help-23

[dim wraith]

Expect random variable be more general concept for you in the future

[safe radish]

@chrome knoll Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[next wedge]

Hi! Trying to do a delta math problem but I’m having issues with factoring… seems like the trinomial won’t factor

[stoic jacinth]

Once you get to this point, you can square the five and then try subtracting that 25 from both sides! that should give you -45 for that last term and then you should be able to factor out a 3 from all the terms and things should work from there 🙂

[next wedge]

Ok, tysm!!

.close

[safe radish]

Channel closed

Closed by @next wedge

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[frail osprey]

anyone able to help me with understanding a question I had on a calc 1 exam about indeterminate form using l hopital rule?

[obtuse loom]

Send the question and the work you’ve done!

[frail osprey]

I just finished the exam so I’m going off of head space but i can tell you the process and vaguely the problem

x —> ♾️ was the limit. (1-x^9)^x (something like that)

On my practice exams were kept finding the anti derivative until it finally worked out but if it was an endless loop we would divide it by 1/x as the denominator so that’s what I did

and it become ln(1-x^9)(09x^8) / 1/x

nvm forget it i’ll just use a practice exam question for example since i don’t recall it

after the ln(1-4/x) / 1/x I’m not sure what exactly to do

[quiet plume]

Well now you have a 0/0 form, so you can use l'Hopital's rule.

[frail osprey]

I think I know where I messed up now, i didn’t the know derivative of 4/x was 4x^-1 and I put it as positive

I was only doing problems that just used l hopital rule where I could just derive constantly without being in an endless loop but this question had you add 1/x and I didn’t exactly know what to do with it when deriving

thank you

.close

[safe radish]

Channel closed

Closed by @frail osprey

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hollow hound]

so, i have two question to check if what i did is right.

So, i need to find the directional derivative for f(x,y) = x/(x^2 + y^2) at (1,2) with direction v=(3,5)

i found some theorem from the book and got: df/dv(1,2) = <9/(25*sqrt(34) , -4/(5*sqrt(34)))>.

[hollow hound]

but i got this after spending about an hour figuring out how to do it myself

i calculated the tangent plane with partial derivatives then found the normal vector for the tangent plane which was N = <3/25, -4/25, -1> then built the plane with it to get z = (3/25)x -(4/25)y + 2/5

then i used the given vector v=<3,5>, turned it into <3,5,0> to use it with the normal vector of the tangent plane N= <3/25, -4/25, -1>, moved that plane to (1,2,1/5) to then get the plane 5x-3y+1.08z = -0.78, tried to do some more stuff to get some sort of curve for the intersection of f(x,y) and the latter plane to get some nice curve to use for the derivative but i was just defeated so i just used some theorem from the book to calculate the directional derivative at that point and got that it was df/dv(1,2) = <9/(25*sqrt(34) , -4/(5*sqrt(34)))>.

My question is, is it futile trying to get some sort of parametrization to get the curve of that intersection to then calculate the derivative at that point?

i figured i could do something like that analogous of how we calculate the partial derivative for some function but i just couldn't get a nice curve

[tardy mango]

Without reading this, directional derivatives are scalars and not vectors

You're better off using
$$D_u f(a,b)=\nabla f(a,b) \cdot \hat{u}$$

[flat frigate]

Civil Service Pigeon

[tardy mango]

ig you can parameterise the curve, but the clean one is just the line $(x(t), y(t)=(1,2)+tu$

[hollow hound]

ohhh, yeah, the theorem was the dot product which is a scalar, my bad

[flat frigate]

Civil Service Pigeon

[tardy mango]

then take $f(x(t), y(t))$ and differentiate at $t=0$

[flat frigate]

Civil Service Pigeon

[hollow hound]

yeah, this is exactly the theorem i found i just didn't apply it well, let me correct it

yeah, the solution should be -11/(25*sqrt(34))

[tardy mango]

,w directional derivative of \frac{x}{x^2+y^2} at (1,2) in the direction of (3/5, 4/5)

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[tardy mango]

whatever

[hollow hound]

wait, how is that the intersection curve? i got something like

after "geogebraing" it

[tardy mango]

the line is the path you follow when moving from (1,2) in the direction of v

so you're effectively turning the two-variable function into a one-variable function

namely $g(t)=f\left(\mathbf{r}(t)\right)$

[flat frigate]

Civil Service Pigeon

[tardy mango]

and ofc the directional derivative is just g'(0)

Hello?

[hollow hound]

i don't know if you didn't understand me or i didn't understand you, i guess i didn't understand you, are you talking about the tangent (the derivative) of whatever parametrization i could have found from the intersection of the plane with f(x,y) (let's call it g(t) like you mentioned)?

[tardy mango]

this parameterisation approach is the formal definition of the directional derivative

I'm saying to set $\mathbf{r}(t)=(1,2)+t \cdot \mathbf{\hat{u}}$ (the line through $(1,2)$ in the unit direction of $\mathbf{v}$), define $g(t)=f\left(\mathbf{r}(t)\right)$, and then $g'(0)$ is the directional derivative

[flat frigate]

Civil Service Pigeon

[tardy mango]

$D_{\mathbf{u}} f=\nabla f \cdot \mathbf{\hat{u}}$ is just a shortcut derived from this definition (apply the chain rule to $g'(t)$)

[flat frigate]

Civil Service Pigeon

[tardy mango]

my point was that you could have found a curve and differentiated (it's fine in a conceptual sense)

but you should've used the simpler line parameterisation rather than a plane intersection

[split kayak]

Im not precisely following, why are we talking about curve parametrizations for a directional derivative? I assume it has something to do with the geometric representation of it-

[tardy mango]

iirc OP likes the idea of parameterising things explicitly a lot

[split kayak]

uh.

[hollow hound]

right, i think i understand a bit what you mean, i'm just not too familiar about your last step letting g(t) = f(r(t)) but i'll think about it, i guess that would be f(1,2) when t= 0 which can be useful for when i try to calculate the derivative for df

[hollow hound]

i'm just using what's familiar to me

[hollow hound]

in class when we calculated the partial derivative for x, y aor any other variable of a function we got a nice parametrization for our function which we could use to calcualte the derivative

[hollow hound]

yeah, i think this is making more sense now

[split kayak]

Id assume that this idea becomes pretty apparent if you write down how r(t) looks like if written as ix(t) + jy(t).

