help-27

[rancid cave]

"breath air" 🗣️

[boreal helm]

Do u know

Every breath u take

[rancid cave]

Is money

[boreal helm]

Brings u closer towards your end

[rancid cave]

Oh

[restive river]

btw my original question was 'best advice for being best mathematician' 💀

conclusion = money

[rancid cave]

I'm gonna start taking more breaths now

[boreal helm]

Lol

💀☠️

Fr bro u body can't heal the dead cells completely

Within your life your body

[cold bone]

Mathematicians don't make much money right?😶

[boreal helm]

Replaces yourself with somewhat a underperforming version of urself

That's why we die

💀☠️

[boreal helm]

They make

By becoming professors

[rancid cave]

You can earn more by doing business

[restive river]

bro one of the best mathsmatician got 20 billion doller as net worth 💀

[boreal helm]

Fr

See

U can earn money

By maths

[restive river]

fr

[boreal helm]

If u solve the million dollar problems

Wanna earn 7 million

[rancid cave]

🗣️ 🔥 🔥🔥

[boreal helm]

Solve 7 of them

Fr 🔥🔥🗣️🗣️🗣️🚨💯

[restive river]

IMMA SOLVE THAT

[cold bone]

Invest in Stocks by maths

[rancid cave]

Bet

[restive river]

QUANT

[cold bone]

seems like some mathematician did that thing in the past

[boreal helm]

Fr

[restive river]

wait so whats tue question?

[rancid cave]

Even my 4 yr nephew can solve those questions

[boreal helm]

Bro's gonna solve 7 of them

Fr

[restive river]

bruh

prove why 1+1 = 3 💀

[boreal helm]

💀☠️

Not gonna cap

[rancid cave]

Because of the space time continum

1+1=3

Ez

[boreal helm]

Each million dollar problems needs a lot of expertise in specific field of math

[restive river]

3=>

[boreal helm]

If u solve 7 of them

[rancid cave]

Now gimme mah $1,000,000

[boreal helm]

This means u are the god of 7 specific fields

[cold bone]

any of them is ever solved or not?

[boreal helm]

Like one is bout topology
One bout analysis and one bout algebra

[rancid cave]

My pet rabbit just solved 4 of those questions

[boreal helm]

See hypothesis or conjectures

[rancid cave]

🐰

[restive river]

bro but i dont understand... does the question have the mark scheme?

[boreal helm]

Lol

[restive river]

HOW CAN U CHECK THE ANSWER WITHOUT MARK SCHEME 💀

[boreal helm]

💀☠️

[restive river]

💀

[boreal helm]

No problem

[rancid cave]

You can prove it

[boreal helm]

First solve it

Imma gonna provide a marking scheme then 💀☠️

[restive river]

bro who made that questoin 💀
does that guy know the answer?

💀

[boreal helm]

Maths is diff

[restive river]

imagine making a question that can't be solved by himself 💀

[boreal helm]

U cannot use something without proving it's true

Even if it works for some trillion or quintillion values

💀☠️

[restive river]

💀

[boreal helm]

Fr

[cold bone]

fr

[restive river]

fr

[boreal helm]

Take any conjecture

And tell me

That it fails for less than trillion or quintillion values

💀☠️

Fr

[restive river]

💀

[boreal helm]

But no

Prove it 🤓 for every thing even if it's out of our computational limits

Fr bro 💀☠️

[restive river]

bro im in library rn and a stranger next to me just farted 💀

[boreal helm]

Lol

[restive river]

🤓

[boreal helm]

Fr

[restive river]

fr

/close

/close

[boreal helm]

No

Nuh uh

[restive river]

da fuqqqqq

[boreal helm]

.close

[restive river]

.close

[devout snow]

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[lyric moat]

For each of the following requirements, write a verse in a language that has a two-local relation sign R and a relation sign =, so that the verse satisfies the structure M=(W^M,R^M) if and only if it fulfills the requirement -
A. R^M equivalence ratio on W^M
B. R^M Partial order relation on W^M
C. R^M linear order relation on W^M

any help?

[devout snow]

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@lyric moat Has your question been resolved?

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[sand shard]

Hi! I just wanted to check if my answers are correct for this problem (its arithmetic series)

1.) even integers between 1 and 101
(My answer here is 2250)

2.) number between 1 and 81 which are divisible by 4
(My answer here is 840)

Thanks in advance!

[winter patrol]

show work

[winter patrol]

values on the page are fine

you misstated your result here

(you typed 2250 instead of 2550)

[sand shard]

Ah right sorry! But it’s correct right?

