precalculus

[viscid thistle]

I’m sorry

Okay lets start with the known identified sides

6.2 and 9.2

If you want to scale 6.2 to 9.2 what do you multiply by?

4.4?

Why?

Because we used 4.4 to scale 9.2 and 6.2 for y

Well okay lets try scaling 6.2 by 4.4.

Does that give us 9.2?

No

6.2+4.4 10.6

Well okay

Thats not what I mean by scale

6.2*4.4 27.28

I mean dialate yeah

Thats clearly not it

So 4.4 isnt the scaling factor

However what about 6.2*(9.2/6.2)

Are you putting this into a calculator?

Yes

You shouldnt

Infact you should be able to know what that is faster than any calculator

This is precalc so youve taken algebra right?

Yes

What is a/a for any variable a?

I give up

I don’t understand this shit

?

I’m sorry

I’m trying

I just don’t understand this

It doesnt seem like you are trying to me

oh

Im unsure what there is to give up on when I am answering questions

Dude

I dont understand anything about this problem

Thats why I am trying to explain it

You haven’t questioned my explanations yet

[round hinge]

Where is 0?💀

If i know, e^x is constant.
And derivative of constant is always 0

[elfin cargo]

e^x is not a constant. It is an exponential function

[round hinge]

Ah

Ok

Bruh, I'm new to calculus

[leaden adder]

you can solve this by taking a formula when you f(x)=e^x f'(x)=e^x x' so it that case e^x times 1 equals e^x thats why ots the same as the base function

[wild falcon]

im assuming u used chain rule there, but in order to use chain rule, you have used the derivative of e^x. :)

theres a method i did in school that used some goofing around with derivatives to find the derivatives of functions such as sin-1(x), e^x, etc

[fading monolith]

Why do you think its a constant?

[fathom sphinx]

For part b how do i know if the sum is correct when subbing n=60 into Σr and Σr^2 respectively and adding them, must the result be 3660? (60 x 61 =3660)

book doesnt have ms

[willow skiff]

clearly the sum is larger than 60 * 61

given that 60 * 61 is one of the terms and there are 59 other positive terms being added to this

so you would need to sub n = 60 into n(n + 1)/2 + n(n + 1)(2n + 1)/6

[fathom sphinx]

yah i got 75640

also hi south

how's uni

[willow skiff]

,w n(n + 1)/2 + n(n + 1)(2n + 1)/6 when n = 60

[willow skiff]

good

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[fathom sphinx]

Do you still study math on the side. (You said you stopped majoring in math)

[willow skiff]

nah stopped studying it at uni

[fathom sphinx]

ah alright

can these questions be done using ''induction''

[earnest whale]

so i took a test for precalc 1 that let me skip it and i passed it but one of the questions i have never learned and i still dont understand it

[chrome ermine]

You can use power rule to get A,B,C

a,b,c are just the exponents of each letter

[fading monolith]

Properties of logarithms are:

1. log(a^b)=blog(a)
2. log(ab)=log(a)+log(b) and log(a/b)=log(a)-log(b)

Using this ones you can solve the exercise

[earnest whale]

ok thank you!

[leaden adder]

ye r u talking about the big formula with the limit of x reahces 0

[winter comet]

what do you study?

[brittle needle]

Can someone just give me a quick check on this?

[slim ore]

For question 1?

[brittle needle]

Yeah

Just a little confused on this addition thing with the finite domain

[slim ore]

Can u write down your answer

It's not very clear in the shade

Or that might just be my eye sight

[brittle needle]

f+g={(1,5),(2,8),(3,-3),(4,5)}

[slim ore]

dont listen to me

wait

[brittle needle]

All I would need is your logic

[slim ore]

I think my logic is wrong

[brittle needle]

My logic is I just took the x values that they have in common and added the corresponding y values

Do you see anything there obviously wrong?

[slim ore]

f+g={(2,2),(5,1),(6,1)}.

[brittle needle]

So what'd you do there?

[slim ore]

You can’t just add ( y )-values for matching ( x )-values. Instead, check if ( f(x) )’s output is in ( g )’s domain and follow the composition rule.

[obsidian monolith]

Zoty

[brittle needle]

Why would I use the composition rule when there's no composition? Or do I just not know the rule

[glad chasm]

I'm doing precalculus next year, and want to start getting ready. Are there any resources or topics I should look at?