[hollow hound]

yeah, i didn't think of it that way since i very rarely write a plane function in vector form, it's always as an equation y = whatever * x

thanks, i think i got the idea now @tardy mango @split kayak

.solved

[safe radish]

Channel closed

Closed by @hollow hound

Use .reopen if this was a mistake.

[tardy mango]

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[tranquil geyser]

Suppose $\kappa$ is a regular cardinal and $\langle \alpha_i : i \in \kappa \rangle$ is a strictly increasing sequence of ordinals. Show that $cf(\bigcup{\alpha_i : i \in \kappa}) = \kappa$.

[flat frigate]

toast

[safe radish]

@tranquil geyser Has your question been resolved?

[median sand]

What have you tried?

[tranquil geyser]

Hmm

I am not 100% sure how to approach the problem

but maybe i need to start with defeinitions

maybe i need to find a cofinal subset of the union, then show the minimum size is kappa

<@&286206848099549185>

is the idea to show its \leq kappa then \geq kappa

[tranquil geyser]

.solved

[safe radish]

Channel closed

Closed by @tranquil geyser

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[jolly sail]

hi, can anyone guide me through this

[jolly sail]

I can't picture my work at the moment, but here's what I wrote:

Observe that 9 > S > 0

Since A has supremum and infimum, there exists x_n and y_n such that lim n -> inf x_n = SupA and lim n -> inf y_n = InfA

maybe I can also write 1/2 <= y < 1, then:

-1/2 >= -y > -1

2 >= 1/y > 1

thats all I got, thanks in advance

[drowsy moss]

so you know 0 < 1/y - y <= 3/2

[jolly sail]

yessir I do

[drowsy moss]

can you show that 1/y - y actually attains 3/2?

[jolly sail]

don't we just merge the inequalities I wrote?

I can also write the expression in S as x(1/y - y)

its just that I am having a hard time proving the existence of supremum and infimum of S

2 <= x <= 6 btw

[drowsy moss]

so x(1/y - y) < 6(3/2) = 9
Then find a sequence of x in A and y in [1/2, 1) so that x(1/y - y) -> 9

[jolly sail]

aaaa

ok so for x, since x belongs to A, we can just use sequence x_n

but for y tho...

a sequence doesn't have to grab all values inside [1/2,1) right?

[drowsy moss]

correct, it just needs to be in the interval

[jolly sail]

ok so let p_n = 1 - 1/(n+2) be a sequence for y?

and before continuing, I jst wanna clarify smth, subsequence is basically a sequence of a sequence right?

[drowsy moss]

so p_n -> 1?

[jolly sail]

yes at infinity

n -> inf i mean

[drowsy moss]

then x(1/y - y) -> 6(1-1) = 0

[jolly sail]

a, then thats for the infimum 😅

so for supremum uh

q_n = 1/2 + 1/2n ?

ohh no i tripped because 1 is not in S

in y i mean

[drowsy moss]

good catch

[jolly sail]

q_n = 1/2 +1/3n this will do

[drowsy moss]

that works

[jolly sail]

ok so basically we have everything, just need to figure out how to write it down

[drowsy moss]

yep!

[jolly sail]

err I think we WILL be using supremum/infimum limit theorem

[drowsy moss]

which one is that?

[jolly sail]

err like if there exists a sequence that converges to c, then sup/inf exists

c is either upper/lower bound

of S

[drowsy moss]

ah, yeah

c is an upper (lower) bound of S, and a sequence in S converges to c, then c is the sup (inf)

[jolly sail]

yessir

since we already found that 0 < S < 9

for supS, can I just safely let c = 9 be an upper bound of S? Or do I need to do smth else b4 this

[drowsy moss]

you should show that S is bounded by 0 and 9

[jolly sail]

didnt we have this already

0 < x/y - xy < 9

[drowsy moss]

you showed it earlier. yeah.

[jolly sail]

sooo its safe right

[drowsy moss]

Yeah, I'm saying you should include it as part of your written proof.

[jolly sail]

alr maybe to make this clear, i can write my steps and send it here

wait

I can now take a pic lol

[jolly sail]

writing really does clear things out

because idk how to proceed lol

in the theorem, I need to find a sequence in S, not in x or y

bruh

@drowsy moss don't mind me 😅

[drowsy moss]

you have sequences for x and for y. put them together so you have a sequence in S

Just as a point, you said "lim n -> inf b_n" but didn't set it equal to anything.
and used the wrong sign for q_n

[jolly sail]

oh yea lol I didnt equate lim b_n, and wdym by wrong sign for q_n

oh

I fixeed the sign to plus

[jolly sail]

so abt this, lemme define a sequence w_n in S such that

w_n = a_n x (1/q_n - q_n)

and proceed from there?

then this means I need another sequence in S for the infimum right?

and im done?

ofc after applying the theorems and stuff

[drowsy moss]

yep

[jolly sail]

alrighty, thanks bro

cya

.solved

[safe radish]

Channel closed

Closed by @jolly sail

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[regal igloo]

hey

[regal igloo]

i need material for calculus basic to bit advance

[covert stone]

im sure you can find study materials or textbooks online

[regal igloo]

I need suggestions

[upbeat swan]

#book-recommendations

[regal igloo]

.close

[safe radish]

Channel closed

Closed by @regal igloo

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[balmy sky]

In part (c), i proved that inequality

how do i go on proving that minimum will occur for p_j = 1/365 for all j

[safe radish]

@balmy sky Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[real pumice]

.

[vague phoenix]

Hi, I have a question. If I have f continuous on [a,b], then how would I show it is bounded from above using bolzano weierstrauss? I just want a small hint of how to go, do not give me answers.

[vague phoenix]

I have worked out a bit:

[flat frigate]

Nefer

[gaunt elk]

that's a good start

[vague phoenix]

Yeah I just restated the definition of Bolzano-Weierstrauss, now I am stuck again.

[gaunt elk]

now you just have to use continuity of f

[vague phoenix]

Using delta-epsilon?

