SeriousApache]

In electrical engineering we still use degrees to measure phase difference.

[swankitydankity]

It's also the case that the Taylor Series for sinx matches a graph of sinx using radians and it does not match sinx using degrees

[Vandarte_translator]

Thanks, I wanted to know that since a long time.