[willow skiff]

sociology

[winter comet]

the study of sociopaths

[slim ore]

You must be stupid

[slim ore]

I study that too

[winter comet]

I am what gave it away

[slim ore]

Idk

[astral apex]

you have it right

[brittle needle]

Alright thanks

[astral apex]

f+g should have the same domain as that of f and g as much as possible; since they're different here, taking their intersection is the only thing that makes sense

[snow galleon]

can someone give a really really hard pre calc review/ practice for semester 1

i’m looking for reviews but they are all easy questions that wouldn’t be on the test

[astral apex]

I can give you a fun, not too easy problem

but I don’t know a good challenging full review off the top of my head

Suppose $m$ and $b$ are real numbers such that the equations $x^2 + (mx + b)^2 = 1$ and $(x-3)^2 + (mx + b - 1)^2 = 1$ have repeated roots $x_1$ and $x_2$, respectively. Then how many distinct lines $y = mx + b$ exist?

[obsidian monolith]

ManifoldCuriosity

[snow galleon]

ok thank you

is repeated roots repeated zeroes

[winter comet]

yeah

[snow galleon]

sorry how do you do it im kinda lost

this is what i have i was thinking you would find what m and b values can make zeroes and then use that but ik thats wrong bc there are infinitely many

[astral apex]

A hint: try working on just one of the equations at first, think about what kind of equation/graph it is (think of m and b as constants) and see if you can find some requirements for m and b, so that it has a repeated root

once you find something and then get stuck, do the same with the other equation

for the record it's a lot of algebra, but you did ask for really really hard

I don't think it's super hard, but rather tedious to do by hand

[wild falcon]

nah idk what its called i just did it

[astral apex]

it looks like you correctly set the discriminant of the first equation to 0, but there's an error when you multiply out terms

you should get b^2 = m^2 + 1 from that part

I forget the details of how to solve it from there

but there's a cool geometric significance in the result

I think you have a sign error too

should be 4m^2 - 4b^2 + 4 = 0

but the algebra is a real mess from there

I haven't checked the rest you did, I've been struggling to do it again myself

I think it's possible to avoid all these calculations to just answer the question of how many lines there are, with some slick argument. But if you want to actually find those lines it's gross

here's the cool way to answer the question, without actually finding the lines:

||Make the substitution y = mx+b into the equations to get x^2 + y^2 = 1 and (x-3)^2 + (y-1)^2 = 1, a pair of unit circles.

The roots of the parabola x^2 + (mx + b)^2 = 1 are also x locations of where the line y = mx + b intersects the circle x^2 + y^2 = 1, and similarly for the other parabola and circle. (This takes some thinking to convince yourself of).

Therefore, the parabolas having double roots means the line y = mx + b intersects both circles in only 1 point each!

So the answer is there are 4 such lines - the 4 lines that are mutually tangent to the two circles.||

[astral apex]

heard it from someone on discord

[fathom sphinx]

What did I do wrong for 8a? ( I tried solving the cubic equation but realized I'd get an imaginary solution)

[summer ruin]

you split the sum of r^2 - 1 into two sums incorrectly, the upper bound ended up being 1 instead of n

[feral raft]

Guys answer to this question is given 1+2a+b=0

i think it is wrong

[fathom sphinx]

Ah I see. Thanks so much Transparent

[willow skiff]

how so?

[feral raft]

Try the equation 3(x²-2.5x+1)

[willow skiff]

oh, well I guess blame the question for not specifying

1+2a+b=0 is a necessary condition, in that all quadratics satisfying this will have at least one root in (0, 1)

it is not a sufficient condition though, as there are other quadratics that also have this property

[feral raft]

Yes

[steady acorn]

simplifing and factoring are the dumbest shit to ever grace my computer sceen when it comes to trig

[slim ore]

lol

[inner topaz]

gyatt

[tidal dawn]

EDIEEEEE WOOOOOOO

THE GOAAAAAATTTTTT

I HAVE FINALLY FOUND THE PERFECT PERSON TO TEACH ME MATH AND PHYSICS

AHAHAHAHHAHAHAHAHA GOOOOAAAAT I LOVE HIM SOOOO MUCHH AND I ONLY WATCHED 1 VIDEO

HE HAS EVERYTHING I HAVE EVER BEEN LOOKING FOR OMG

AHAHHAHAHHAHAHAHAHAHAHAHAHAHAHAHA

I think am blessed by god

[olive quartz]

slide

[tidal dawn]

Wdym?

