precalculus

[round geyser]

Bc of 45-45-90 right triangle

[low slate]

you're right.

there's soemthing wrong with the numbers

unless iam mistaken.

apologies

[undone pumice]

I didn’t have time for ts I’m only in precalc so I’m no the best with my calc yet with like optimization and that type shi

[valid topaz]

hmm

[undone pumice]

A question on our calculator section 🥀

[low slate]

oh my

GOD

[round geyser]

500 is the 500 from the tower and 1200 is from the 45-45-90

[low slate]

no there's nothing wrong with the numbers

jake you're right

[round geyser]

You add them up then it’s 1700 m

[low slate]

I'm so wrong, I used the wrong trig function

[round geyser]

It’s okay

I’m also doing trig

With y/r, x/r, and y/x

[low slate]

cos(45) would be h/hypontenuse

wouldnt do you much

[undone pumice]

Ts was the function btw 🥀

[low slate]

I'm far into calculus 😭 I'm a senior

I'm just very silly sometimes

[round geyser]

I’m also a senior but in HS

[low slate]

I also meant hs

[undone pumice]

I’m js a silly freshman I can’t figure ts out

[low slate]

but where are you from? learning about trig in senior hs year is odd?

[undone pumice]

Here precalc has trig and there’s seniors in my class (I’m in precalc)

[valid topaz]

scary

[undone pumice]

So scary hmph

[low slate]

was that your function?

[undone pumice]

Yes..

[low slate]

can i get a clearer image

[undone pumice]

I sent the pic of the problem like two minutes ago

Here lemme send it

[low slate]

of the function, not the yappage.

[undone pumice]

Ah

[low slate]

it looks like a trig function... a very horrendous one.

[undone pumice]

200cos(pi(t)/7)+130sin(5pi(t)/12)+390

Is the function

[low slate]

is pi(t) a function of some sort or do you mean multiplied

and do you know derivatives? I dont see a lot of other ways

maybe try figuring out when cos(pi(t)/7) reaches a maxima

then add that to when sin(that) also reaches a maxima

[valid topaz]

ye this is a precalc test

derivatives aren't learned yet

[low slate]

the maxima will occur when these two individual expressions reach their maxima.

so.

[low slate]

.

[low slate]

.

ignore what I said

[drowsy herald]

Why i am trying to have fun + learn more

[low slate]

I assumed you were asking people to solve it for you

not that you wanted to help others do it "with a challenge"

[drowsy herald]

Ohhh i get you now

No worries

[low slate]

yeah this shit is nasty without calculus

sorry I surrender.

[drowsy herald]

If anyone has great questions, please don’t hesitate to send them

[round geyser]

Lary

I have one

[drowsy herald]

Go for it

[drowsy herald]

Ok i’ll solve

[raw hill]

,w random number from -174 to 5850

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[raw hill]

$$\prod_{n=1}^\infty \frac{1}{1 - \tan^2(2^{-n})}$$

[obsidian monolith]

Civil Service Pigeon

[valid topaz]

||turn into cubic and solve for the real root||

[drowsy herald]

a= 1.5

[raw hill]

That makes the left hand side irrational

Did you confuse $2^a=3$ with $2a=3$

[obsidian monolith]

Civil Service Pigeon

[drowsy herald]

I had to use a calculator at the end

[drowsy herald]

Wow my first time seeing this symbol

[raw hill]

Tbf it rounds to 1.6, not 1.5. But there's nothing wrong with just leaving it as $\log_2 3$.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

$$\prod^{\infty}_{n=1} a_n=a_1 a_2 \dots$$

[obsidian monolith]

Civil Service Pigeon

[drowsy herald]

What does the symbol stand for?

[valid topaz]

productorial

so like ∑, but u multiply every term

[undone pumice]

Multiplied

[undone pumice]

Yes I do but I’m not supposed to use them in this class since it’s precalc and I’m js ahead 🥀 it’s a calculator question but like

[low slate]

I'd say its an ugly optimisation problem that I wouldnt do without calculus.

[charred rapids]

There’s an error

You used wrong some properties

[raw hill]

oh wait yeah lol

wrong process right answer

[charred rapids]

Second to third step

[valid topaz]

hmm solving the cubic wasn't the best choice

[round geyser]

How about ∑F=ma

[valid topaz]

that's js newton's second law of motion

[round geyser]

My teacher made it $F_{net}=ma$

[obsidian monolith]

Jake

[valid topaz]

hmm

[river drift]

$F_{\mathrm{net}} = \sum F$ by definition

[obsidian monolith]

cloud ☁

[round geyser]

Yet

How about $J=F_{\mathrm{net}}t$

[obsidian monolith]

Jake

[valid topaz]

isn't that like the impulse momentum theorem?

my physics knowledge is so crappy

[drowsy herald]

What is it

[charred rapids]

[
2^{a}\cdot 2^{2} \neq 2^{2a}
]

[obsidian monolith]

Rodro

[charred rapids]

[
2^{a}\cdot 2^{2} = 2^{a+2}
]

[obsidian monolith]

Rodro

[drowsy herald]

Ohhhh yeaahhhhh

God

This bot is smart btw

[charred rapids]

What bot?

[brisk raft]

no that's $J = \int \dd p$

[obsidian monolith]

Altanis

[brisk raft]

wait Omg

i misread mb

[valid topaz]

ye i rly need to brush up on physics

wait nvm

[brisk raft]

nah that is the impulse momentum theorem, J = ∫ F dt is definition

$$J = \int F \dd t = \int \dv{p}{t} \dd t = \int dp$$

[obsidian monolith]

Altanis

[brisk raft]

where J = ∫ F dt is the definition of impulse, F = dp/dt is newtons second law, and the third thing is by u-sub

[dusky jacinth]

oh father almighty

wwhat is the use in real life

[brisk raft]

who said that's a right angle

[low slate]

you cant solve a triangle with just an angle and a length 🙁

[hasty mica]

<@&268886789983436800>

[charred rapids]

<@&268886789983436800>

[hasty mica]

Who wants free money!!!

[willow dagger]

omg free money

[hasty mica]

Nooo my free money😢

[mortal crest]

[undone pumice]

Oh fun..