[winter patrol]

values on the page are fine

[sand shard]

Ok! Thanks! ^______^

[rancid cave]

you should do .close

[sand shard]

.close

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[pearl geyser]

ermm whats Z in maths

[rancid cave]

are you learning Sets?

[pearl geyser]

idk 😭

just doing homework

[rancid cave]

can you show where it was used

[pearl geyser]

and uhh

they says x is uhhh

lemme translate

[winter patrol]

this fancy $\Z$?

[woven radish]

ℝαμΩℕωⅤ

[pearl geyser]

it belongs to z

yeah

fancy ahh Z

[rancid cave]

yeah thats the interger

like its the set containing all Integers

[mild sorrel]

Z denotes the set of intergers.

[pearl geyser]

ermm

ty

[rancid cave]

[pearl geyser]

ty

[rancid cave]

do .close

[devout snow]

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[lunar harbor]

[In response to this: #help-12 message]

@clever spruce I was wrong - I picked f(n) that doesn't even output integers 💀

In fact, the statement is true - see https://math.stackexchange.com/questions/2527439/if-an-infinite-sequence-diverges-to-infinity-does-it-mean-that-all-of-its-infin

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[royal laurel]

Hello

[rancid cave]

You dont start a help channel with just a "Hello"..

[royal laurel]

I have a question about matrix multiplication.

I was taught some counter-intuitive and rote way to operate it at school.

But I'm wondering if I can consider the multiplication of two matrices as applying transformation to vectors.

[royal laurel]

for example, the left side of the equation outlined by red ink, involves a matrix multiplication

nobody wants to mess with it damn

[gloomy gazelle]

the whole thing is outlined by red ink..?

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[turbid flame]

Hey guys, I didn't know how to tackle this question (5.4) at all. All I could think of is by solving the derivative of f, but I don't think that's the solution they want us to do. Is there something I'm missing here - a way to "observe" the answer by the nature of the equation they've provided?

[turbid flame]

Here was the graph I sketched in 5.3 if that helps

[trail eagle]

For a product of 2 things to be positive, they need to have the same sign.

I.e. $ab\ge 0$ iff $a,b \ge 0$ OR $a,b \le 0$.

[woven radish]

Azyrashacorki

[trail eagle]

So that means that if x*f'(x) >= 0,

Either x and f'(x) are >=0

Or x and f'(x) are <= 0.

From the graph, can you spot when f'(x) >= 0 ?

[turbid flame]

Hmm, my calculus isn't so good so I'll make a guess and say that it's by the y intercept?

How are you able to make a conclusion based off of the graph f?

[trail eagle]

The sign of f' tells you if the function is increasing

If f'(x) is positive, then f increases at x

So from the graph do you think you're able to tell when the function is increasing?

[turbid flame]

Yeah, on the graph f, it increases from -infinity and approaches the x asymptote, 1

and then from 1 (not exactly 1) it increases again, approaching positive infinity

[trail eagle]

Yep exactly, so it's not really decreasing anywhere right?

[turbid flame]

I don't think so

[trail eagle]

Good. Now if we go back to this.

In the first case, we know that f' is always >= 0 (where it's defined), so what condition do you need on x?

[turbid flame]

Ah I see why it can't decrease. I was gonna ask why it isn't decreasing opposed to increasing

for x to be positive?

Hmm wait no that's wrong aint it

[trail eagle]

Yep. So we need x>= 0, without taking x=1 because f is not defined there.

[turbid flame]

Ahhhhhhh

[trail eagle]

And then the second case is never met, since we never have f'(x) <= 0

So we're done

[turbid flame]

I understand where the logic comes from but could you explain why the derivative function is positive?

Ah wait nvm

Cause the graph increases never decreases

so f'(x) cannot be < 0

[trail eagle]

Yup. As an aside, if you compute the derivative, it'll be like 1/(x-1)^2, and this is always positive

But from the graph here it's fairly straightforward to see once you've labelled everything

[turbid flame]

👍 Thank you very much :)

.close

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[storm atlas]

this is my equation that iwas supposed to solve, i can't think of how to get rid of the exponents

[haughty thicket]

put x+3=t^2

[storm atlas]

wait

let me do that

[storm atlas]

okay i did it, and got a cubic equation

i assume i can solve for each value

and check if it satisfies the answer

[haughty thicket]

you can

its gen 1 or 2

the 1st root

[storm atlas]

on a sidenote, is there another way i can do it without letting x+3 be t^2

[haughty thicket]

idk tbh

[storm atlas]

alright its okay

thxxxxxxx

closing this if no one replies in 5

4

3

2

1

.close

[devout snow]

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[storm atlas]

.reopen

[devout snow]

✅

[storm atlas]

oops haha i saw someone type

[cold bone]

what do you need?