Ah no lim?

[gaunt elk]

yes limit

[vague phoenix]

But do I need to derive anything else from this theorem?

I pointed out the convergence of xnk already.

[main mural]

hint: ||apply f on both sides of the limit||

[vague phoenix]

Apply f both sides? How?

[main mural]

because f is continuous, you can put it inside/outside limits

[vague phoenix]

So I would go for something like $\lim_{k\to \infty} f(x_{n_k}) = f(c)$?

[flat frigate]

Nefer

[main mural]

yeah pretty much

do you see the contradiction now?

[vague phoenix]

But f(xn) > n

[main mural]

yes

[vague phoenix]

Then f (xnk) -> infinity since k -> infinity

It cant limit at a constant and approach infinity at the same time

[main mural]

yes

[vague phoenix]

Alright let me write it out a bit

[main mural]

you can say $f(x_{n_k}) > n_k$

[flat frigate]

artemetra

[vague phoenix]

Yeah I made it like this:

[flat frigate]

Nefer

[vague phoenix]

Is it look good now?

[median sand]

Looks good.

[main mural]

yep good job

[vague phoenix]

Thanks!

I am weak in these calculus

.close

[safe radish]

Channel closed

Closed by @vague phoenix

Use .reopen if this was a mistake.

[main mural]

you can also say that by definition there exists $k$ s.t. $f(x_{n_k}) > n_k > f(c)$ leading to a contradiction instantly

[flat frigate]

artemetra

[vague phoenix]

I see

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[safe radish]

Please don't occupy multiple help channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[full arch]

Hello there, where might I get the resources?

[median sand]

#book-recommendations ?

If you are asking for books.

Maybe videos if you ask in #study-discussion .

[safe radish]

@full arch Has your question been resolved?

[tardy mango]

(btw, help channels are for specific questions)

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[ember gate]

Can someone help me with fonction affine I don’t rlly understand it

[whole hill]

!status

[safe radish]

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

[ember gate]

Everything

Wait no

1

[whole hill]

Do you have any questions you'd wanna go over?

[ember gate]

Yes I don’t understand the chapter I do understand fonction tho just not fonction affine

[obsidian oracle]

So affine functions are functions f specifically of the form f(x) = ax+b, where a,b are constants

When you graph them, they look like lines

If you start at x=0, you will be at y=b

And everytime you move horizontally by 1, you move up (or down, depending on the sign of a) by a

[ember gate]

What is constants

[obsidian oracle]

Do you already have questions about those facts @ember gate ?
Also I'm guessing you're french, so we can continue in whichever language

[obsidian oracle]

Things that don't change

[ember gate]

Oh okay

[obsidian oracle]

If you pick an affine function f

[ember gate]

Yes

[obsidian oracle]

Those a and b won't change whereas x can change

[safe radish]

@ember gate Has your question been resolved?

Channel closed

Closed by @ember gate

Use .reopen if this was a mistake.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[upbeat swan]

#competition-math

[azure harbor]

Or #elementary-number-theory

[safe radish]

@blazing smelt Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[spring saffron]

In triangle ABC PQ is parallel to BC and O is circumcenter of APQ. Circumcircles of PHB and QHC intersect at S. Prove that O,S,H are collinear

[spring saffron]

I already found some angles, but I don't know how to prove that OSQ=a

It is actually so easy...

.close

[safe radish]

Channel closed

Closed by @spring saffron

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[safe radish]

Please don't occupy multiple help channels.

[tawdry plover]

<@&268886789983436800>

[safe radish]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

Please don't occupy multiple help channels.

[tawdry plover]

<@&268886789983436800>

[safe radish]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

Please don't occupy multiple help channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[distant storm]

here I can get the new equation by considering i-1/2 as x and substituting to original equation as i-1 is subjugate pair. But then a,b,c variables persist, and when I try to find a,b,c I see that they can have many values, so which one should i take? a=k, b=-2k, c=2k. Or am I getting smthing wrong

[severe pond]

not sure what you mean

[distant storm]

ok see, a,b,c have infinitely many values, so why do we take the simplest one and well, assume a=1?

or do we not assume that at all

[severe pond]

i mean yea you can do that

[pine vale]

Roots only determine a quadratic up to a nonzero constant multiple

a = k, b = -2k, c = 2k. There are infinitely many versions because multiplying the whole equation by a nonzero constant does not change the roots

So the answer depends on the convention: monic gives coefficient sum 1/2, simplest integer coefficients gives coefficient sum 1

[distant storm]

ohhh ic, is there a reason why quadratic expressions with whole number roots are always having a=1 or a factorable "a"

[pine vale]

Yeah, the reason is that if the roots are whole numbers r and s, then the quadratic must look like

a(x-r)(x-s)

for some nonzero number a

[pine vale]

If we choose a=1, we get the simplest monic polynomial. But a does not have to be 1

Example: roots 2 and 5

(x-2)(x-5) = x^2 - 7x + 10

but also

3(x-2)(x-5) = 3x^2 - 21x + 30

has the exact same roots

[distant storm]

OHhh

tysm

[pine vale]

So whole-number roots make the factors clean, like (x-r)(x-s). The extra a is just a scale factor

[distant storm]

icc

tysm

ill close, ty for ur help

.close

[safe radish]

Channel closed

Closed by @distant storm

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[median sand]

What have you tried?

[pine vale]

For a truss like this there is usually no one special shortcut formula for every stick right?

Yes, vectors are exactly the cleaner way

Instead of writing separate sin and cos formulas every time, give every joint coordinates

Then for each bar from point A to point B, make a unit direction vector

Something like:

u = (B - A) / |B - A|

Then you force in that bar is just:

N u

N is the unknown force in the bar

And at each joint you write one vector equation

sum of all bar force vectors + external forces = 0

That equation contains the horizontal and vertical equations

So you don't have to manually write them

N1 u1 + N2 u2 + N3 u3 + F = 0

You too

.close

Do this command

[safe radish]

Channel closed

Closed by @willow jackal

Use .reopen if this was a mistake.