[shut galleon]

i got 83 on my quiz :(

[undone pumice]

🥀nuu its okay after the curve on the quiz i got back today well uh it was an 82 (13/17) sigh

wait no 14/17

[frail lion]

So like how do we solve this

[undone pumice]

gng idk im asking for help on ts problem 😭

[frail lion]

This is such a random function

[undone pumice]

it was on our test sob

i got that one wrong...

i guessed wrong..

[frail lion]

Yes so your tests are not discussed?

[rough leaf]

desmos it✌️

[undone pumice]

no they're not

my teacher just handed them back and was like... one point curve, ya'll did worse than usual (ahem i wonder why)

[rough leaf]

wait do you get desmos or no

[frail lion]

Yes

But it's no use

[undone pumice]

no

we're only allowed a graphing calc

[rough leaf]

oh

[undone pumice]

during tests

[rough leaf]

we only get desmos on likr

unit tests

[undone pumice]

oh

all our tests r on paper

[rough leaf]

or quarter/mid quarter ones

[undone pumice]

we can use desmos on the ap exam but not during any tests in class

[frail lion]

You get these allowed ?

In exam ?

Cool

[undone pumice]

we can use graphing calcs, any one thats approve by college board

i have ti nspire cx cas ii cus my teacher reccomend that one

[rough leaf]

bro what

none of the answer choices woro

work*

[undone pumice]

no thats why i got confused too

it has to be from t=0 to t=12

[rough leaf]

i forgot thag part

yeah it’s the maximum is

[undone pumice]

ill try desmos igs

[rough leaf]

695.8

[valid topaz]

hmm

[undone pumice]

ah okie

thx

[rough leaf]

idk if i did much bur yw😭✌️

[undone pumice]

lol

[frail lion]

Really wierd question, can't be solved algebraically, u need a graphing calc or a very big risk

[undone pumice]

yupp

i burned like 5mins on it

[frail lion]

Like when Asinx + B cosx + C is asked for min and max , it's C+√(A^2+B^2)

If the angles were like same it would be around 628

[undone pumice]

and then i gave up and moved on since the exam was timed and i already burned too much of that time

[frail lion]

Maximum

[rough leaf]

this is such a horrid question icl

i don’t know what it’s supposed to test

[frail lion]

So closest would be 695

[undone pumice]

yeah it was C cus my teacher marked that it was but

sigh

[valid topaz]

umm

[rough leaf]

bro i would’ve js guessed it

[rough leaf]

yes

[valid topaz]

hmm

[undone pumice]

frfr that quiz (quarter unit) was like two days ago and i have a test (half unit) next tuesday so igs i gotta try and cook on ts

cus this quiz dropped my grade 😔

[rough leaf]

youll do better bext time

trust

[undone pumice]

i hope so..

[rough leaf]

nah you will

[undone pumice]

as long as my teacher feels nice and doesn't throw another demonic function like that then..

and i dont have time to studdy cus i got a ela group project to do over the weekend

rah

[valid topaz]

i've always hated ela

[undone pumice]

sigh same

romeo and juliet and every option forthe project involved recording a video

so in my group they made me juliet, my friend is romeo, my other friend is a therapist, and we're gonna act out couples therapy 🥀

and we have to all ts outside of school bcs we dont get no time in class bcs we're still not done with this stupid play rah

[valid topaz]

hmm

[manic crown]

could someone help? I don't really understand how to find domain in equations..

[native snow]

ok so

sec is 1/cosx?

so cos x cannot be 0

cos x is zero at

pi/2 + pi*k

,tex all x except when $ \frac {1} {2} (x - \frac{\pi}{2}) \neq \frac{\pi}{2} + \pi k$

[obsidian monolith]

arrow

[native snow]

so

,tex $ x - \frac{\pi}{2} \neq \pi + 2\pi k$

[obsidian monolith]

arrow

[native snow]

,tex $ x\neq \frac{3\pi}{2} + 2\pi k$

[obsidian monolith]

arrow

[native snow]

so its c

[frail lion]

*d

[native snow]

oh yes mb d

[random swallow]

I was able to solve it before seein yo reply, but what if the og question has cos in it, or sin?

Sorry for the dumb question

I forgot ts lowk

[frail lion]

Then defined everywhere if sin or cos

Domain all real

[random swallow]

So we don't go back sayin sin=1/csc or cos=1/sec?

[frail lion]

No bro

[random swallow]

Like we did for sec and csc

[random swallow]

Hmm

And for tan, cos≠0, right?

[frail lion]

What

Yeah

Cos not equal to zero

[random swallow]

Kk

Ty

[maiden mesa]

tips on anti deraritives in itegrals

[undone pumice]

thats #calculus

tho i can't rlly help u, integrals are my weak point 🥀 glgl tho

[gloomy vector]

Can I solve for x here or is this just a function?

This is my work.

[gloomy vector]

Never mind in the video they just graphed both functions to approximate the solution. https://www.youtube.com/watch?v=7JkY19bYF28

[exotic barn]

Possibly with Lambert W ansatz; generally when you have two very different forms of functions it is hard to isolate the variable algebraically

[gloomy vector]

Ohhh tysm.

[south anvil]

Does anyone have time that can help me with the Unit circle

[tender quest]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[strange spire]

What do you exactly need help with?

[gloomy vector]

https://www.youtube.com/watch?v=1m9p9iubMLU

[round geyser]

I have a friend that needs help with the bottom page and doesn’t how to do those

Can someone help me asap

[round geyser]

Hello

Please help me asap

[undone pumice]

ah which bottom page? the two pictures are different...

[round geyser]

Second bottom page

[undone pumice]

this one?

[round geyser]

And the first one also

[undone pumice]

wait so all the problems in the pictures?