[storm atlas]

solving this

cat gave me a solution

but i was thinking if there was a way that i could do it without subsituting x+3 with t^2 to get rid of the fraction exponentws

[cold bone]

any method other than this will have much trickier calculation

[storm atlas]

yea i think so

[cold bone]

cat's solution is the most simplest

[storm atlas]

i dont really think pre u courses give a crap about how you are solving the question as long as it abides the rules

[cold bone]

idk about that btw

[storm atlas]

middle school exams had a certain way i had to solve my maths questions according to

ill just consult my lecturer tmrw haha

[cold bone]

kk

[cold bone]

noice

[storm atlas]

thx man

[cold bone]

i didn't helped

[storm atlas]

dw

.close

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[violet blaze]

can anyone help w this

[acoustic leaf]

in general a rational function will have an oblique asymptote if the degree of the numerator is higher than the degree of the denominator by 1

[violet blaze]

so im guessing iii and iv?

or am i wrong

[acoustic leaf]

yes

[violet blaze]

ok can also

is this correct? or is it iv

Just wanna make sure

[acoustic leaf]

if you plug in -2/3, you should get 0 on the numerator for any function that has that x-intercept

[violet blaze]

so it’s iv? or i

[devout snow]

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[vivid ember]

how would I perform a test interval?

[devout snow]

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[bold geyser]

Hii! I’m stuck on this 😭 I got angles 1 and 2 but at struggling on 3

[placid narwhal]

Im guessing the arrows mean those 2 sides are parallel

Use that

[bold geyser]

Yeah, they’re parallel, would that make 3 alternate interior with something else then?

[umbral shuttle]

,rotate

[umbral shuttle]

well for now ignore all the other lines other than the two parallel lines and one of the lines running down the middle

so what do the two angles I marked look like?

[bold geyser]

Ohhh

[upper schooner]

(alt: think about the "other Z" and )

[bold geyser]

Oh 😭😭 thank u so much, it clicked 😭😭

It just wasn’t computing for a quick second ^^ tysm!

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[winged stream]

for this question do i need to set up an income stream integral?

[tall knoll]

you don't need to, but you can

[winged stream]

would that be the correct integral?

for PV

[tall knoll]

this assumes the salary is being paid continuously

[winged stream]

yea in the question it says compounded continously

at bottom of first paragrah

[tall knoll]

the question says the interest is compounded continuously

the salary is paid monthly

[winged stream]

oh

so i need to multiply 6000 by 12? to get yearly salary?

[tall knoll]

that would get you the yearly salary but that won't really help you

[winged stream]

or divide .12 by 12

[tall knoll]

there's a discrepancy between your interest compounding period and your payout frequency

[winged stream]

the 120?

ohh i get it

the 120 is months but the 0.12 is yearly

so i need to make them equal in terms of time?

[tall knoll]

that too

[winged stream]

i can do 0.12 divided by 12 to get 0.01 interest per month

[tall knoll]

i feel like this question becomes much simpler if you just convert the continuous rate into a monthly rate

[winged stream]

how would that be done?

[tall knoll]

how have you been taught to convert between compounding frequencies before?

[winged stream]

like from comounded anually to continously and vice versa?

[tall knoll]

sure

[winged stream]

no, we just learned how to do each speretly

separately

[tall knoll]

that's inconvenient

[winged stream]

wouldnt that give u a different answer tho?

cuz continussly give u the most money

[tall knoll]

for the same numerical value, yes

12% continuous provides more money than 12% annual

[winged stream]

yea

[tall knoll]

but there's an equivalent annual rate that provides the same amount (each year)

it'll just have a higher number than 12

[winged stream]

oh ur thinking of changing the % to a monthly rate that is not 12% but will match it

[tall knoll]

that's what i mean yes

[winged stream]

yea thats beyond my courses scope

[tall knoll]

at the end of each month, your 12% continuous rate will have accrued some amount of interest; there's an equivalent monthly rate that accrues the same amount of interest each month

well that's dumb

[winged stream]

so i need to convert the 12% to 1% to match the 120 months and the 6000$/month salary

so everything is in terms of months

[tall knoll]

sure

[winged stream]

now im here

[tall knoll]

again, you can't do this because the salary is not being paid continuously

if the salary was being paid at a rate of 6000/month then this would be acceptable

[winged stream]

but it is being paid 6k/month

[tall knoll]

but it's being paid all at the same time, at the end of the month

the compounding is continuous, but the withdrawal is only at the end of the month

[winged stream]

oh

[tall knoll]

hence why i wanted you to convert the interest rate to a monthly rate to match

[winged stream]

at the beginging you said we dont need to make this type of integral is any integral at all

what is the other way we can solve this cuz ur saying this integral wont work

[tall knoll]

the other way is to convert the continuous rate to the equivalent monthly rate

then it's a rather easy present value problem

[winged stream]

so ur saying the pic of the integral i just sent wont get me the right answer right?