[warm vector]

Like whats the channel

[fathom sphinx]

https://tenor.com/view/solo-leveling-sung-jin-woo-solo-level-saahas-gif-27485947

w pfp

[fathom sphinx]

Agreed

his vids are so good

[olive quartz]

What's the channel

[olive quartz]

W pfp

[fathom sphinx]

broo omg s2 of solo leveling is so peak. I hate having to wait every week for new episodes like ew

think ill switch to mangwa (or whatever its called)

[fathom sphinx]

yessir

[olive quartz]

The manga is really good

[tidal dawn]

Broski just write Eddie woo math on YouTube

Switch on your brain

[olive quartz]

why so aggro lmao

Asked a simple question

No need to get so pressed

[tidal dawn]

Thats a phrase my biology teacher used to say every day

But like if you already know his name is eddie woo, just search up his name bruh

[exotic lion]

I need help with No. 10(d), I've done it but got a wrong answer

Here is my working

[tidal dawn]

I would actually be crying if they gave me a book like that

[winter comet]

you want the area between the curves

so you would integrate x - (x^2 - 2x) dx from 0 to 3
where x - (x^2 - 2x) is the positive distance between the curves (which when integrating would give you positive area)

I believe you just integrated one curve (distance from the x-axis) instead rather than the positive distance between the two curves

[finite tapir]

uh what i do wrong here

[orchid thunder]

Wait is this precalculus

I though it was calc

[winter comet]

not really, its calculus yea

[orchid thunder]

been telling my friends I am studying calculus

[winter comet]

sometimes they do it in precalc tho 🤷‍♂️

[orchid thunder]

Ahh lmao alright

[winter comet]

-3 <= x <= 7 and 7 >=x can be condensed to x >= -3
i think you meant x <= -8 rather than x >= -8

[finite tapir]

i keep mixing up the x<=8 and x>=8 stuff

[winter comet]

😂

[finite tapir]

sigh

[winter comet]

x is positive when its les than or equal to -8 so x<= -8 yea 😔

jus gotta use brain a bit more or smthn fr fr

[winter comet]

such helpful advice

[finite tapir]

oh

-3

like this

@winter comet 😭

[winter comet]

yuh

[finite tapir]

nice

[finite tapir]

is this right

[winter comet]

that's where it is increasing...

[finite tapir]

☠️

[winter comet]

💀

[finite tapir]

so like this

😭

[winter comet]

thats the same interval as last time bruh, you just wrote it differently ☠️

😭

[finite tapir]

im gonna go cry

brb

[winter comet]

like its decreasing over this interval right

[finite tapir]

yes

[winter comet]

cuz the tangent lines would have negative slope if you drew them anywhere on that interval

[tidal dawn]

I would be crying if I had to find the area by hand 😭

[winter comet]

so whats that interval :l

[finite tapir]

LIKE THIS

EZZZZZZ

[winter comet]

with integration is not bad ;-;

[tidal dawn]

Sometimes i sleep next to my beloved graphing calculator

[winter comet]

brooo 😭

bro just said 6 is less than 0

[finite tapir]

.....

[winter comet]

XD

[finite tapir]

...

[finite tapir]

THIS IS RIGHT

I CAN FEEL IT

[winter comet]

._. no

[finite tapir]

._.

[winter comet]

the endpoints of the interval its decreasing on are 6 and 14

do u see why :l

[finite tapir]

the dot on the 14

._.

[tidal dawn]

Smallest numbers always at the left when writing a range, something to remember

[tidal dawn]

Ew he’s a Tottenham fan, ofc bro can’t do math

https://tenor.com/view/arsenal-north-london-derby-nld-arsenal-vs-spurs-gabriel-magalhaes-gif-23237625

[winter comet]

uhh wut? u can say 6>y>0 or 0<y<6 (altho they arent correct)
you just cant say 0 > y > 6 😭

[winter comet]

yus

[finite tapir]

sigh

[tidal dawn]

Well true, but who tf does that

[winter comet]

tru

[finite tapir]

i have a 1 in 6 chance of getting it right

[tidal dawn]

Learning domain and range for the first time was so annoying

Cause I didn’t get shi

[tidal dawn]

I think you should maybe use greater or equal to sign

[finite tapir]

nah it was right

[tidal dawn]

I see

What website is that?