[round geyser]

Yes

[round geyser]

also the first one

[undone pumice]

ah ok i wasn't sure

cus there was writing in the 1st pic

[round geyser]

Like explains the ans key

How did my teacher approached it

[undone pumice]

so the key thing to remember with the inverse functions

is like its the reciproal, so 1 over something. so you can flip it over if it makes it easier to solve wit hthe basic 3

and undefined is over 0, so eg: cot(0)=und, 1/tan(theta), tan(theta) must be 0, so what could that be... (also, some of these have 2 answers)

[undone pumice]

appears to be writing the ratio and deterining it as either quadrantal or non quadrantal, drawing diagram

then for the cofunctions part, just by doing the horizontal shifts thing

[round geyser]

Btw me and my friend are in the same class

[undone pumice]

ah

[round geyser]

Thanks though

I’m having a test tmr

On these

[undone pumice]

oh

[round geyser]

And the identities

[undone pumice]

i also have a math test tmr

[round geyser]

sin(90-theta)=cos(theta)
cos(90-theta)=sin(theta)

Then it’s reciprocal

[undone pumice]

ah cofunction thingy

csc sec and cot?

[round geyser]

And cot(90-theta)=tan(theta)

It’s like if I see these

[undone pumice]

ah i see

[round geyser]

Like cot(11-9theta)=smh

[undone pumice]

lol

[round geyser]

Set them equal to 90 and solve

Will we see theta has a whole number

Like rational

[undone pumice]

oh i see

hmm

[round geyser]

Like this

Who thought of that

Just set it equal to 90

[undone pumice]

ah i see

[round geyser]

Yes

[undone pumice]

probably some random mathematician from like 15 centuries ago...

[round geyser]

Ok

[slow glen]

Can someone check where ive gone wrong?
I've tried it multiple times but I always get 2 cases

Lemme know if this is the wrong channel for it

[fiery spear]

I think a barrier for us might be familiarity with the specific notation.

The ⊕ is xor but what's the other one

⊙ xnor hm

[slow glen]

Yupp

[jolly karma]

(Last line) can I cancel both (sinxcosx) pieces on top with the bottom or-

All of that last line is over sinxcosx

[drowsy sundial]

hiii, would anyone be a dear and help me with a simple pre calc question? It’s very easy but I don’t understand how the professors answer is correct? I’m freshman undergraduate

[jade basalt]

i can give it a shot

[drowsy sundial]

thanks!

this is the question

This is the professors answer

[jade basalt]

so what bit did u not understand?

[drowsy sundial]

I was stuck here for reference

[drowsy sundial]

how he got the domain for the f/g

how is it -1 and not 1?

[echo sinew]

Can g be equal to 0, if you're doing f/g ?

[drowsy sundial]

nope

not at all

the denominator cannot be 0

[echo sinew]

Awesome

That's why x can't be -1, because x=-1 would make g equal to 0

[jade basalt]

if x is -1, g(x) becomes 0

in the original expression

[drowsy sundial]

OHH

wait so

do we just try to see what equals g to 0

and not include it in the domain?

[jade basalt]

yes, otherwise the division would be null

[drowsy sundial]

sorry if I sound silly. But what does null mean?

[jade basalt]

the x+1 terms can only cancel if they arent 0, u cant cancel 0 from the numerator and denominator

[drowsy sundial]

I took math in Arabic my entire life and I took it In English during my undergraduate, so I’m new to the definitions, sorry.

Does null mean error?

[jade basalt]

so at x=-1, the step of canceling the factors is wrong

[drowsy sundial]

ohhhh

[jade basalt]

it means like invalid

[jade basalt]

no problem, i took it in hindi most my life 😅

[drowsy sundial]

ohhhh

[echo sinew]

I guess it's more a CS term

[drowsy sundial]

so when we cancel it instead of not including only -2 and +2 we also add -1 since it became a denominator in the equation

ohhhhh now I understand

thank you so much :D!

[jade basalt]

yes

[jade basalt]

nppp

[drowsy sundial]

thanks so very much!

[jade basalt]

dont mention it

have a great day ❤️

[toxic turret]

I made this question by myself 😊

Could any body find the answer for this

And it doesn't give gibberish values

[undone pumice]

#calculus

[toxic turret]

Ohh sorry

[undone pumice]

all g

[brisk verge]

polar coordinates is pre calc?

[echo sinew]

I guess so

[undone pumice]

yeah

[fleet roost]

Yep it is in all books of pre calc

[undone pumice]

in my precalc class i think its on the curicullum but my teacher said its not really tested so we're skipping it i think

tho i alr know polar from before this class anyway

[rough leaf]

yup

it’s not that bad

[brisk verge]

yeah i've already done it but was just wondering what it counts as

[pale halo]

When does precalc become calculus

[ancient inlet]

the moment u learn dy/dx

[pale halo]

Like, dx/dy ^-1?

Wait no I'm stupid

[ancient inlet]

...

[pale halo]

😭

[ancient inlet]

derivatives of functions

[pale halo]

But what about the calculus stuff tho bc this is in the preuni section

Most ppl do derivatives before uni

[ancient inlet]

true

[pale halo]

What comes immediately before learning derivatives

[ancient inlet]

no idea

[strong kernel]

Is there a channel for calculus?

[raw hill]

yes

#calculus

[strong kernel]

Name checks out

Thank you

[raw hill]

[gleaming phoenix]

Functions?

Maybe even limits

Basic ones without L hopital

[pale halo]

really?

damn

[pale halo]

ive heard of that but dont know it

[gleaming phoenix]

I guess idk it might differ based on the curriculum of ur country

[gleaming phoenix]

Dw about it when it becomes more fun its calculus

[pale halo]

yippee

[gleaming phoenix]

More me we never had precalc we just did algebra functions and then moved straight onto calc

What do they teach in precalc anyways?

[pale halo]

weve done some calc just not l'hopitals

mostly integration tbh

not much limits at all

[gleaming phoenix]

U didnt do differentiation?

[pale halo]

well yeah ofc but the integration is the harder stuff

[gleaming phoenix]

Aaah then u've been doing calc havent u 😭

[pale halo]

yeah

but barely any limits

[gleaming phoenix]

Ye dont worry about it

[pale halo]

the only limits i can think of is for solving problematic integrals and for differentiation from first principles

[gleaming phoenix]

U mean integrals where u cant directly define the value for one of the ends given in the integral?