[tall knoll]

it will not

[winged stream]

but i dont think its that serious tho

like im trying to say i dont think it matters that much if the 6k is being paid once

another idea

what if we used a finite geometric seiris equation

[tall knoll]

that will be the end result of my suggested solution, aye

[tall knoll]

that probably works

gimme a minute

[winged stream]

ok

i get 421383.384

which should represent the intial investment (lump sum payment) the business has to make to pay the employee 6k per month for 10 years (or 120 times)

[tall knoll]

my answer is slightly different (using a different method)

[winged stream]

what did u get?

[tall knoll]

417190.55

[winged stream]

wdym by different method? did u do the thing u were saying before (chainge from continous to monlthy)?

[tall knoll]

i did

,calc 421383.384*e^(-0.01)

[woven radish]

Result:

4.1719054927386e+5

[winged stream]

if i solve

this

[tall knoll]

ah i see the discrepancy

[winged stream]

i get that which is closer to ur answer

so i do think that integral is correct

[tall knoll]

when you set up your geometric series, you need to factor out an e^-0.01 term

[winged stream]

why?

[tall knoll]

because the first payment happens one month in the future

the first term in your series is thus 6000e^-0.01

[winged stream]

ohk

so my integral is around 2000 off from ur answer

[tall knoll]

i assure you, the integral isn't going to get you there

[winged stream]

but then why is the answer so close to urs?

[winged stream]

this is from the integral

[tall knoll]

well they're all going to be close since e^-0.01 isn't a very large number

[winged stream]

oh

[tall knoll]

if you multiply this by e^-0.01 you get my answer

[winged stream]

ok

ima ask my prof about this shit cuz its been killing me for over 2 hours

thanks for all of ur help! it made me alot smarter than who i was before this convo

[tall knoll]

good luck moving forward

[winged stream]

hopefully i see u soon to tell u wat my prof says

bye for now

.close

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[heady coral]

I am struggling to intuitively understand the supremum in this exercise. The supremum cannot be the limit as ( n \to \infty ) because the function is decreasing. It also cannot be at ( n = 1 ) because ( -\frac{1}{3} ) is not an upper bound. I am therefore confused about the correct approach to find the supremum.

Let ( A = \left{ \frac{n^2}{2n^2 - 5} : n \in \mathbb{N} \right} ).

Calculate the limit:
[
\lim_{n \to \infty} \frac{n^2}{2n^2 - 5} = \frac{1}{2}
]

Calculating the first derivative, I have:
[
f'(n) = \frac{-10n}{(2n^2 - 5)^2}
]
This derivative is less than zero for all ( n ), indicating that the function is monotonically decreasing. Therefore, (\sup(A)) should occur when ( n = 1 ). However, evaluating the function at ( n = 1 ), we get:
[
f(1) = \frac{1^2}{2(1)^2 - 5} = \frac{1}{-3}
]

Additionally, evaluating the function for a few values of ( n ):
[
\begin{aligned}
n = 2, & \quad f(2) = \frac{4}{3} \
n = 3, & \quad f(3) = \frac{9}{13} \
n = 4, & \quad f(4) = \frac{16}{27}
\end{aligned}
]
This shows that the function is only monotonically decreasing for ( n \geq 3 ). Thus, there is a contradiction because the first derivative suggests it is decreasing for all ( n ).

[woven radish]

Mαя

[devout snow]

@heady coral Has your question been resolved?

[heady coral]

<@&286206848099549185>

[tawny pewter]

i think you got trolled by an asymptote at $\sqrt{5/2}$

[woven radish]

pola_touche

[heady coral]

but, A is a subset of R, A is not empty, and the limit of A exists, then, A is bounded, so, by the completeness axiom, the sup(A) exists in R

[tawny pewter]

don’t make this complicated the sup is f(2) proof by desmos

[heady coral]

thank you

I think that finally I know how to proceed

.close

[devout snow]

Channel closed

Closed by @heady coral

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gentle hatch]

can someone

explain the steps to me to get to that answer

[warm breach]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[gentle hatch]

I mean i tried to do it

since i know what equals what

[warm breach]

rewrite cosec as 1/sin

[gentle hatch]

alr did that

then i rewrote cot(u) as cos(u)/sin(u)

then multiplied the cos(u) to get cos^2(u) / sin(u)

and the got (1 - cos^2(u)) / sin(u)

thats as far as I was able to get

idk how to simplify or change it any further from here

[rancid cave]

what's the relation between sinx and cosx?