[safe radish]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[spark leaf]

please @ me also if there is a helper helping please do not interupt unless they make a mistake, thanks

[spark leaf]

my status is 2pi*6

[cedar stream]

hi , im gonna assume you know the formula for the area of a circle and the formula for the area of a segment

[spark leaf]

i do

[cedar stream]

okay so first youll plug in the radius into πr²

[spark leaf]

36pi

[cedar stream]

so the area will be π(9)² without taking the fence into account

[spark leaf]

yes

[cedar stream]

the length of the rope is 9

[spark leaf]

m

[cedar stream]

9² is 9x9, which is 81

[spark leaf]

yes

[cedar stream]

so the area without the fence is 81π

[spark leaf]

yes

[cedar stream]

with the fence youll need to calculate the area of a segment do you know that

[spark leaf]

yes

can we call it sector so i dont get confused

[cedar stream]

sector and segment are different

[spark leaf]

whats the diff?

[cedar stream]

a sector is a pie slice

a segment is cutting the circle in a straight line

[spark leaf]

ohhh isnt that diametre?

[cedar stream]

uuuuh the diameter has to be through the centre

[spark leaf]

ohh so its a straight line anywhere

[cedar stream]

yeah, the line is called a chord and the two areas are called segments

[spark leaf]

lemme find a pic online

isnt that just sector deduct triangle

[cedar stream]

yea

[spark leaf]

so thats a segment

what does the d mean

[cedar stream]

yes i think you will have to find the angle of the sector

[cedar stream]

uuuuh the image is not loading pls wait a sec

[spark leaf]

hi pluto!

[errant ravine]

-# hi hi dont mind me just observing keep going u got this :3

[spark leaf]

ok thanks

[cedar stream]

okay nvm the inage doesnt seem to be loading what is the d that youre talking about

[cedar stream]

okay sadly not loading

[spark leaf]

ok pluto can u tell me whats the d

[errant ravine]

okay imagne circle with center o and sector P and Q imagne line PQ moey is saying that the lin perpedinculat to PQ and goes to CENTER o is of lenth D

[little finch]

it is the distance(perpendicular) of the segment from centre

[spark leaf]

thank u 😄

[errant ravine]

(bassicly the D would be = 6 in the example above ((the question)))

[cedar stream]

ah okay

[spark leaf]

now i need to find the angle of the segment

[cedar stream]

so we can find the angle with trigo

[spark leaf]

cos?

[cedar stream]

you can split the triangle down the middle into two right triangles

yea cos

[spark leaf]

yay

[cedar stream]

no paper so please accept this sketch

wait no the right angle is between d and the fence

[spark leaf]

i did it

[cedar stream]

okay what did you get

[spark leaf]

wait it should be sin

shouldnt it?

no its cos

[cedar stream]

its cos i think as we are dealing with the hypotenuse and adjacent

that is only half of the angle btw

[spark leaf]

360-2(48.19)?

[cedar stream]

correct

[spark leaf]

,w 360-2(48.19)

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by syrian_moey

[spark leaf]

thats the angle

[errant ravine]

-# yup well done ur pretty much nearly done!!

[spark leaf]

ik the formula for a sector but not segment

[cedar stream]

the area of a segment is (1/2)r²(θ - sinθ)

[errant ravine]

-# its the same idea bassicly its getting the area of THE ENITRE CIRCLE and then dividing into pizza slices so uget the area of each slice

-# but remeber we use Area here instaed

[spark leaf]

can we use ur way

[errant ravine]

-# i think this is too direct diamonial maybe we hosuld break into down into sector and segment?

[cedar stream]

ah okay

[errant ravine]

-# also sorry for interupting

[cedar stream]

its fine this is my first time helping

[spark leaf]

ur doing well

[spark leaf]

all good 😄

[errant ravine]

okay so just to explain what diamonail just did this formula is dervided from the sector formula and the traingle area formula.. so its just done all in one go but if you like we can break itdown!

[errant ravine]

-# ur doing amazing btw!! keep going!!

[spark leaf]

ok i think ik what to do

ill do and show u

[cedar stream]

yea okay

[ionic blaze]

an alternative to the sector rather than getting the cosine if you don't have a calculator/aren't allowed a calculator is finding the base by pythagorean theorem

notice that the triangle would be an isosceles triangle with base b, which is halfableish into two right triangles with base b/2
w that u can do 9^2=6^2+(b/2)^2

[cedar stream]

true, its a couple more steps 5ho

[errant ravine]

-# again this all depends on what level meoy is i m ath hypothetically diamonial answer (using segment rule) is most effecient. but nautilus info is also usefull espaccily if moey doesnt have calc on exam.

[ionic blaze]

cosine is a lot more steps

[spark leaf]

<@&268886789983436800>

[errant ravine]

HOLY THAT IS FAST-

[spark leaf]

so fast

[errant ravine]

chatbit go brr

[spark leaf]

hows my answer

[cedar stream]

√45 × 2 isnt √90

[azure harbor]

This

[spark leaf]

i did 45*2 then sqrt

[azure harbor]

Err

[cedar stream]

wait i'm not quite following then

[ionic blaze]

2 * sqrt45=sqrt4 * sqrt45 = sqrt(4*45)

[azure harbor]

a√b isnt equal to √ab

Instead its √(a^2 × b)

[ionic blaze]

you'd have to multiply it by a factor of 4 and also when you're doing that, it carries over

or osmething

carries over to the other side but I'll let the other dude do what they can

[errant ravine]

-# he used pyhtagerom therom to find half the chord length then did x2 to find the enitre chord (but obv qrt(45) x2 =/= sqrt(90)

[ionic blaze]

-# how long did it take for you to get the better shade of blue as a name

[azure harbor]

-# err like 2,3 months in discussy

[ionic blaze]

-# I don't have the time damn 🥀

[spark leaf]

am i stupid?

[faint whale]

-# can we stop hijacking this thread?

[errant ravine]

-# @cedar stream would u like to continue?

[cedar stream]

yes ofc uhh

[errant ravine]

-# for refrence moey is using the triangle area rule and the sector area rule to find the area we need

-# which is bassicly the long vers of the segment rule.