Like integration lnx from 0 to 1

[pale halo]

yeah or 1/x^2 from 0 to 1

[gleaming phoenix]

Then u kinda already know limits

[pale halo]

for an integral in the interval [a, b] if f(x) is undefined at x=T you just solve for [a, t] + [t, b] and set t = lim t->whatever T aproaches

[pale halo]

is it that simple

lmao

[gleaming phoenix]

Ye

So u havw done calc

At a highachool level atleast

[lime ore]

i understand differentiation but i still have confusion with limit ;-;

[gleaming phoenix]

Just practice i guess

Organic chem tutor explains it pretty well if u need

[undone pumice]

Algebra review trig logs and others. No calc stuff

Tho ik calc from outside study yawn. Supposed to do basic calc (like difference quotient) after ap exam in may tho it’s not on our curriculum

[heady bluff]

guys i have a quick question: when factoring how do you know when to use factor by grouping vs gcf factor method? is there a particular case where one is valid and the other is not?

[olive torrent]

if the terms have something in common, then factor it out

gcf factoring is usually valid

[heady bluff]

ohh ok

tyy

[olive torrent]

np!

[heady bluff]

wait so it doesnt matter the amount of terms?

[olive torrent]

yes

if there are terms that you can group

then do it

[heady bluff]

oh ok

[olive torrent]

yea use gcf when they have a greatest common factor. use groups for when there are 4 (i think) terms that you can pair up

[heady bluff]

kk

thx

[gleaming phoenix]

So like revision basically

Of prerequisites

I see

Seems useful

[teal oriole]

Does anyone have a good way to explain logarithms? I know them well but my friend has a lot of trouble

Like a way to represent them

[clear glade]

Structural Analysis Request: Weighted Logic System (3:3:4)
​I am seeking a peer review of the following mathematical framework. This is a system designed for Structural Optimization using a 3:3:4 weighted ratio across three variables (x, y, z):
​The Objective Function:
Let the total system be S.
S = 0.3x + 0.3y + 0.4z Variable Definitions:
​x (Reduction Variable): The process of simplifying a complex set into its base axioms.
​y (Equilibrium Variable): The identification of isomorphisms and balance between those axioms.
​z (Integrity Variable): The stress-testing phase; applying external constraints to verify the stability of the system.
​The Logic Question:
Given that z (Integrity) is weighted at 40%, while x and y are weighted at 30% each, how does this affect the Systemic Stability when external pressure is applied? Is this ratio (3:3:4) a mathematically sound distribution for maintaining a "Steel" (rigid/unbreakable) structure, or would a different ratio provide higher harmony?

[undone pumice]

Yeah pretty much. I know like everything we learn alr except concavity was new

[gleaming phoenix]

That thing related to the double derivative of the function?

Whether its concave up or down wrt to the x axis?

Isnt that differential calc? Or did i accidentaly miss learning something?

[undone pumice]

just the basics of it

as in, this function is concave down on this interval

and such

tho it is the double derivativething since the rate at which the rate of change is at is basically second differences of a functions y values aka the second derivative

[sonic hill]

To represent them?

A logarithm, say like log(55) (log as in base 10) asks, 10 raised to the what power gives you 55?

And log(55) gives you whatever that number is

[undone pumice]

i mean like besides graphing them... hmmm

my teacher had us draw stuff with arrows like this but idrk cus i alr knew logs before pc so... its kind of tricky to figure out at first

[stark tree]

Yea is just adding the base to the bottom of the right side equation

Same goes to 2ln X=10 and you add e on the bottom of it to cancel the base itself

[undone pumice]

yeah

[rugged spruce]

What did u guys use to understand the unit circle like understanding the special terminal points and sin cos tan stuff

[icy verge]

Just imagine the circle with radius 1 on the centre of coordinate plane and x points on it is cos and y is sin

[undone pumice]

I js memorized it last year

Uhhh

My teacher this year taught it like for q1 the y values is going down from 1 to 0 and the x values are going up from 0 to 1

And it’s all over 2

And for the numerators it’s going up or down sqrt3,2,1 (and sqrt 1 is 1 so 1/2)

[undone pumice]

You can also draw triangles and use 306090 or 454590 to further understand

That’s all the advise I can give tbh I alr knew it before precalc

[gleaming phoenix]

Aaah i see then

Gg's

[swift shuttle]

You pretty much need to know the main 4 points 0 = 2π, 90° = π/2, 180° = π, 270° = 3π/2 = -π

You could learn some points like π/4 I guess
But the main thing is that you can memorize each angle depending on its corresponding quarter

Assume angle x:
For the first quarter [0; π/2]: the angle x is just x
[π/2 ; π] : π - x
[π; 3π/2] : π + x
[3π/2 ; 2π] : -x

So any angle you get you pretty much convert into one of those and work around with it

The purpose of having those conversions is because they're related to each other

For example x and -x have the same cos value, x and π-x have the same sin

Just imagine or draw the circle and your main 4 directions and think of your angle as a triangle, the x axis is your cosine value, and the y axis is your sine value

It might be overwhelming at first, but it's really simple. Just try to work your wonders on it and understand it your way

[zealous rain]

Let Asin²x + Bsinx + C = 0 (i), and
A + 2Bcosx + 4Ccos²x = 0 (ii).

Let α = [-B + √(B² - 4AC)]/(2A), and
β = [-B - √(B² - 4AC)]/(2A).

If B² - 4AC >= 0, A ≠ 0, and x is an acute angle, then the correct option is

A. (α)² + 1/(2β)² = 1 or (β)² + 1/(2α)² = 1 always.

B. A√2 + B = 0 when x = 45°.

C. x = 45° when A√2 + B = 0.

D. None of the above.

[copper ledge]

<@&268886789983436800> ?

[rugged spruce]

Yea I found a guy on YouTube that’s explaining it pretty perfectly

He’s underrated imo probably better then the organic chemistry tutor

Can you guys explain these problems to me tho

[undone pumice]

soooo t is the angle. and that's in radians

and a whole circle is 2pi radians and half of one is pi radians

and you can use that to figure out where on the circle its talking about. negative (whatever) angle means go (whatever) clockwise from teh x-axis instead, or convert it to positive by adding 2pi

the terminal point is just wherever that angle interesects on the unit circle

i do see that these questions appear to have answers on them already, so im not sure if you want me to still explain that part?

[rugged spruce]

Yea explain also what do the denominators mean and why are we multiplying by 2 on some of them

[undone pumice]

the demoninators is just... part of the value

which part is confusing?

[rugged spruce]

So it doesn’t matter?