[finite tapir]

deltamath

[tidal dawn]

@willow skiff Yo south is that you bro?

Remember me?

From IB server 🤣

Did you get your IB diploma?

[finite tapir]

what did i mess up

[astral apex]

the curve "bounces" off the x axis if the multiplicity of a root is even

and crosses through if that multiplicity is odd

so your regions between x = -3 and 0, as well as between 4 and 6, are wrong

[next drift]

How can you solve for the degree of vertical asymptote algebrically?

someone pls help me

I know on a graph you can see if both ends hit the same direction

[willow skiff]

yeah a long time ago by now

uni's going well, how about you?

[tidal dawn]

Thats nice to hear

For me I didn’t get my diploma, so am doing a retake

[stone pasture]

i totally agree

[tidal dawn]

Yessirrr

[feral raft]

my question is why they removed pi

[uncut mulch]

where

[upbeat ivy]

cengage

[upbeat ivy]

they removed Pi, because f'(x) is 0 there. And you want strictly increasing and decreasing conditions

[uncut mulch]

f'(x) isn't 0 there

cos(pi) is -1

[elfin niche]

In my math class we are doing sinisodials specifically syr cxr tyx but for radians and I am having trouble finding the right quadrant to put my triangle

[winter comet]

it takes 2pi radians to go all the way around a circle
so if you only go 4pi/3 rad around the circle, you went (4pi/3) divided by 2pi -> 1/3 around the circle (1/3 of the circumference)
if you only go x radians around the circle, you go x/2pi of the circumference around the circle

[elfin niche]

I tried getting the answer for number one again which is -2 and I think I got it

[winter comet]

you got the answer right but for the wrong reason

oh i screwed up

[winter comet]

i should have said 2/3 of the circumference

(4pi/3) / 2pi = 2/3

mb ;-;

[winter comet]

but anyway the triangle should be in the third quadrant, 4pi/3 rad around the circle

you have it 2pi/3 around the circle but i typod 1/3 so thats mb ;-;
sec(2pi/3) happens to equal sec(4pi/3) but 💀

[elfin niche]

my teacher says to find the quadrant, if I did'tn say, by finding the least common denom, but then I get even more confused because two of what I have transformed could fit the bill

[winter comet]

huh?

[elfin niche]

so the way my teacher wants us to do this by taking the radian version of the circle, 0pi,pi/2,pi,3pi/2 and 2pi, finding the least common denom of what is given, ex sec 4pi/3 and then finding the quadrant and then doing the triangle stuff and then getting the answe

[winter comet]

what do you mean the least common denominator?

between what two fractions?

[elfin niche]

okay so lets say i'm solving for sec 4pi/3, since the radian versions of the circle don;t match it I would use the lcd, whitch I think would be 3 and then convert all the radians into something that could match it then that would hopefully find the quadrant

[winter comet]

🤔

[elfin niche]

i'm sorry for not being very good at exaplaning

[winter comet]

why not just say
"how much of 2pi is 4pi/3"
x * 2pi = 4pi/3
the answer is 2/3
go 2/3 around the unit circle, construct a triangle and find the hypotenuse/adjacent ratio

[winter comet]

naw all good XD

i mean do you fully understand the process you described?

if you simplify the fraction they give you (which i think is what you mean by lcd),
then "convert all the radians into something that could match it"
something you could match it -> degrees? or a fraction of the circle's circumference? or what does this refer to

[elfin niche]

Okay so last unit we did what we were just talking about but with degrees

Now we are doing it with radians

we also can’t convert or use a calculator

[terse aspen]

Hey can someone help me with a simple bearing problem?

[astral apex]

[tulip idol]

This is a question for ap pre calc

Or multiple ig

I posted in 2 other channels cuz I didn’t know there was a pre calc channel mb

[terse hare]

sorry in advance if this is not the right chat box
Is anyone looking for M1 (Cambridge) basic notes? Feel free to knock if interested.