[azure harbor]

triangle*

[cedar stream]

so we get 105.32 as the area of the segment

and we just subtract that from the circle area from earlier

which was 81π

[spark leaf]

12pi?

why was it 81

i forgot

im dumb

[cedar stream]

it was π(9)²

[errant ravine]

-# sorry to intterupt but @spark leaf question why did u use 13.42 as R in the sector rule?

-# what is r again?

[spark leaf]

sqrt 45 *2

[spark leaf]

radius

and i used smth else

https://tenor.com/view/ups-error-facepalm-gif-15403364

[cedar stream]

uuh just suggesting you use 2 * sqrt(45) as its a bit less ambiguous

[errant ravine]

13 is chord length.

for area of sector we would use R which is?

[spark leaf]

6 or 9 idk which

9

[cedar stream]

r is 9

[spark leaf]

probs

[errant ravine]

-# also sorry for interrupting diamonail just needed to point out the miscalculation tahts all!!

-# @spark leaf if u just redo the last part(wtih correct R) everything should be correct

-# anyways i will let u continue diamonail

[spark leaf]

ok

[cedar stream]

okay so we just plug in the correct values

[spark leaf]

whats next

one sec my cat is calling

[cedar stream]

okay so we get 7.06 as the segment area

we subtract 7.06 from the total area of the circle

[spark leaf]

back he was stuck

[cedar stream]

πr² r=9
=π(9)²
=81π

[faint whale]

-# can't we simply find the area of the greater segment 👀 ?

[spark leaf]

,w 81pi

[errant ravine]

-# true but moey does not know segment rule yet.

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by syrian_moey

[cedar stream]

||true however moey probabky doesnt know||

[faint whale]

-# it's just (θ_major / 2π) · π · r² !!

[spark leaf]

mean

[spark leaf]

i dont like using stuff i havent learnt in class yet

[errant ravine]

-# yes but the point of it is to actually solve usnig what he actually knows / took not just giving him a random formula that he still didnt take / understand and tell him to just but the variables in

[errant ravine]

yess good on you!!!

[spark leaf]

.

so my answer?

[errant ravine]

-# @cedar stream this is your moment ;3

[cedar stream]

correct!!!!!!

[spark leaf]

lets check the answer book!

[cedar stream]

||we pray||

[spark leaf]

it says 227m

[cedar stream]

hn

[spark leaf]

ok lets check the intended solution

[errant ravine]

ur angle.

[cedar stream]

let me verify your calcs

[errant ravine]

in sectoer area.

[errant ravine]

the angle 48.18 is only HALF of the total angle of the secter.

[spark leaf]

thats the intnded solution

[spark leaf]

ohhh yes need fix

[cedar stream]

okay uhh

[errant ravine]

-# area of traingle seems right.
-# area of sector seems right
-# sector minus traingle area is correct

[spark leaf]

so its just that we approximated

[errant ravine]

no-

[cedar stream]

please give me a minute im calculating this

[spark leaf]

ok

[cedar stream]

too big a difference to be an approximation error

[faint whale]

-# how did we find the area of minor sector AB without θ / 2π · π·r²? 👀

[spark leaf]

area of sector

[errant ravine]

-# same rule just in degrees

-# i also got it as 213??? 😭 maybe i am doing something wrong idk

[spark leaf]

.

[errant ravine]

OH IK WHY

AREA OF TRAINGLE

b x h x 1/2

[spark leaf]

thats the simplest part

[errant ravine]

we are using THE SIDE not BASE

9 IS THE SIDE no the base!!

6 is height

[spark leaf]

ohh

whats the vase

base

[errant ravine]

thats why we need sqrt(45) x 2 x 6 x 1/2

[spark leaf]

hmm?

shy sqrt 45

then whats the 9 for

[errant ravine]

cause pytheagerom therom 9^2 - 6^2

radius

-# nvm all is on order 😭

[spark leaf]

c^2-b^2

[errant ravine]

okay so fixing this calcualtion mistake all should be good ;3

[spark leaf]

idk what to do

[errant ravine]

fix traingle area!

[spark leaf]

what values?

[errant ravine]

-# also iam really sorry fortaking over @cedar stream would u like to conitnue from here?

[cedar stream]

it fine you can take over

im still tryna process what went wrong

[errant ravine]

-# no no i insisit this is ur first time helping i want you (ofc only if you would like) to finish this

[errant ravine]

-# traingle area we assumed 9 was the based when actually it wasnt.

[cedar stream]

ohkayy.....

[spark leaf]

what values do i use

[cedar stream]

for what exactly ?

[errant ravine]

-# traingle area.

[cedar stream]

for the triangles area we can use (1/2)(6)(√45)

[spark leaf]

so no 9

[cedar stream]

yers tjat was an error

[errant ravine]

-# also dontforget an extra x2 cause its two traingles ;3

[spark leaf]

ok

[cedar stream]

oop ty

ermmm soooo for the sector area i got

27.878

[spark leaf]

im stupid

[cedar stream]

are we on the same page

[vague phoenix]

Why are you calculating for OP

[errant ravine]

-# op arleady calcualted just made an error thats all.

[cedar stream]

||by OP do you mean the line OP or original poster||

[vague phoenix]

I assume you know what am i referring to

[vague phoenix]

Great

[errant ravine]

u frogot the x2 ;3 since only half the base is sqrt(45)

[spark leaf]

x2 where

ohh right

[cedar stream]

theres two triangles

[spark leaf]

we did it!!!

[cedar stream]

yay!!!

[spark leaf]

https://giphy.com/gifs/PureSavage-yahoo-wahoo-skistar15-mFw98wZTjrZpMCgBZF

[spark leaf]

appreciate it

[cedar stream]

yea i just calculated as well the answers match

226.591

[spark leaf]

https://giphy.com/gifs/pizza-unicorn-i-love-4ayiIWaq2VULC

@errant ravine u should get the refrence

[errant ravine]

CONGRATIULATIONSSS!! TO BOTH OF YOU!!

moey for solving ittt and
diamonial for finish ur first ever help req!!

