Why do we skip writing radians? There is no such thing as pi angle, right? The angle is actually pi radians...

Why do we skip writing radians? There is no such thing as pi angle, right? The angle is actually pi radians. Shouldn't writing sin(pi) be nonsensical and instead written as sin(pi * rad)?

Cause it's faster and implied

because radians are actually unitless so it's really just pi nothings, you don't have to write "rad"

they aren't unitless
1 radian is equal to ~57.3 degrees
degree IS a unit, so how can you skip writing a unit?
it's like we were to skip writing kilograms or meters using plain numbers
but where does this rule originate from? it doesn't make any mathematical sense

a radian is the angle subtended by the part of the circumference equal to the radius, it's like dividing length by length you get no units
the angle is implied

Degrees are a fossil of centuries-outdated mathematics that's still taught in primary schools for no good reason. They've always carried the degree symbol, because it's not clear from context that they aren't just ordinary numbers.

[math]\pi[/math] is so niche that it's never ambiguous that you're talking about angles when you write down [math]\frac{11 \pi}{6}[/math].

The units are usually dropped for simplicity

I know that but this still doesn't make sense to me
a sine is a function of an angle
angle is not a number, it has its own units, so why do we skip them?
the angle of whole circle is 2pi radians, not 2pi
but why is it allowed? are there no such cases in which it makes a difference?

*tips slide rule*
m'Chauchy

[math]\varphi = \frac{s}{r}[/math] where [math]s[/math] and [math]r[/math] is a distance.
>[math]\mathbb{muh\,units}[/math]
Degrees are a meme

yeah but a radian is an arbitrary unit, it's not counting anything besides how many of them there are but it's still an angle because it's related to degrees
Say a sandwich costs 5 dollars and then you start measuring money in terms of sandwiches, dollars are like degrees and radians are like sandwiches

...

>π is so niche that it's never ambiguous that you're talking about angles when you write down 11π/6
so how do you know whether I'm talking about degrees or radians when I write down sin(180)?
that's why it doesn't make sense to skip the unit

because radians are written in multiples of pi

180 is also a multiple of pi
180 * pi/pi

Angles are dimensionless quantities because they're defined by the ratio of an arc to a radius. Those are both lengths so the units cancel. So we don't have to worry about the unit in calculations.

13 is a also multiple of 7
13*7/7
brainlet

then how do you express a single radian as a multiple of pi?

I don't because i'm not a brainlet

then you have no idea of knowing whether sin(180) is referring to radians or degrees and we conclude there is no reason to skip units

1 != pi
go fucking figure

so what you're saying that sin(1) refers to degrees, so does sin(2) and sin(3), but then magically sin(3.141592...) refers to radians?
how the fuck does that make any sense?

No, sin(x) is always radians unless it explicitly says otherwise. Radians is default.

180 dollars will buy me a pie

2 pies or 360 dollars will buy me a math test

There are no units in math.
(cos(x),sin(x)) is the point on the unit circle given that you have travelled x distance starting from the point (1,0) and going counter-clockwise.
that distance x is called angle and retards like engineer call it "x radians".

...

Radians are for cucks.

Radians don't exist retard

Here's how you know they have to be unitless:

You know (God help us if you don't) that sin(x) can be written as an infinite series. I'll just write the first two terms: sin(x)=x-(1/6)x^3

If x has units of r, then the first term has unit r, and the second term unit r^3. But you know we cannot add things of different units together. The only way it works is if x is unitless.

nope sin is a function from the real numbers to [-1, 1].

infinity doesnt exist

and yet sin somehow chugs along

>God help us if you don't
what's wrong with not knowing that? I didn't know that until university, they don't teach calculus until university where I live in EU

I wish we were never taught degrees, my brain is only comfortable with degrees. I hate working with radians I always convert to degrees and then back to radians.

at least I'm not alone

You took trig, right?

A better question would be why pi only represents half the pie. Seems like a dupe.

thanks for sharing, guys, I'm glad to know I'm not the only one

Off yourselves brainlets
How hard is it to visualise fractions of the number 2

That's ok user.

Because this is an 18+ website fag.

you finish highschool at 19 in my country, fag

Kek

You're mixing up math and physics. We don't use units in mathematics.

> i j k

How are those units?
They're literally (1,0,0), (0,1,0) and (0,0,1).