[undone pumice]

by multiplying by 2 it seems um

that its multiplying by 2/2

so basically

[rugged spruce]

Ok so for question b and d why are multiplying by 2

[undone pumice]

when u multiply by 2/2 you're making an equivalent fraction

its just too

make it have

a denominator of 6

so that you can count it by the already marked segments of pi/6 HOWEVER this is not a required step

you could just go.... 4pi/3 is like this many degrees and goes here... . i personally never did that step but i believe its to help make it easier at least for now

does that make sense, choco?

[rugged spruce]

When it comes to that step no

Bc it’s like when do we know to multiply by 2 when we get a problem like that yk

[undone pumice]

you dont

cus u dont need to do that step

its optional

and completely up to your preference

excuse my terrible drawing but the blue lines represent every 60 deg or pi/3, and the red lines represent every 30 deg or pi/6

[rugged spruce]

Ok so without doing that step how would I solve it

[undone pumice]

lets take 4pi/3

you would look only at the blue lines measuring every pi/3, find the one in quadrant 3 representing 4pi/3, and find where it intersects

[rugged spruce]

Hmmmm

[undone pumice]

the typical unit circle looks something like this with every commonly asked (non calculator) angles and their values

so like, you wouldn't just break it up until 60degrees or 30 degrees. so that conversion step on that picture you sent isn't really required

[rugged spruce]

So the professor is just confusing ppl

[undone pumice]

honestly, i have the values memorized because i knew the unit circle before precalc so im not really sure how to help

[rugged spruce]

This my first time learning it

[undone pumice]

its okay, just keep practicing and you'll get it

[rugged spruce]

Ok

[undone pumice]

i personally instead of multiplying too get a value over 6 would simply learn how to build quadrant 1 of a unit circle and learn how to apply that to the other quadrants

especially since you'll never see on a test (at least, a standardized one) like, 8pi/6, you will always be given a simplified fraction so, it's best to learn how to be comfortable with them

[valid topaz]

hmm

[swift shuttle]

Think of it like this, each quarter has 3 distinctive points, for example π/6 π/4 and π/3

Those points correspond to the values √1 / 2, √2 / 2, √3 / 2

Whether sine values or cosine values

The closest you are to the center, the smaller the number on the numerator

So for example, π/3 is the closest to the center on the cosine axis, hence why its cosine is 1/2

[muted widget]

Guys if I want to do lnx-1>0 is the solution just x>e or x>0 and x<1 and x>e

[swift shuttle]

Is it ln(x) or ln (x-1)

I assume the first option, in which case:

• the inequality is defined for any x ∈ ] 0 ; +inf [
• ln x > 1 meaning x > e
• Your solutions are the intersection of your domain and solutions, which gives x > e

I'm not sure how you would get x < 1

[molten pagoda]

trigonometry!!1!

[undone pumice]

yahh igs a lot of precalc classes are on trig rn, mines is too

[mild estuary]

I need help with trig

[undone pumice]

elaborate, which part?

[viscid thistle]

guyz could u suggest some tricks or formulas which could be used in jee maths

(like beta function and some what gamma)

and if u hav please provide a yt video for tht 🙏

[molten ember]

Someone pls help with my pre calculus

[uncut mulch]

just ask, ideally claim your own personal channel
#❓how-to-get-help

[viscid thistle]

can i get help?

[uncut mulch]

yes, just follow the instructions of the message you replied to

[ivory fractal]

does anyone know how to do these questions? i've never seen these on math oly's.

[copper ledge]

Have you studied Combinatorics?

[ivory fractal]

no

[copper ledge]

Well the question is from that part of mathematics

[coral pilot]

does anyone know how to do this question?

[ivory fractal]

could u explain it?

[thorny breach]

Not much help but I did notice Sn= Tn+ 1/3n

[copper ledge]

I recommend you watch some youtube videos, it would be tough to explain the whole concept here

[valid topaz]

recognize riemann sums probably

[ivory fractal]

ah i see alright

[wraith condor]

‘how many distinct permutations of the word BANANA exist’ is just asking you in how many unique ways can the letters in BANANA be arranged. let’s look at the letter count. it is 6. we know that there are 6 choices for the first position, 5 choices for the second, 4 for the third, 3 for the fourth, 2 for the fifth, and only 1 remaining for the sixth. if you know the fundamental counting rule, this can be rewritten as 6! ways overall, or in other words, 6 • 5 • 4 • 3 • 2 • 1 .
BUT, in BANANA, some letters repeat. these repeated letters can cause duplicate arrangements, for example: if you switch 2 A’s, the word still looks the same
there are 3 A’s, those A’s can switch places in 3! = 3 • 2 • 1 = 6 ways
there are 2 N’s, those N’s can switch places in 2! = 2 • 1 = 2 ways
divide the total overall ways (6!) by the duplicates to get 6!/(3! • 2!) = (6 • 5 • 4 • 3 • 2 • 1)/(3 • 2 • 1 • 2 • 1) = (6 • 5 • 4)/(2) = 6 • 5 • 2 =
60 permutations of BANANA

god i wrote a paragraph

but there you go, small lesson in combinatorics. look into the formal formulas for permutations and combinations

[ivory fractal]

thank you so much🤗

[wraith condor]

np!))

[gleaming phoenix]

u gotta have a pretty good idea of limits as a sum

u gotta also know integral calculus for this

tend the entire sum to infinite

then use this concept

[gleaming phoenix]

A,D?

u gotta make it into limits as a summand remember these 4 things

1. if function is increasing and limit is from (0 to n) then it is greater than overall sum

2. if function is increasing but limit is from (o to n-1) then it is lower than overall sum

3. if function decreasing and limit from (0 to n) then it is lower than overall sum

4. if function decreasing and limit from (0 to n-1) then it is greater than overall sum

for more clear explanation u can check out https://www.youtube.com/live/M_UMSn3cHtI?si=X1D5zuTJxgBfzsvT 3:53:59

[wraith condor]

oh yeah, integral calculus is needed here. def check out what razzberry sent

[green crown]

Can i write QED at the end of my induction proof if i have shown that for instance a formula is not correct?

I think so

Right?

[tame shard]

QED literally stands for "what was to be shown". Yea you can put it at the end of any proof.