[errant ravine]

pizza slicesss ;33

[spark leaf]

thanks

[errant ravine]

also i should mention that what u just did with the traingle and sector is bassicly the segment area rule that @cedar stream shared earlier but thats a topic for another time ;3

-# when u take the rule feel free to ask how we got ti here

anyways if ur done dont forget to .close!!

thanks @cedar stream btw!!

[spark leaf]

dont dont

[cedar stream]

yww

[cedar stream]

u have another wuestion?

[spark leaf]

another topic

[cedar stream]

post it :3

[spark leaf]

please @ me, and if there is a helper please do not interupt unless they make a mistake, thanks.

[spark leaf]

,pin

[errant ravine]

.pin

[spark leaf]

ohh its .pin

i need the bathroom tho

so

brb

[cedar stream]

yiu will need a protractor and penfil methinks..!

as well as a compass

and ruler : 😹:

euuu i dont think thats what the question meant

[errant ravine]

-# theeen no one saw that :3 shhhhh sneaks away

[cedar stream]

||👀👀👀||

youll just need to know how to construct sin cos and tan from a circle

[spark leaf]

im back

before anything can u teach me whats a unit circle

[median sand]

Draw out the unit circle and observe.

[spark leaf]

how do i draw it

[median sand]

Construct a Oxy plot.

Then a circle centre at (0,0), with radius 1.

[spark leaf]

never heard of it

[median sand]

XY plane.

[cedar stream]

a circle with radius 1

[spark leaf]

can i just use desmos?

[errant ravine]

-# prefferbly no u dont really need it

[spark leaf]

we call that a scatter plot

[cedar stream]

do u know how to get sin cos and tan?

[vague phoenix]

That's what she said, the plot ;-;.

[cedar stream]

from the unit circle

if you don't i will help but maybe your teacher taught you this

[spark leaf]

whats next

[spark leaf]

my teacher taught that yesterday, i wasnt at school at that time

[errant ravine]

-# that is not of radius 1 but i guess we can just assume that it is of radius 1

[spark leaf]

so ik nothing

if i do radius 1 itll be too small

[cedar stream]

it has to be radius one

[spark leaf]

lets assume it is

forget the values

do u think its better if i learn what a unit circle is from yt?

[vague phoenix]

Draw the radius start from 0,0

[vague phoenix]

Probably

[cedar stream]

so we'll draw a line with angle theta and theta is being measured from the positive x

axis

and it passes throguh the origin

[errant ravine]

https://tenor.com/view/matematica-gif-7322246

[cedar stream]

look at the intersection of the circle and line

yesss exactly

cosine is how far on the x axis the point is

sin is how far on the y axis the point is

and you can find tangent with tanx=sinx/cosx

[spark leaf]

im confused

even the yt vid confuses me

im dumb

[cedar stream]

on what exactly

[spark leaf]

what is a unit circle

[cedar stream]

the definition of a unit circle or how to get sin cos tan

a circle of radius 1 with its centre on the origin

[spark leaf]

0,0

can someone tell me whats the unit circle with out simplifying

[cedar stream]

yeah

its exactly that

a circle with radius 1 with a centre 0,0

[errant ravine]

-# not to interfere but unit is basicly 1 unit of measurment so unit here means 1 and circle means circle so it means circle with radius of 1

bassicly its like if u put ur hand out and ur hand is 1 meter long and u spin for 360 degrees ur gonna draw a circle with radius 1

[spark leaf]

what ik so far is a full turn is pi a 90 degree turn is pi/2 a 180 degree turn is 2pi a 270 degree is 3/pi

[cedar stream]

coreect

[faint whale]

-# the set of all points in 2D space whose distances from a centre are all equal to 1!

[cedar stream]

360° is 2π rad

[spark leaf]

wait no 270 is 3pi/2

[cedar stream]

||this may be a little confusing||

[spark leaf]

it is

[faint whale]

π is a half-rotation
2π is a full-rotation

[spark leaf]

so umm can somone explain how we got the rest of the values?

[faint whale]

90° is a quarter rotation

[faint whale]

60° is a third of a half-rotation

thus 60° = π / 3

[faint whale]

it's all relative to this

[spark leaf]

can we start 1 by 1

[faint whale]

Ok

[faint whale]

we begin from 0

[spark leaf]

why do we have pi/6\

[faint whale]

a straight line is 180°

what is a sixth of 180°? it is 30°!

[spark leaf]

yes

[faint whale]

what is 180° equivalent to? it is π !

so a sixth of 180° is a sixth of π

hence 30° = π / 6

[spark leaf]

is it?

[faint whale]

Yes

what is the circumference of a circle?

[spark leaf]

2 pi r

[faint whale]

r is 1 for a unit circle

2π is hence a full circle

[spark leaf]

ok

i get it i think

[faint whale]

radians is the perimeter or the part of a circumference of a unit circle

we use the perimeter of a unit circle to define rotations

[spark leaf]

im sorry but i need somone to explain it simpler

[cedar stream]

we take a full rotation to be 2π

[spark leaf]

is pluto out there?

[errant ravine]

-# heyyoooooo 😭

[faint whale]

Hmm… maybe 3b1b's animations could help

[spark leaf]

if u dont want to its fine

[faint whale]

he had a video on trigonometry

[errant ravine]

uhhmm i can try i guessss? 😭 i mean @faint whale and @cedar stream already explained it prettyy well!! but i can try to break it down even more!!

[errant ravine]

no no ofcourse i will help!!

[cedar stream]

so a half rotation is 2π/2

[faint whale]

a complete rotation is defined as 360°

and it is also defined as 2π

[spark leaf]

yes

[faint whale]

360°=2π

everything else is relative

any factor you scale 360° by, 2π is scaled likewise

[errant ravine]

okay so first things off remeber arcmeters from earlier you know how they are alternative to degrees?? wehave this thing called radians as in we measure in another way think of it as miles vs kilometers

[faint whale]

a half-rotation is half of both 360° and 2π

[spark leaf]

ik whats radians

[spark leaf]

180 and pi

[faint whale]

what is the third of a half rotation?

or the sixth of a full rotation?

[spark leaf]

360/6

[errant ravine]

-# in radians

[faint whale]

yes or 2π / 6

[spark leaf]

ohh so 360 is just 2 pi then i divide it by 6

[faint whale]

yes

[errant ravine]

exactlyyy!! weldoneee!!

