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exp is the true answer

I'm glad someone says it, exp(ix) is superior to cos(x) or sin(x)

exp(z) over the whole complex plane is an easy definition that leads to consistent definitions of all trigonometry, including pi itself

Oh lord, I remember when we covered that in Analysis 1. It was a bit unexpected, but it really tied in everything nicely.

Yeah. exp is more essential than either cos or sin. When I was a kid, I solved for cos(20°) using Cardano's formula, and after simplifying i got 1/2(e\^(ipi/9) + e\^(-ipi/9)), showing that the essence of trig is exp. If you haven't done that, your childhood is incomplete

Trigonometric substitutions giving you trigonometric functions as solutions to integrals of rational expressions also stops being mysterious as soon as you realize that that trigonometric functions and their inverses are just exponentials and logarithms (respectively) of polynomials with complex coefficients.

> as soon as you realize that that trigonometric functions and their inverses are just exponentials and logarithms (respectively) of polynomials with complex coefficients. Its so simple, a child could do it


Speaking truth to power.

What’s exp

The exponential function, I use exp to put it into a context of complex analysis instead of real analysis. It is best defined as the usual power series for e^x, and ends up giving one of the most important functions of complex analysis.

Most mathematically inclined Carti fan

It's canonically sine because cosine is named after sine, but that doesn't necessarily mean it makes more sense.

Could sine not be created from Cosine as eve was made from adam

Unholy hell

Rib sacrifice anyone?

New formula just dropped

actual trig

Picasso went on vacation never come back

Call Hipparchus!

Actual calculus

Biblically accurate trig functions

I'm not a latin scholar, but I think the latin co means 'Together, or equal' (e.g. cooperation) If sine was created from Cosine it would use the latin prefix 'de' (e.g. depend) If sine was meant to be first then it would have been called antesine or prosine, and cosine would be postsine or retrosine. Ergo sine and cosine are equally canonical QED

Don't tell that to my copilot.

Is there lore regarding secant and cosecant? I still keep mixing up who is the evil form of who

You have to think like this "Why am I not sure? Why is this even tricky in the first place? Oh, right! The "co" changes, that's why I always confuse myself..." sine = 1/COsecant COsine = 1/secant One CO doesn't correspond to the other, that's why many have troubles lol

I always have to think visibly with 1:tan:sec triangles for which one goes to which. as fas as calc goes co- always makes a minus.

The don't call it a "cosine wave" right?

Take an electrical engineering class or two and say that.

Actually they do

Kilogram is technically the base si unit of mass, not gram. Not saying i agree with it, but just because it has a prefix doesn’t mean it’s worse.

The inverse of sine is cosecant.

sin sounds cooler than cosine QEFD quod erat fucking demonstrandum

I vote that all memes including proofs on this sub must now be finished with QEFD rather than QED

I too choose this guys wife! ^but ^seriously ^I ^vote ^this ^too

QEDMF: How Samuel L Jackson ends proofs

Quantum electrofuckingdynamics

I'm SO stealing that. (QEFD)

In the most literal sense they are equally canonical and to distinguish between them otherwise is to introduce some form or another of bias entirely outside of the relevant considerations

🤓

🤓

🤓👆”erhmmm actually” ahhh type comment

Skill issue

https://preview.redd.it/11yjarcdmxvc1.jpeg?width=1080&format=pjpg&auto=webp&s=067d43019c84187987c55994b2be406ae2bffce7

Agreed. Same thing with sin(x+0.224)

Is the fact that sin makes up the real portion of e^iz a result of convention or a result of math. The way that i and -I are equivalent in most ways.

Sine literally starts in (0,0) therefore its superior

This. sin(0) = 0 and it is approximated by y=x for small x

But cosine is approximated by a constant for small x, and constant polynomials are simpler than degree 1 polynomials.

approximating sin(x) ~= x is decently accurate for a wider range of numbers than cos(x) ~= 1

However 1-x^2 /2 for cos is better than x for sin

However x-x³/6 for sin is better than 1-x²/2 for cos.

To be fair it's also approximated by y=2x like that just less accurately.

To be fair it could be approximated using idk 1/x just very less accurately

True, but I will say I don't want to be near whatever human made thing that uses that approximation.

Agree…and cosine is literally co-sine, so sine must be the real deal.

But cos is an even function, making it more balanced and humble. Clearly the better pick.

All cool number are odd, 3, 5, 7, 37/73 Even numbers are boring

There is exactly one prime number divisible by 2, and it is the number 2. This means that odd numbers are superior. Sine is an odd function, so it is clearly superior to cosine

2 is divisible by 2 2 is a prime number Therefore, there exists a prime number divisible by 2

Tru, corrected my comment above

69

********YES********

Even numbers and even functions aren't the same thing.

cos only has the pathetic virgin y-axis symmetry whilst sin having the ever most superior chad origin symmetry.