[green crown]

Oh okai

[smoky schooner]

Does anyone need flashcards for derivative rules

[exotic barn]

you can also use $\square$ or $\blacksquare$

[exotic barn]

check out #proofs-and-logic as well!

[fossil kindle]

what even is precalc

is it just a combination of trig and more complicated algebra 2

[smoky schooner]

Its an introduction of calculus

It focused on finding deep answers of measuring changes and statistics its like so u need a lot of knowledge of algebra and and trig cuz they are involved in it a lot if u understand them well u can understand pre calc and if u understand it u will understand calc and so on

[candid condor]

anyone have good resources for probability?

[random swallow]

My only resource is eddie woo

Does induction count as precalc? If not, what does it count as?

[vernal cypress]

hey guys im kinda confused, my current subject is calculus but like not advanced, i think it's calc 1 and the beginning of calc 2? are those a topic of discussion over here or am i lowkey in the wrong place

[random swallow]

Wrong place

#calculus is for you

Well you've chosen the role pre uni math

[vernal cypress]

yep

thank you

[random swallow]

Go to the channel and roles and select calc or uni math

[vernal cypress]

i went in there tho

[vernal cypress]

oki

[random swallow]

Gud

[vernal cypress]

im still pre uni so its kinda confusing between countries but tyty

[random swallow]

Mybe you're at the end of high school or js a math enthusiast

[vernal cypress]

both heh

[heady fossil]

Any ways to prepare for pre calc next year

[solid dust]

if i like logs am i gonna like precal and calc

[vernal cypress]

yeah

[vernal cypress]

strengthen trigonometry, polynomials and logs i think those were my really basic ones

[heady fossil]

Okay Thats good to hear my year 11 algebra class is doing Advanced Trig After spring break and where doing logs right now

[random swallow]

Cool

[rugged spruce]

I HATE LOGS

And I don’t understand them

[vernal cypress]

how come? do you find their properties difficult to remember?

[rugged spruce]

Yes and then the condensing and expanding

[vernal cypress]

come onnn those are easy silly. it can be hard to get right at first and i remember struggling with matching them right but after a while it just clicks and falls into place

especially since i needed it in chemistry 🥹

[rugged spruce]

Yea it’s my first time learning them so that’s probably why it’s difficult rn

[vernal cypress]

yess but don't worry about it, you'll figure it out in the long run and with enough usage of them

[undone pumice]

yall theoretically how bad did i have to do on the second test of the semester where tests are worth 60% of our grade for my grade to drop 8% 😭 my teacher put in scores but hid them from us, so idk what i got but ik its gotta be bad

[raw hill]

<@&268886789983436800>

[grim rock]

hey guys i’m in 8th grade and in my school program we are doing algebra one- maybeee a bit of 2. i am self studying calculus and enrolling in college classes but i have a placement test to take. it’s mostly kn pre calc stuff i assume. what should i know? i’m comfortable with logarithms, unit circle, trig identities, etc but what should i grind

[valid topaz]

hmmm

[grim rock]

hi patrick

[raw hill]

<@&268886789983436800>

[undone pumice]

wow thats ambitious. hmm js make sure ur good with concavity rationals uhhh a bit of polar an matrix work, sequences and stuff

[fossil kindle]

how did you enroll in college classes

[undone pumice]

could be dual

[fossil kindle]

isnt that a highschool thing tho

[undone pumice]

there could b

be

exceptions

[fossil kindle]

unless they arent in the usa

[undone pumice]

my district gave me an exception

tho i didn't take it

[fossil kindle]

which is prolly more likely

[undone pumice]

^^ so possible

just need some working out with college first

and im in the us so ykw js depends

on the college, the high school, how advanced the student is, etc

[fossil kindle]

hmm interesting

[undone pumice]

yeah it was something the district wanted to discuss

idrk but its def possible for middle schoolers to take dual

especially in something where it's "easy" to advance if you understand

cant speak about the op's situation but

[smoky schooner]

Wdym dual

Like i can go take a calculus 2 class

Rn

[zinc juniper]

Do we have to be good at skibidi?

Because skibidi is the toilet right???

[smoky schooner]

No.l

[echo sinew]

Do not troll

[zinc juniper]

Huh

[bronze geyser]

https://klipy.com/gifs/skibidi-sigma-1

[grim rock]

yea dual enrollment

[grim rock]

it’s quite a process i believe

[winter comet]

i mean its the middle of the semester...

[winter comet]

wdym

[valid topaz]

i wish i could enroll for college classes

[winter comet]

why can't you?

[valid topaz]

my counselor keeps dodging my questions fsr

[fossil kindle]

does precalc even directly relate to calc

i swear the only relation is both have the word calculus in it

although precalc helps prepare for calc

[grim rock]

fr

idek it’s a requirement so i’m grinding khan to make sure im locked

i should be okay

but i gotta take multiple placement tests so

[fossil kindle]

oh

is it like a dual enrollment thiny

thing

[grim rock]

yea i obviously still have my normal middle school program but i take the calc course sepetrakty

[undone pumice]

oo cool gl

we had counselor visits today, my counselor wasn't a bish like in 8th grade visit time yey

[swift shuttle]

Does anyone remember the geometric proof for dy/dx for y = 1/x

[undone pumice]

uhh

did it involve a rectangle

[swift shuttle]

As per usual

[undone pumice]

hmm

saw it in a 3blue1brown video i think

uhh

i think its like

if the rectangle area always has to be 1

one side is x and one side is 1/x

[valid topaz]

ye

[undone pumice]

then like the increase in x by a little bit increases the vertical sliver and then you lose like some of the top to balance it out and still make its area 1

then like you get, y(dx)=x(-dy)

rearranging you get (dy/dx)=-y/x

[swift shuttle]

Yup that

[willow wraith]

What

whats the proof needed?

[undone pumice]

i mean ofcs its js power rule

but igs

if u wanna prove

it works

uh

[swift shuttle]

Hmmm I see

[undone pumice]

where y = 1/x, so dy/dx=-(1/x)/x=- -1/(x^2)

[undone pumice]

yeah you js get this from, the area gained = area lost

i think

im pretty sure i did it right

hopefully...?

icl ive been lazy and not hopping on the calc grind recently

[swift shuttle]

Oh you're totally correct

[undone pumice]

yay

[swift shuttle]

Well, I guess I've yet to fully grasp this concept. Thanks for the further clarification

[undone pumice]

ah

why not just power rule it instead of geometric proof?