[spark leaf]

but why 6 not anotha value

[faint whale]

-# that's why τ is better. rotation is scaled 0 to 1 instead of weird factors in degrees or those multiplied by 2, xd

[spark leaf]

whats this τ

[faint whale]

cause we are looking for the sixth of a full rotation

so we divide by 6

we can look for arbitrary divisions

[spark leaf]

so a question will say what we looking for?

[faint whale]

yes, context will say

[spark leaf]

ok

then if its 8th its gonna be 2pi/8

[cedar stream]

correct 👏

[faint whale]

now try figuring out a lot of rotations, and always think in π
it's like switching to 24h time format from 12h

[spark leaf]

ok now how do we get to pi/2 from 2pi/8

[faint whale]

90° is a quarter rotation

2π / 4 = 360° / 4

[errant ravine]

-# pi /2 is = 2pi/4

[spark leaf]

thank u (IK im stupid)

[errant ravine]

-# STOP SAYING UR STUPID OR I WILL KICK YOU OFF PLUTO >:c

[spark leaf]

ok ok

[faint whale]

-# pluto is inhabitable anyway

-# nvm I like cold cimates

[spark leaf]

is there 2pi/5 ?

[faint whale]

there is everything

2π/5 is 360°/5

[spark leaf]

ok i get the part up to pi/2

[faint whale]

72°

[errant ravine]

remeber pi is bassicly a measurment of degreees this is like asking if 72 degrees exsist

[faint whale]

-# in the perfect world rotation is defined from 0 to 1 🥲

[spark leaf]

what do i do after pi/2

[faint whale]

wdym

[errant ravine]

okayy sososo here is the thing

[faint whale]

you treat it like 90°

same thing you do with degrees

[errant ravine]

this is the part where u get sin and cos!!

[spark leaf]

which is pi/2?

[errant ravine]

pi/2 is 90 degrees

[spark leaf]

but after it what comes

[errant ravine]

now now remind me what is sin?

[faint whale]

-# Ahh

[errant ravine]

well idk u can go pi and then 2pi/3 and then 2pi

[spark leaf]

opposite/hyp

[errant ravine]

if u want to go 90 - 180 -270 -360

[errant ravine]

adv?? what is adv??

[spark leaf]

its hyp

what

[errant ravine]

so sin = opp/hyp right?

now i want you to imagne the side OPPOSITE to the angle that we draw

look at this gif here

https://tenor.com/view/matematica-gif-7322246

[faint whale]

think of the sin function as the y-coordinate / altitude of a particular point in the circumference of a unit circle
as the distance from 0 to that point along the curve is what we call radians

[errant ravine]

you see this? we can think of this (the red line) as SIN because it is opposite to the angle

[spark leaf]

theres 2 red lines

[nocturne tusk]

but the opposite like HAO

[faint whale]

-# I like to think of cosine as complementary sine

[errant ravine]

(they are the same hieght essentiall its just one is drawn on the left for easier understanding)

[errant ravine]

which is also true!!

[spark leaf]

read the title!

i say sin is y and cos is x

[faint whale]

yes

[errant ravine]

YES PERFECT!!

okay soo looking at the gif notice how as SIN gets bigger (taller) cos(width) gets shorter?

and vice versa

[spark leaf]

yes

[spark leaf]

this is satisfying

[errant ravine]

SOO we know that there is ratio between them so now can uimagne having a right angle traingle where R is our hyptonuse

u can imagne us calculating how long each side would be acording to the angle

[spark leaf]

we use pi stuff?

[errant ravine]

-# no no thats is just for the angle dw abt that rn

[errant ravine]

if i tld u that angle A = 45 would u be able to calculate the opp and adj sides?

[faint whale]

think of the opposite side as r·sin θ
and the adjacent side as r·cos θ

this is by definition
for r=1, the are equal to the sine and cosine functions

imagine the triangle inside the circe, where hypotenuse r is the radius

[spark leaf]

cos(0) is 0 no?

[faint whale]

what is the length at rotation 0?

x-coordinate

[spark leaf]

0.5

[faint whale]

it is from the centre till the circumference

[spark leaf]

greatar than 0.5

[errant ravine]

noope think about it at angle 0 how much is the width?/

look at the blue line in the gif!

[faint whale]

what's the length from centre till circumference?

[spark leaf]

too many helpers!

can i get 1 by 1

[errant ravine]

-# alright i shall poof

[faint whale]

@errant ravine please take over brother

[errant ravine]

WAI WHA- uhh okay suree!!

[spark leaf]

no pls

[errant ravine]

thanks!!

[spark leaf]

i like u

[errant ravine]

okay look at this once again

at angle 0

can u make a guess how long the width is?

(cos)

[spark leaf]

if its 0 then its 0

[errant ravine]

okay question

at angle 10

look at how long the blue line is

(width)

pretty long right?

[spark leaf]

yes

[errant ravine]

okay now imagne it at angle 5 instead

[faint whale]

it says 0.5

[errant ravine]

it would get longer right?

[faint whale]

xd

[spark leaf]

yes

[faint whale]

that must be why

[errant ravine]

now imagne it at angle 0

[errant ravine]

-# huh wdym 😭 Oh its cause its from 0 to 0.5 to 1

[spark leaf]

1

yay

[errant ravine]

CORRECTTT!! using the same logic can u guess how HIGH sin (the hieght) would be at angle 0?

as in sin(0)?

[spark leaf]

1/2

[errant ravine]

hmmm nooope think about it

[cedar stream]

euuu not quite

[spark leaf]

hmm

[errant ravine]

look at when the angle is 10 (the red line on the left is very short right?)

[spark leaf]

0

[errant ravine]

CORRECTTT!!

[spark leaf]

yayyy

[errant ravine]

that is because R at angle 0 PUT YOU AT A POINT where ur as HIGH as the origin so ur at the same hieght!!

[spark leaf]

yesssss

[errant ravine]

BUTT now imagne as the angle increases u can imagne sin getting talller

and taller

[spark leaf]

yes

[errant ravine]

now look at the gif and make a guess how tall would sin be at 90?