[boreal helm]

Oh

[gentle hatch]

sin^2(x) + cos^2(x) = 1??

that one?

[rancid cave]

Yes

[boreal helm]

Yes

[rancid cave]

Now apply that

[gentle hatch]

how tho

[boreal helm]

Think

[gentle hatch]

wow

[boreal helm]

U have a massive muscle in your cranium

Use it

[gentle hatch]

fair

[rancid cave]

What will be the value of sin^2(x) using this?

[boreal helm]

Yes ok we help

Tell this

do u know what cotx is in terms of sin and cos

[gentle hatch]

am i supposed to figure this out or can i use a calculator

[boreal helm]

Write it

[rancid cave]

He already did that

[boreal helm]

Write cot u in terms of sin and cos

So what u get

[rancid cave]

.

[boreal helm]

cosu.cosu/sinu

And cosec is 1/sinu

@gentle hatch Now think

We have

[rancid cave]

He got $/frac{1-cos^2x}{sinx}$

[boreal helm]

Same denominators

Think

Okokok

[gentle hatch]

bro pls one at a time

[rancid cave]

Meh

[boreal helm]

sin^2x+cos^2x=1

[rancid cave]

How to do fractions again?

[boreal helm]

Ok u tell imma come late

[gentle hatch]

i am confused

i see that it has something to do with the rule you talked about

but i dont see how that applies here

since how would i get csc(u) to become sin^2(x)

[rancid cave]

Just write down your progress

[gentle hatch]

alr

this is as far as i got

[rancid cave]

Alright so

How do you write sin^2x in terms of cos^2x?

[gentle hatch]

1 - cos^2(x)

?

like this?

[rancid cave]

Yes

And isn't that your numerator?

[gentle hatch]

oh yeah

OHH

ok bro

i see it now

tysm

[rancid cave]

[gentle hatch]

lmao

.close

[devout snow]

Channel closed

Closed by @gentle hatch

Use .reopen if this was a mistake.

[boreal helm]

O

It got Solved

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[latent mulch]

Why isn't sin(180-a) equal to cosA and cos180-a equal to sin a?

[polar wagon]

Because they're complementary over 90 degrees. Think of a right triangle.

[latent mulch]

Could ya explain further?

[polar wagon]

I'll draw a picture. Give a second. It'll be much easier to visually show.

[latent mulch]

I was also thinking of the same

But why aren't they equal

Since they point to the same point

[cold bone]

wait what?
cos(180-a) is not equal to sin(a)

at least not for all the angles

[latent mulch]

What is the formula

It's-cosa

[cold bone]

cos(180-a)=-cosa

[latent mulch]

Yes

So it is not sina

[cold bone]

huh?

why?

-cosa is -cosa

[latent mulch]

That's what I'm asking

Wait

So cos180-a = -cosa

[boreal helm]

Yes

[latent mulch]

But why isn't it sina

[boreal helm]

Cz cos is -ve in 2nd quad

[latent mulch]

Or -sina

[boreal helm]

See

[latent mulch]

Bruh

[boreal helm]

Sina and cosa are complementary

[latent mulch]

Yess

[boreal helm]

That is

If we say

sina=k

Then cos(90-a) is k

[latent mulch]

Yes

[boreal helm]

Now see

cos(180-a)

cos(90+(90-a))

we know

cos and sin is complementary

[boreal helm]

so cos(90+a) will be -sina

[latent mulch]

Someone said that this isn't a triangle of measure 180-a instead it's 90-a

How would you draw a triangle for 180-a on the unit circle @polar wagon

[polar wagon]

Do you mean starting at 180 and then moving clockwise back a degrees?

[latent mulch]

Yes

How else?

Is there another way?

[boreal helm]

See I wrote everything

[latent mulch]

Yeah

I got what you're thinking

That's how I also approached my question first

[latent mulch]

Whats this bruh

[boreal helm]

Read everything and ur question will get answered

[latent mulch]

Sure?

[boreal helm]

Yes try

[latent mulch]

I can't read the angle measure

On the left

[boreal helm]

90+theta/180-theta

[latent mulch]

I'll try

Ok

Whats that after cos(90-(a-90)@boreal helm

[boreal helm]

cos(90-k)=sin(k)

[latent mulch]

Shouldn't cos(90-(a-90) = sin(a-90)

@boreal helm

[boreal helm]

Yes

But what is sin(a-90)

[latent mulch]

And if we take negative

[boreal helm]

Think

Yes

[latent mulch]

-sin(90-a)

-cosa

[boreal helm]

Yes

[latent mulch]

Look

[boreal helm]

Did u understand?