[willow wraith]

Honestly for 1/x

I think it’s stupid and an idiot

So me personally

I would just say f(x) = 1/x

[swift shuttle]

The power rule is stupidly easy

[willow wraith]

and

[swift shuttle]

It's just a further enhancement

[undone pumice]

igs

good for u igs

im kinda lazy so idrk many geometric proofs

[willow wraith]

(f(x+0.001)-f(x))/0.001

😃

There

[undone pumice]

xd fair fair

like diff quotient type stuff?

[swift shuttle]

Not quite

[willow wraith]

Approximately yes

as change in x approaches 0

[swift shuttle]

To be precise:

[f(x+h) - f(x)]/h as h approaches 0

[undone pumice]

yeah its just like, similar to a limit, as it approaches , this is basically limit definition/difference quotient

[willow wraith]

it is th limit definition

I’m too lazy to write more zeros

[swift shuttle]

That's the thing, don't plug values

[willow wraith]

I will plug in values

[swift shuttle]

You're not exactly wrong, just not precise

[willow wraith]

if I can plug in values because

[undone pumice]

i remember in my non ap precal class we had to do like two page long worksheet of the diff quotient

[willow wraith]

the limit of gravity as your distance becomes infinity from an object is 0

and I can plug distances in for that so

I can plug in anything I want

the universe doesn’t give a damn usually

[swift shuttle]

I remember last year or maybe two years ago, we weren't allowed to use direct derivatives

So deriving something like x² had to be done thru that

[undone pumice]

oh

im not in calc yet so

yeah we can't either

we had to like plug in the function, cancel out the non h values

[willow wraith]

-0.2499999875 is approximately equal of -0.25

[undone pumice]

and meanwhile the kid next to me copied off me because

[willow wraith]

good enough

[valid topaz]

so u had to use the def of derivative?

[swift shuttle]

Brotherman did you read any of what I said

[undone pumice]

"mannn its not my fault i dont understand, because the notes said f(x) and this function is g(x) so i can't use that formula"

[swift shuttle]

Yup, you had to do lim as h approaches 0

[willow wraith]

It’s precision is good enough

[valid topaz]

must've been painful

[swift shuttle]

Funnily enough, the most annoying part was writing "lim h->0"

[undone pumice]

they were also a senior and told me how they only did this class because their friends were in it

[valid topaz]

i forgo the limit sometimes

[swift shuttle]

Could be better tho 👀

[valid topaz]

js keep the number in my head

[undone pumice]

lol fr

[willow wraith]

instead of h I use Δx because we all know that’s better

[undone pumice]

h easier to write..

[willow wraith]

no

[valid topaz]

but Δx is fancy

[swift shuttle]

I don't know if that's a good idea

[valid topaz]

and fancy is most important

[willow wraith]

if you’re about to say

It can be confused with dx

[undone pumice]

ick me no like fancy

[willow wraith]

anyone who understands differentiation

will not confuse it with dx

🙏

[mighty bear]

hey guys

[undone pumice]

fr lol

[mighty bear]

im doing calc

like

i did it

[swift shuttle]

Not that it can be confusing, it's just symbolism

[mighty bear]

im going to calc 2

suck it losers

muahaha

[willow wraith]

It’s the change in x what’s wrong with that

[mighty bear]

just kidding

[willow wraith]

ok

[valid topaz]

calc ii is most difficult imo

there's no direction tbh

[willow wraith]

it’s much more well defined than h

[swift shuttle]

That's kinda like saying f(y) = y² or having your base vectors as ô ê

[willow wraith]

that’s nothing like that at all

[swift shuttle]

You're kinda just saying screw the norm

[willow wraith]

the norm in institutions here is Δx

because h can be used to represent so many other things on a graph

[swift shuttle]

Cuz Δx is more common for considerable differences, hence why dx exists

[willow wraith]

while Δx on a graph is just

[bronze geyser]

exactly

[swift shuttle]

Like what

[undone pumice]

but like we dont use h for anything else

[valid topaz]

hi

[bronze geyser]

what is gng on abt

[undone pumice]

we js use x and y and m and b... but no h

[bronze geyser]

hi patrick

[willow wraith]

ANY variable

[bronze geyser]

i finished the 2023 fryer

i suggest you check out question four

ill send it

[swift shuttle]

There's better alternatives for that

[willow wraith]

My school uses it for

[valid topaz]

alr

[bronze geyser]

its very fun

[valid topaz]

i'll check it out

[willow wraith]

Conics for some reason

And then

[bronze geyser]

https://cemc.uwaterloo.ca/sites/default/files/documents/2023/2023FryerContest.html

here ya go

question three is difficult for me for some reason

[willow wraith]

It’s very often used in this area with k to represent a vertex of a parabola

like

x is just x

[undone pumice]

oh

igs vertex form

[willow wraith]

even if it represents something on the graph like position

it’s just x

[undone pumice]

haven't done vertex form in forever lwk forgot abt that

[bronze geyser]

vertex form is interesting

we can derive quadratic formula from it

[undone pumice]

i swear i haven't seen vertex form like at all this year

[willow wraith]

so Δx -> 0 is very easy to understand and much better 😃

[undone pumice]

with like completing the square or sumn?

[bronze geyser]

I think theres multiple ways

[undone pumice]

ah

[bronze geyser]

Looking at pythagorean theorum poofs is interesting too

[undone pumice]

i remember i had to sit thru like a long ahh video in 8th grade where they derived the quadratic formula

[bronze geyser]

even though i dont understand 99 percent of them

[bronze geyser]

LOL

[swift shuttle]

So you just do f(x + Δx)?

[bronze geyser]

your very advanced if thats grade eight

[swift shuttle]

Doesn't that look weird to yoy

[bronze geyser]

im in canada and we dont do shit for math

[undone pumice]

yeah i skipped a grade in math

[bronze geyser]

Jeez

math whiz over here

[undone pumice]

past the boring "advanced" 9th grade class they wanted us to take in 8th

so i could take precal now

anyway off for dinner now

[swift shuttle]

Nerd

[bronze geyser]

cya enjoy

[swift shuttle]

Have fun

[willow wraith]

Yup

[bronze geyser]

ahem.