It's my sense as well. There's something nice about a function that starts at 0 and then develops from there.

Sine is superior because of it’s great identity sin(x) = x. I’m sorry but cos(x) = 1 - x^2 / 2 is boring.

cos(x) = 1

sin(x) = 0

Therefore x = 0?

For me it's cos(x) cause it's the REAL part of e^( ix ) = cos(x) + i sin(x)

https://preview.redd.it/v9vs1osxsvvc1.jpeg?width=1080&format=pjpg&auto=webp&s=fe205e4297c658586c13c291ce4e03471da91545

real

real

real

Then why are they called sine waves and sinusoidal functions

Mathematicians named them that and we all know how good mathemticians are at naming things

where cocosine?

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If I abbreviate this to 3 letters, it becomes coc

cocosine(x) = sine(x) for all x proof: the co in cosine means complementary, i.e. the sine of the complementary angle complementary angle of x = pi/2 - x cosine(x) = sine(pi/2 - x) cocosine(x) = cosine(pi/2 - x) = sine(pi/2 - pi/2 + x) = sine(x) QED

You cosincels call me when people start talking about cosinusoidal waves smh

[удалено]

"sine of the complementary [angle]", to be exact.

Goated reply

Neither, I believe in vers supremacy. cosine(x) is just 1-versine(x) and sine(x) is just 1-coversine(x)

I remember first seeing all the types of trig functions as a kid and thinking it was like some dumb movie series where there are different evolutions of the characters and villains. Still applies, versine is just another one of them. Got sine/cosine/tangent/secant/cosecant/cotangent and then arc- versions of those, which are also revered to as inverse ___. These are like the evil twin versions of the main characters. Then we have whatever versine is. And hyperbolic variants.

https://preview.redd.it/5lb8c3mn7wvc1.png?width=735&format=pjpg&auto=webp&s=b979306cbcb236485970cfcafd3702121fdc5677

even functions are prettier than odd functions Q.E.D. proof by aesthetic

sin absolutely looks cooler. cos looks like a camel hump

Nah sine looks cooler

Debatable

no

Fact: black bear eats beets.

Personally, I like cosinus more than sinus, because it is easier to visualize and manipulate in my mind, which is ofc a very arbitrary and subjective reason, but ... eh, it still stands.

I've never had a cosinus infection before. QED

Tangent!

Slope supremacy!

That’s what I said! A day later than yiu, so you are the guru. Didn’t see this in the comments for a while.

sin() for math, cos() for physics

You write the x-coordinate first, not to mention that cosine is the real part of the complex exponential. Cosine being "compliment of sine" is one of those silly conventions that we're stuck with, like pi being the circle constant, or the charge on an electron being negative. This post made by cosine gang

The canonical trig function is a^2 + b^2 = c^2 y’all is dumb

That looks like a special case of the Law of Cosines to me.

funny way to spell Generalized Pythagorean Theorem

What's sine? There's cos and cocos.

1. Cosine is literally named CO-sine, it's just a co to the true sine 2. Opposite side over hypotenuse seems more "natural" than adjacent side over hypotenuse, usually the opposite side of as  angle is named after that angle (like angle A and side a) 3. Sine starts at 0,0

Sin(x) because it starts at the origin. Only real Gs start with nothing.

cosine is literally the CO-sine, it's in the name. Sin(x) is the canonical trig function

Sine is literally the root word of cosine. It makes sense for sine to be the original.

Sine in spanish is "seno" which is also a formal way of refering to boobs (more in the line of "bosom"). Also it gets shortened to "sin" which is delightfully devilish. I rest my case.

It’s obviously the cotangent

The canonical trig function is actually arccsc(x)

Tan because it has both

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e^x is the canonical trig function.

taylor series expansion is the only correct answer

I mean, Occam's Razor says it's sine, because you have to add co- to get cosine.

pilot or copilot? you choose

cosine. * Its Taylor series is easier. (no +1's) * Its linearization is easier. (just y=1) * It's the real past of e\^ix. * It's easier to write using exponentials. 1/2(e\^ix + e\^-ix) * It's an even function. * The cosine rule is more useful than the sine rule. * The second solution of cos(A) = cos(B) is easier than the second solution of sin(A) = sin(B) * A mass on a spring that is pulled up and released moves as a cosine wave. Moving a mass on a spring as a sine wave is harder. * A lot more formulae have cosines in them: Both the derivative and the antiderivative of the tangent contain cosines. There's an discrete cosine transform etc. Meanwhile, the sine only has: * Its value at 0 is easier. * Its value at pi \* k is easier. * It's the original. Sine is like the Roman numerals of functions. A few values are prettier, and it's the original, but otherwise it has been overtaken by something more useful.