[spark leaf]

1

def

[errant ravine]

https://tenor.com/view/matematica-gif-7322246

[errant ravine]

CORRECTT!!

how about cosine

how wide is cos at angle 90?

[spark leaf]

0

[errant ravine]

CORRECTTT!!

nownwownow a trickkyk questionnn

[spark leaf]

yayyyyy

[spark leaf]

ok im ready

[errant ravine]

how about angle cos(180)

[spark leaf]

do u want cos or sin first

[errant ravine]

cos

ehh sin (180) is ez

[spark leaf]

sin is -1

[errant ravine]

why is sin a 180 = -1?

look at the hieght when the angle is 180

[spark leaf]

wait no

[errant ravine]

do we have any hieght?

[spark leaf]

i was looking at 260

https://tenor.com/view/ups-error-facepalm-gif-15403364

[errant ravine]

its okay!!

AND YES FOR 270 SIN = -1 is correct wel ldoneee

[spark leaf]

if its 180 sin is 0

[errant ravine]

okayy how about cosine?? 👀

[spark leaf]

cos will be -1

[errant ravine]

CORRECTTTT!! do u udnerstand why? 👀

[spark leaf]

yayyyyyyyyyy

yes

[errant ravine]

oaky pefectt!!

now how about 360?

[spark leaf]

isnt that same as 0

[errant ravine]

yup!!

how about 450?

[spark leaf]

thats 90?

[errant ravine]

yupp!!

there u go ur donee!!

[spark leaf]

yay

[errant ravine]

now just solve this!!

[spark leaf]

that was simple

[errant ravine]

and we know that tangent is what in terms of sin and cos?

[errant ravine]

it is really simple!!

[spark leaf]

idk

what is tangent

[cedar stream]

its tan

[errant ravine]

-# although the unit circle has other points but i belive u will probably take that tmr at school.

[errant ravine]

well tangent = opp/adj right?

[spark leaf]

tmrw is weekend

[errant ravine]

i mean next lesson ;3

-# if u want i can explain it to you after this Q but for now u dont need to know all that

[cedar stream]

tan(x) = sin(x)/cos(x)

[spark leaf]

yes pls

so its 1/0 or 0/1

[errant ravine]

okayy so remind me what is sin? and what is cos? as in thier rules

[spark leaf]

s=opp/hyp cos=adj/hyp

no

made a mistake

fixed

[cedar stream]

do u know sohcahtoa?

[errant ravine]

so if sin = opp/hyp and cos = adh/hyp
and tan is opp/adj then we can say that tan = (opp/hyp) divided by (adj/hyp)
because they are both divided by hyp we can simply say tan = sin/cos

[errant ravine]

hene what diamonail said here!! ^^

[spark leaf]

tooo much text i need to break it down 1 sec

[errant ravine]

u dont need to know this btw just explaining where it came from ;3

[errant ravine]

tyt!

[spark leaf]

i get it

thanks

[errant ravine]

okay soooo now we can get tan any angle by using our sin and cos!! as diamonail said earlier ^w^

[spark leaf]

in radius 1 is tan always 1/0 or 0/1

[faint whale]

https://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Circle-trig6.svg/1280px-Circle-trig6.svg.png

[errant ravine]

tan isnt always anything it depends on the angle!!

[faint whale]

wow…

nice embed

[spark leaf]

too confusing

[faint whale]

of course it is. nothing rendered

[errant ravine]

-# this is probabbbly too advanced for moey 😭

[spark leaf]

pls delete it

[spark leaf]

that was personel

[errant ravine]

sorryyy i mean i barely get it too

[spark leaf]

all good

should i go do questions?

[errant ravine]

sure!!

[spark leaf]

brb

[errant ravine]

and you already know how to get raidains cause of itsmstiziad and diamonail!!

[spark leaf]

@errant ravine idk what to do for tan

[errant ravine]

undifeined or just leave it as 1/0 or -1/0 acordingly

although undefined would be probably be moree coorect

[spark leaf]

i wrote Er for error

i gonna guess my radians is wrong

[cedar stream]

thats only if youre a calculator i tjink!

[spark leaf]

i am a calculator

[cedar stream]

do u know what 270° is ?

[spark leaf]

opp of 90

[cedar stream]

as in how many full turns

[spark leaf]

3/4

[cedar stream]

so , in radians it is 3/4 * 2pi

do u follow?

not pi/4

[spark leaf]

6pi/4=3pi/2

[cedar stream]

yes cotrect

correct

[spark leaf]

yay

how about 450

[cedar stream]

450 is 360+90 roght?

[spark leaf]

its gonna be 5/4 turns

yes

do i say 10pi/4?

[cedar stream]

right yeah

[spark leaf]

yay

[cedar stream]

so its 5/4 x 2pi

[spark leaf]

yes

[cedar stream]

also, 0° is 0 radians, because its 0 full turns

[spark leaf]

yep

what is 30 degree in radians is there a pattern?

[cedar stream]

yes

whats 30/360?

[spark leaf]

idk

[cedar stream]

cmon u can do it

[spark leaf]

,w 30/360

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by syrian_moey

[spark leaf]

that

[cedar stream]

okay yeah 1/12

multiply that by 2pi

[spark leaf]

2pi/12

[cedar stream]

yeep

[spark leaf]

but what if idk whats 30/360

[cedar stream]

then u gotta use a calculator

[spark leaf]

what if its a non calc test

[cedar stream]

uhhhh

ur kinda supposed to remember ur times tables

[spark leaf]

skill issue?

they expect me to know 30/360

[errant ravine]

30/360 is the same as 3/36 so no diffuclt when u consider that 3x10 = 30 and 6 is jsut 2 x3

[cedar stream]

yea

[spark leaf]

i see

[cedar stream]

anyways you just have to remember that angle in rad = (angle in deg/360) * 2pi

and you can simplify from there

[spark leaf]

thanks

ok lemme do 2

[cedar stream]

okay

are there any other problems u need help with ?

[spark leaf]

so its not 0 or 90 or 180 or 260 or 360 so idk

[cedar stream]

uuuuh okay

so a coordinate on the unit circle is (cos theta, sin theta)