[swift shuttle]

Had to let it out, I get it

[willow wraith]

Not at all

[bronze geyser]

yo elite ball knowledge

https://klipy.com/gifs/lebron-elite

respect to you hb

homeless boy

[willow wraith]

it’s your inputted x value plus an small change in x

there is no h axis

[swift shuttle]

I know what Δx is

[swift shuttle]

That's irrelevant

[willow wraith]

It’s less intuitive

[swift shuttle]

h is just a variable, it has nothing to do with literally anything

[willow wraith]

You’re observing an incredibly small change on the x axis

[swift shuttle]

The only information you need to know about h is that it's a number that's finitely small

Which is given when you say h ->0

[willow wraith]

Yes but if you’re teaching this definition to someone you don’t want h to be confused with a vertical change

After all h is usually a vertical change in other fields

[swift shuttle]

How about we use f(x) - f(x0) / x-x0

As x approaches x0

[willow wraith]

that’s still Δx

🥀

[swift shuttle]

So is h

[willow wraith]

yes but you don’t need to do all of the work to have h be in place for Δx

[swift shuttle]

How about, h is easier to write

:))

[willow wraith]

that’s just dependent on how you write

[swift shuttle]

Nah

It's objectively easier

[willow wraith]

🙅‍♀️

[bronze geyser]

https://klipy.com/gifs/blackbeard-blackbeard-writing

[swift shuttle]

Ok that's getting stupid

[willow wraith]

μ

[waxen yew]

is calc considered a pre-university course? I dont see the channel

[undone pumice]

it is not

there is a calculus channel in "early university"

id:browse #calculus

[waxen yew]

Ohh ok ty

[tight coral]

why is it called pre calculus? like what do you need to know before calculus

[undone pumice]

idk it covers like

[waxen yew]

trig ig?

[undone pumice]

trig

[waxen yew]

limits and derv

[undone pumice]

and uh

[tight coral]

oh yea

[waxen yew]

those are kinda imp

[undone pumice]

like logs and stuff

[waxen yew]

yeaa those

[undone pumice]

i didn't know what concavity was before this class

[waxen yew]

we got rational functions too

functions are imp

[undone pumice]

which would have been possibly problematic in calc when like second derivative type thing

[waxen yew]

whats that

[undone pumice]

concavity is like

up and down

[waxen yew]

transformations?

[undone pumice]

and its based on how the rate of change of a function is

changing

no

like

is the rate of change increasing or decreasing in an interval

[waxen yew]

ohh ok

kinda like the slope i think

[tight coral]

why is there no statistics maths channel I really need help on that side esspecially probability.

[undone pumice]

where the change in the rate of change is equal to 0 that's where the concavity switches and this is called a point of inflection

[waxen yew]

hmm

[undone pumice]

#probability-statistics

theres a probability-statistics channel

is that what you're looking for?

[tight coral]

oh yeah I didnt see it thanks

[waxen yew]

thanks

[undone pumice]

yeah idk i mean its kinda not that needed but like theres some topics like second derivative dealing w/ it in calc

not rlly sure what else because im not in calc yet so not sure what else from precal carries over

[waxen yew]

ohh ok

[waxen yew]

ill learn it later then ig

maybe in calc

[undone pumice]

yeah igs

idk

we covered it like the first day i was in precal when i transferred so i js know it

[waxen yew]

idk if next year i should go for calc ab or just regular calc in my school

they seem the same

[waxen yew]

damn ok

[undone pumice]

like most ap classes they cover similar content but ap covers more in depth and possibly faster

idk

we had counselor visits for freshmen today in our ela classes and my conuselor put me in calc ab so

igs im in ap calc

[waxen yew]

oh so ur not in pre calc rn

[undone pumice]

no like

i am

we were doing counselor visits

to plan our classes

for next year

so next year im in ap calc

[waxen yew]

ap calc as a sophmore 😭

[undone pumice]

yah

[waxen yew]

your smart

[undone pumice]

meh theres like a few other freshies in ap pc i know

like... three others?

[waxen yew]

my school doesnt let freshmens do that

[undone pumice]

meh they had to let me

i took integrated 2 and 3

so the next course was precalc after that

so i transferred into ap precalc two weeks into the school year

from regular

cus my counselor was a hater and didn't tell me ap precal existed-

[waxen yew]

ap pre calc is kinda like

mid if im being honest

but if u like the class take it

[undone pumice]

icl

i js want the gpa boost

[waxen yew]

we all do

[undone pumice]

yeah

[waxen yew]

i transferred my sophmore year

[undone pumice]

oh

[waxen yew]

wasnt allowed to take any aps or honors

[undone pumice]

oop

wow

[waxen yew]

i took a few my junior year

thats going well ig

[undone pumice]

nice

[undone pumice]

this is precalc... i see definite? integrals in there...

[reef parrot]

Where should i post this 😅

I dont see a calculus channel

[reef parrot]

I dont know where to post

[undone pumice]

its under early university

[undone pumice]

#calculus id:browse

look in browse channels to see all the channels... and it belongs in the calculus channel

[reef parrot]

Thanks!

[smoky schooner]

Guys whats a good math program for learning advnaced

[tame linden]

hey everyone, I'm new here and I'm started discrete mathematics by Rosen Kenneth and precalculus

[fossil kindle]

khan academy

[smoky schooner]

No like a program not website or app

[fossil kindle]

uh

idrk

tutoring (?)

[bronze geyser]

https://klipy.com/gifs/scam-suspicious

[undone pumice]

<@&268886789983436800>

[keen bone]

what type? contest, advanced (basically skipping grades), or tutoring for what ur learning rn?

[bronze geyser]

i think hes asking for in person enrichment learning

hes asking if theres any programs for that

[keen bone]

yes, i go to 2 diff programs one for comp one for advancement so which one does he need?

[bronze geyser]

which one does he need?

thats a question for him

[bronze geyser]

comp program?

extracurricular or school provided

[valid topaz]

wat

[smoky schooner]

Advanced

[keen bone]

extracurricular, i told u my schools education sucks

[keen bone]

which country?

[valid topaz]

hmmm