[latent mulch]

I get what you're saying

And that was also jow I tried to understand the thijg

But

[boreal helm]

Okok

[latent mulch]

But

[boreal helm]

Yes

[latent mulch]

I want you to tell me

[boreal helm]

Ok

[latent mulch]

Whats wrong with what I said

[boreal helm]

Oh i see

[latent mulch]

You took so much time bruh

[boreal helm]

Bro appreciate him

[polar wagon]

Well, I can make the pictures easy to look at or I can make them quickly.

[boreal helm]

He is giving u good visual

Explanation

[latent mulch]

A very good visual representation

Neat

Immaculate

[boreal helm]

cos(180-a) is not sina

[latent mulch]

More aesthetic than anywhere

[boreal helm]

Bro because we just proved it that it's not

[latent mulch]

Haha

[boreal helm]

• they are not supplementary

They are complementary

[latent mulch]

But here's the thing

Look

[boreal helm]

U can try for the sin also

[latent mulch]

What would be the coordinate for 180-a?

From the diagram above

[polar wagon]

Use the image I just made. See how the 180 causes a reflection over the y axis.

[boreal helm]

It would be in 2nd quadrant

Where x is -ve

But y is +ve

And in 2nd quadrant cos is -ve

[latent mulch]

Wait

Ok

[boreal helm]

That's why cos(180-a) is -ve

[latent mulch]

What are the coordinates for 180-a

[boreal helm]

Wait imma give u clear pic

[latent mulch]

Just tell me the coordinates first

[polar wagon]

First, what are the coords for just a?

[boreal helm]

A clear picture

[latent mulch]

-cosA, sina

[latent mulch]

-cosA, sina

[polar wagon]

That is for 180-a

[boreal helm]

Yes

[latent mulch]

And why not for a?

[boreal helm]

see for a

Bro

[latent mulch]

Why are we reflecting it on the first quadrant

[boreal helm]

It will be simply cosa,sina

cos a is cos a

And sin a is sin a

[latent mulch]

For a in the first quadrant

[boreal helm]

Yes

Yes

Yes

[latent mulch]

And coordinates for 180-a

[boreal helm]

Yes so 180-a comes in the 2nd

[latent mulch]

Yes it does

[boreal helm]

Refer the pic

[latent mulch]

What do you think my confusion is?

[boreal helm]

Your confusion is

Why

Cos(180-a) is not

sina

And why

Sin(180-a) is not cosa?

Right

[latent mulch]

From the triangle we drew first

Yes

Without taking the triangle frawn on the first quadrant into consideration

[boreal helm]

See

U have taken theta

[latent mulch]

Hmm

[boreal helm]

From the first quadrant

Right?

[latent mulch]

No

[boreal helm]

Let me explain

Y and x axis intersect and form four quadrants

[latent mulch]

I drew theta counter clockwise fro the 2nd quadr

[boreal helm]

The first one signifies angles from 0 to 90

[latent mulch]

Its getting so basic lol

I love it

[boreal helm]

2nd one from 90 to 180

[latent mulch]

Yes

[boreal helm]

3rd one from 180 to 270

And 4th one from 270 to 360

Now see if we take theta from first quadrant

0<theta<90

[latent mulch]

Ok

[boreal helm]

And we subtract it from 180

[latent mulch]

Theta acute

That also gives 180-a

Yess

[boreal helm]

So 180-theta

[latent mulch]

Keep going

Yes

[boreal helm]

Will lie b/w 90 and 180

[latent mulch]

What will?

[boreal helm]

Now

180-Theta

180-theta will

[gray mirage]

Something that might help your intuition:
play with the a slider and see the different phase shifts of sin compared to a normal cos:
https://www.desmos.com/calculator/jkwgiikho9

[boreal helm]

See

theta is b/w 0 and 90

Now if I subtract if from 180

Don't u think 180-theta will lie b/w 180 and 90

Now if 180-theta lies b/w 90 and 180

[latent mulch]

I'm lookin

[boreal helm]

It means it lies in 2nd quadrant

As 2nd quadrant signifies angles from 90 to 180

[latent mulch]

How would that look graphically?

[boreal helm]

Okok

U know lines

[latent mulch]

Yes

Hahah

[boreal helm]

This is the point

That's why 180-theta signifies 2nd quad.