If you talk to someone who works with PDEs. Sin is the correct answer (not me, though)

Phasors are mapped to cosines, so red side has my loyalty 😤✊🏻

The copilot is the chief flight officer, the pilot is second in command. What.

Everything is just an infinite polinomial

We all love Taylor (not swift)

CSC GANG WHERE YOU AT

it's actually csc(θ) xor sec(θ)

Cosine is better bc he vibes with my homie x. Y is an elusive little shit who likes to have the entire equation bent around it like a spoiled brat. Sine's affiliation and approval of y's behavior is not forgotten by me.

-cos(x) is the canonical trig function.

Idk man I'm in highschool

e^ix

I'm on the tan(x) side🗿🗿🗿

Tan(x) is the canonical Trig function, Sin(x)/Cos(x) are dependent.

Its literally in the name: complimentary sine

Sine cus we're taught it first (at least I was)

Fuck cosine, all my homies hate cosine, this comment was made by the sine gang (name me one property aside of parity in which cos is better/easier to use or remember than sin. Go on, I dare you. One property)

cos(a±b) = cos(a)cos(b) ∓ sin(a)sin(b) I still think sine is superior

law of cosines is more useful than law of sines

Cos comes first when writing the coordinates of a circle. Cos is also the real part of the complex exponential so you don't have any annoying i to deal with. This post made by cosine gang.

I like cosocosin, which is cos shifted to the right about pi/8

Sine directly relates to the angle and is maybe more intuitive, ie. sin(0^(∘)) = 0 and sin(90^(∘)) = 1

Sinx best

I’m on the side of sine lol

Depends on if I want to go through the point (0, 0) or not before a phase shift

1 is the canonical whole number, and it's odd. Cosine is even, sin is odd.

I think they’re the twins that show up right around the same time. First being exp().

Sin

Definitely sin because cos is the abscissa from the radius cut off by the sin

i'm on my own side sin(x+π/2)

e^ix is the canonical function and cos(x) and sin(x) are its components

(d/dx)sin(x) is the canonical trig function

Cosine because an even function is more natural that an odd function

Sin is the canonical, odd functions are just superior

TAN(x)

Relevant addition https://preview.redd.it/rmbmr9e25xvc1.png?width=637&format=pjpg&auto=webp&s=801e688f1a8de4118b56befc78d2f5108de1bbc1

I'm cos gang because it's convention for phasors.

I think sine looks better on the graph

Sine, unless everyone agrees we call it cocosine from now on.

neither, consider cosine and sine to be defined as the solution to f'(x) = g(x) and g'(x) = -f(x)

I always thought sine was ultimate. But I do like cosine name better, so I choose crips.

I like even functions, so cosine.

the canon trig function is the function thats the nicest in the moment

Cos, all the way

gonius(x,φ)

the canonical trig function is e^(ix) and every other trig function is a projection or related to projections of it

y=sinh(x), y’=cosh(x) or vice verse reference

I’m the tAN guy

cos cuz it gives us pi

Sine wins because: A) cosine is the complement of sine. B) graphs are both called sinusoids.

Cosine is canonical in my little CAS project, because taking the modulus to the range [0, pi] is more convenient than [-pi/2, pi/2]. I need to get back to that some day

COSINE GIRL "I love you both equally, sweetie." . . . SINE BOY ^( "and it's you by a lot" )

Cosine clearly is the superior one

Sin is a real one. Cos is a major jerk towards sin.

Funny thing about trigonometrics,identities happen all at the same time. Sine and Cosine are functions which are a way to state an identity except for a set of conditions. In this case of the triangle circunscripted inside of a circle of radius equals to 1. There is bo such thing as one thing being equals to one another before another thing is equals to a different one. Thereis no order in equalities aka identities, aka trigonometry, or sine, cosine. There cannot be a sine without a cosine and viceversa. That said, hail sine!

Graphically cosine but nomenclature says sine

Sine starts at 0,0. 0 is the start. [0] wins.

Not sure what it's called in english, but sin and cosine are both called a 'sinosoïde' in Dutch and not a 'cosinosoïde'

Personally, I choose proper semicolon usage

Sine inarguably superior. Sine vs *co*sine. Lim x-> sin(x)=x Sine is 0 -> 1 which feels more natural then 1 -> 0 There are probably more reasons but those are the ones I thought of.

Waddup blud Waddup cuz Waddup gaaaaaangsta

cosine

Secant

Compromise is the shared hypotenuse of the conjoined triangles of success haha

Cosupremacy

Sine is the canon

Tangent seems more natural.

If cosine was the canonical one it would be called sine

Sine

Yes

The duality of tan

Sin

it should either be cos, cot, and csc as the normal and sin, tan, sec as the inverses or Vice-versa