Can someone explain Pythagorean identities (sin^2+cos^2=1) in a way that my autistic prof can't

In a triangle A^2 + B^2 = C^2
Sin and Cos are both parts of a triangle that has a hypotenuse of 1. Sin (B) is one side (of the Y axis) and Cos (A) is another side (Of the X axis) so when you square and add those two up they have to Equal C which = 1.

It's like you want me to figure out where you live just so I can fucking kick your dick inside out.

It's the very definition of sine and cosine to be the sides of the right triangle of hypotenuses 1 aka the y and x components respectively of the unit circle at a given angle.

...

Pythagoras, I swear to god if you are time travelling I will go back in time and curse you with Athena.

...

Athena is a top tier Waifu

Then congrats, she's yours Pythagoras.

Hope you and her have a happy life together.

That's why I kept my name as Zeus, because I swear to god that bitch is lit. insane.

>dumbass thinks pythagaras speaks english LUL

Stupid poster misspells Pythagoras in an attempt to appear superior.

See, University Professors? This is why nobody fucking likes you.

>d[key]=d[key]+1
Why the fuck do you people do this shit all the fucking time

the FUCK should I know. I'm just an Author Of NOVELS, Not An Author Of Novella IDEAS.

>it's more accurately a definition
It is actually not a definition. That is not actually a proper definition for the sine and cosine functions (or for the number 1). That is simply a functional equation involving sine and cosine. And as cosine is just sine shifted, it is actually a functional equation for sine.

A definition for sine would include that, and other functional equations that actually properly completely define sine. But this route is mostly nonsense. The best way to define sine and cosine is geometrically and then using completeness to prove that indeed functions with these properties must exist and be unique.

take your meds

I Have No Medications Prescribed To Me, Nor Has Any Medical Practitioner (Physician Or Psychologist) Strenuously Implied That I Require Constant Monitoring Or Medication.

are you a musician or a mathematician?

I am NEITHER.

I am an 'author'. If you had half a brain and followed my fucking 'writer name' you would DISCOVER that I write under the name S.Vagus/Solivagus.

www.svagus.co.uk

Fucking idiots.

(o/h)^2 + (a/h)^2 = 1
o^2 + a^2 = h^2

I don't give a shit about your website. Why do you use the name "Simon Troy Cosgrove"? Who is that? And why do you always post in chinese

It's my fucking legal birthname, what other name am I supposed to use if I want people to know who the fuck I am? Anonymous?

Yeah, I'll totally go out in public and say, "Hi! I'm Anonymous! Let Us Be Friends!"

If you want people to recognize you then just use one name exclusively. Otherwise it tends to confuse people who aren't really interested. And I take it this person is of no relation? simoncosgrove.net/live/

>If you want people to recognize you then just use 1 name exclusively.

Okay, should I just have called myself God upon birth or something? Is THAT your idea?

Is it really common for white people raised in Indonesia to not speak English as their first language?

Why would it be? It's INDONESIA. They speak Bahasa Indonesia Or Javanese as their lingua franca and whatever billion other fucking sub-languages their islands have.

[math]\sin(x)=\frac{1}{2i}\left( e^{ix}-e^{-ix} \right)[/math]
[math]\cos(x)=\frac{1}{2}\left( e^{ix}+e^{-ix} \right)[/math]

[math]\sin^2(x)=-\frac{1}{4}\left( e^{2ix}-2+e^{-2ix} \right)[/math]
[math]\cos^2(x)=\frac{1}{4}\left( e^{2ix}+2+e^{-2ix} \right)[/math]

[math]\sin^2(x)+\cos^2(x)=1[/math]

Well generally European expats still tend to speak English natively in the colonies (South Africa, Hong Kong, etc.

That's Junior High math, user.
[math]
\sin ^2 (\alpha) + \cos ^2 (\alpha) = x_{\alpha}^2 + y_{\alpha}^2 = 1
[/math]

Fuck me dead.

Define a circle as 360 degrees and then you BEAT your students with all this other shit?

360 degrees was an ARBITRARY CHOICE you FUCKING MORONS.

A circle needs AT BARE MINIMUM 9 DEGREES BEFORE YOU CAN CALL IT A FUCKING CIRCLE.

2.25° per circle

Sure, you can use ° as the 'glyph/sigil/rune/letter/unit/pineapple'

Whatever the fuck makes you guys happy.

2.25 = 9 circles

> Define a circle as 360 degrees
A circle is the set of all points equidistant from the center.

Genius, why didn't 'I' think of that.

A Full Complete Circle Only Has One Degree.

> A Full Complete Circle Only Has One Degree.
What the fuck are you talking about?

A circle is the set of all points equidistant from the center.

1 is the greatest number and the 'center of all points that are not zero'

this is why 2pi sounds like 'stupid'

Correct.

It can be used to define sin and cos, alongside with sin and cos of sum formulas, I think these 3 equations uniquely determine these 2 functions

Use Laplace transforms

Take the unity circle and do implicit differentiation on the coordinates of a point on its circumference.

upcoin.com/?ID=4b1a0f0c

Let's look at the graph. The peak is 1, and you can see the bottom graph is always 0. When 1 is 0.5, the other is 0.5 too. QED

Pythagorean: [math]a^2 + b^2 = c^2[/math]
trigonometry:
[math]a = c ( \sin \theta )[/math]
[math]b = c ( \cos \theta )[/math]
substitute these into Pythagorean, and Bob's yer uncle.