As angles b/w 90 and 180 are signified by 2nd quadratic with respect to postive x axis

[boreal helm]

Yes tell

[latent mulch]

Here it is still in the first quad

[boreal helm]

Check the angle what is it

It's simply theta

And see the other one

[latent mulch]

On the right

[boreal helm]

What is the angle in iy

It*

[latent mulch]

180-theta

[boreal helm]

That's what I am saying

[latent mulch]

But ti starts from the first quadrant

And ends at 2nd

[boreal helm]

Which

[latent mulch]

180-a in the edited image

[boreal helm]

See im just giving u eg with reference to the angle

[latent mulch]

Waut

[boreal helm]

I am just saying that

[latent mulch]

So when we say something lies in the 2nd quadrant

Or any quadrant

We say

[boreal helm]

When u move 180-theta anti clockwise with respect to +ve x axis

U reach the 2nd quadrant

[latent mulch]

That terminal side is on that quadrant

[latent mulch]

Yes

I get it now

Ok

[boreal helm]

Now

We move theta

So we are in first

[latent mulch]

Yes

[boreal helm]

We move 180-theya

We are in 2nd

[latent mulch]

Yes

[boreal helm]

If we move 180+theta

We come in 3rd

And so on

[latent mulch]

Yes

[boreal helm]

But there is other definition too

Like see

[latent mulch]

So wait

Wait

[boreal helm]

Ok

[latent mulch]

If we move 180-a from the second quadrant we reach the first quadrant

?

[boreal helm]

If we move 180-theta from the 2nd quad?

[latent mulch]

Yes

[boreal helm]

Oh you mean from -ve x axis

And clockwise

[latent mulch]

Yes

[boreal helm]

Sure u will

[latent mulch]

Yes

Ok

But

[boreal helm]

We have one more definition

[latent mulch]

Ok

[boreal helm]

See this

If we move with respect to 90 degree

Aka the vertical

[latent mulch]

Wait

Lets see

[boreal helm]

We also reach the 2nd quad

[latent mulch]

I move 180 from the first quadrant

I reach the 2nd quadrant

[boreal helm]

Yes

With respect to x

[latent mulch]

And If we move theta counter clock wise

Since theta is acute

[boreal helm]

See measuring from +ve x axis u moved 180 u reached the 2nd quadrant limit

[latent mulch]

It stays in the same quadrant

[latent mulch]

Yes

[boreal helm]

If u keep on moving theta counter clockwise u will eventually reach every quadrant and then back to firsy

First*

See in other terms we can say

In first quadrant we have angle 90

[latent mulch]

That's a long revolution

[boreal helm]

If I add 90+something

It will reach me to 2nd quadrant

That's why we have 2 definitions

[latent mulch]

Lemme see then

So I want the coordinates for 180-a

I can either move a degress from the standard position

[late kernel]

Help with navier-stokes equations

[latent mulch]

And I'll have 180-a

[boreal helm]

What

The unsolved navier stokes ?

💀☠️

[late kernel]

Yah 🤣🤣

[boreal helm]

@late kernel #❓how-to-get-help

! occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[late kernel]

Would win the "Millennium prize" 🤣🤣

[boreal helm]

We also have a physics server

#old-network

You can join that from here

And get better help

[late kernel]

I am 17

[boreal helm]

Okok

@latent mulch

[latent mulch]

Same here

[boreal helm]

Did u understand

[latent mulch]

Not quite yet

[boreal helm]

Okok we continue

[latent mulch]

You tired 😅😅

Exhausted?

[boreal helm]

No

[latent mulch]

Or sm

[boreal helm]

No

[late kernel]

I just wanna understand "Rocket propulsion"

[boreal helm]

No

[boreal helm]

Variable mass system?

Bro

Make your help channel

@latent mulch

Where u have doubt

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[late kernel]

Quasi-linear pdes??

[latent mulch]

Lets see

So if I move theta from the 2nd quadrant

[boreal helm]

Check #odes-and-pdes

[latent mulch]

Then 180-a would also lie in the 2nd quadrant right?

[boreal helm]

Now anonymous u tell

For real

180-a would lie in the 2nd quadrant

Only

If a is b/w 0 and 90

[latent mulch]

180-a first quadrant?

No

Ok

[boreal helm]

2nd I meant

Now see cos(180-a(

[latent mulch]

So I move 180 from standard position

[boreal helm]

(180-a)*

What standard position

[latent mulch]

I reach 2nd quadrant

[latent mulch]

Like how we measure angles in the unit circle

[boreal helm]

U move 180-a from +ve x

Ookok

[latent mulch]

Like the vertex is the origin

[boreal helm]

Ok

Show me

[latent mulch]

Wait

[boreal helm]

So that I can fully get u understand

[latent mulch]

So this is my unit circle

Now if I move 180 degrees from here

[latent mulch]

From 0 degrees

I move here

[latent mulch]

Now I'm in the 2nd quadrant

Ok now that I'm here

I move theta degrees counterclock wise

Like this

Right

And I'm still in the second quadrant

And what would the measure of the other triangle be?

180-a

[latent mulch]

So this triangle would represent 180-a right?

@boreal helm

[late kernel]

Haha 😂 simple trigonometry

@latent mulch

[latent mulch]

So you know where I'm stuck?

[late kernel]

That theta!

[latent mulch]

?

So let's say I wanna draw a triangle on unit circle with measure 120

How do I do that?

[boreal helm]

Okok

[latent mulch]

Oh

Where were you

[late kernel]

😂😂 it's pretty simple

[latent mulch]

@boreal helm Look I have a better way to frame my question maybe

So I wanna draw a triangle for 140 on unit circle

K?

First of all how do you do that

And second of all

I want to find its coordinates

But I can also find its coordinates from 40 ° counterclock wise from 2nd quadrant

[late kernel]

Could u help me with sieberg-witten equations in string theory??

@boreal helm ??

[latent mulch]

You have to wait for that

[late kernel]

@latent mulch 👍🏻

[latent mulch]

I'm late

In my response

I would've said youve wait for a little more than half a decade

But I was late

[boreal helm]

What

Are u doing

[latent mulch]

Who?

[boreal helm]

@late kernel #❓how-to-get-help

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[boreal helm]

Don't u understand my guy

[latent mulch]

Help

[boreal helm]

@latent mulch ookok

[boreal helm]

Where were we

Bro

If u want to help him help

But don't ask

Your doubts

[latent mulch]

I can't help him

[boreal helm]

Nono

I am saying this to medhat

[latent mulch]

Oh

[boreal helm]

He is asking his doubts

It's your channel

[latent mulch]

Yeah

[boreal helm]

Ok so where were we

[latent mulch]

Here

[boreal helm]

Aah 120 degree unit circle

[latent mulch]

140

[latent mulch]

120 is 90 +30

Ok

But 120 can also be measure by 60° counterclock wise from the 2nd quadrant

[boreal helm]

Yes

It would be clockwise movement

[latent mulch]

So shouldn't their coordinates also be the same

[boreal helm]

Bro*

If u move from 2nd to 1st don't u think u are moving clockwise

[latent mulch]

Oh yeah

Clockwise

[boreal helm]

See we don't consider clockwise

Generally

We prefer to move anti clockwise in general notation

[latent mulch]

Yeah

[boreal helm]

That's why we say 90+theta is 2nd quad

When we move from +ve axis counter clock

[latent mulch]

If its some checkpoint plus theta then we write the function in terms of tehta

[boreal helm]

And 180-theta bcz here we move clockwise from -ve x axis

[latent mulch]

Ok

[boreal helm]

Ask if any more doubt

[latent mulch]

So

120 is just 90 + 30

So we write in terms of 30

Cuz its just 30

Just on a different quadrant

Right

?

@boreal helm

[boreal helm]

Yes

We write in terms of 30

As it's in first quadrant

[late kernel]

@boreal helm could u help me with "Kähler Potential and Superpotential"?

[latent mulch]

Ok

Oh ok

[latent mulch]

Go on

I get it now

[boreal helm]

Bro

[latent mulch]

Wait

[boreal helm]

Imma

Get this guy

Oof

[latent mulch]

Hahah

Ok boss

[boreal helm]

3rd and last time in saying

[latent mulch]

I'll wait

[boreal helm]

🙂

@late kernel #❓how-to-get-help

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[late kernel]

@boreal helm okay?

[boreal helm]

This is anonymous channel

Not urs

🙂

[late kernel]

it;s tough i mean it;s calabi-yau manifold ? QFTs?

[boreal helm]

Bro I m

Gonna

[late kernel]

nvm i'm leaving..

[boreal helm]

Make your other channel don't interfere

Here

@latent mulch

Any other doubt

[latent mulch]

May I continue

[boreal helm]

?

[late kernel]

yah

[boreal helm]

Okok

[latent mulch]

Havent cleared it yet

[latent mulch]

Just listen to me

[boreal helm]

This guy is a menace

[boreal helm]

Okok

U tell

[latent mulch]

Ignore

Soo

When I say 120

It's basically just 30

Just on a different quadrant

Right

?

@boreal helm ?

[boreal helm]

Yes

[latent mulch]

Ok

[boreal helm]

Ist 90+30

[latent mulch]

So since 30 lies in the first quadrant

[boreal helm]

It's just 30 w.r.t the y axis

[boreal helm]

yes

[latent mulch]

Imma compare it's coordiantes

With 30 in the 2nd