[terse aspen]

Hey I have a ti inspire cx ii and I want to get the x value of cosx~ -0.451 but it doesnt give me x

[boreal heath]

arccosine (-0.451)

if you dont know arccosine means cos^-1

[terse aspen]

Thank yiu

[silver mist]

Guyd

does anyone know how to do this

I genuinly have no idea

Our teacher literally didn't teach this

And I have a whole packet of this due at 8 am in the morning

[tawny creek]

both are a graph of quadratic over quadratic function

[silver mist]

but how do I find the equation

[tawny creek]

The first one is $$f(x)=\frac{2x(x+1))}{(x+5)(x-3)}$$

[obsidian monolith]

TargetVN

[silver mist]

how?

what about x-4

[tawny creek]

The way is to determine the denominator

the graph has 2 vertical asymptote x=-5 and x=3 so the denominator has to be (x+5)(x-3)

[silver mist]

but what about the hole

[tawny creek]

Oh

wait a sec

didnt realize that hole

[silver mist]

this is the answer

ty tho

[tawny creek]

oh, so that explains the hole

[silver mist]

yeah

what about 8

[silver mist]

How do I do 8

[tawny creek]

it's the same thing, determine the denominator through the vertical asymptote then determine the numerator through the roots of y=0, multiply both denominator and numerator by (x-1) so that the graph can have a hole there (or simply to make the function undefined at x=1), then calculate lim f(x) when x-> 1 and complete the function

[silver mist]

Wait

@tawny creek

I got it wrong

why is it wrong

[tawny creek]

huh

that shouldn't be wrong

[silver mist]

Bruh

😭

[tawny creek]

i even regraphed it on desmos

[silver mist]

bro idk at this poing

Could you help with a few more

[tawny creek]

the 9th one is standard linear over linear function, which can be determined through VA, HA and zero. it has a hole, though, so do the same thing like what you did in the previous questions

the 10th one is linear over quadratic function, 2 VA, 1 HA, 1 zero and 1 hole

[silver mist]

nvm

i got it

[tawny creek]

yeah its x-3

[silver mist]

what about the rest

[tawny creek]

10th one

[silver mist]

like 11 - 15

[tawny creek]

honestly idk how it's false

[silver mist]

You said there was a HA

right?

[tawny creek]

the HA is automatically y=0

[silver mist]

oh

[tawny creek]

which is kinda pointless here

for the 11-15 one, it's best to factor stuff out

$$f(x)=\frac{x(x-1)}{x(x-1)(x+1)}$$

[obsidian monolith]

TargetVN

[tawny creek]

now you can see more clearly: no x-int, 1 y-int, 2 holes, 1 HA, 1 VA, domain is shown right on the denominator, and range is R \ {0}. To solve f(x) <= 0, you can graph it, but it is apparent that the inequality is reduced to 1/(x+1)<=0, so x<-1

[silver mist]

?

[tawny creek]

yeah that's a lot, but trust me, everything is already shown right after factoring

[tawny creek]

^

[silver mist]

Oh

forgot +

not -

How do I find the holes

[tawny creek]

oof

the holes are the terms appear on both denominator and numerator

at those point, the limit exists but the function is undefined

[silver mist]

(1,0)?

[tawny creek]

(0,1) and (1, 1/2)

2 holes

[silver mist]

why?

where did you get 1/2

[tawny creek]

x and x-1 appear on both denominator and numerator so those are where hole exists

limit of f(x) when x -> 0 is 1
and limit of f(x) when x->1 is 1/2

[silver mist]

?

[tawny creek]

or simply cancel out those terms and treat f(x) as 1/(x+1)

(easier to understand that way)

[silver mist]

how did you get the x values

[tawny creek]

its the terms that cancel out when simplifying

[silver mist]

oh okay

one second let me right this down

[tawny creek]

just remember how we created the hole in the previous questions

[silver mist]

What would the y - int be

[tawny creek]

oh yeah

its none, because it's undefined at x=0 (you could also say there's a hole at (0;1))

[silver mist]

What would the HA be

[tawny creek]

y=0

[silver mist]

why not 1

isn't it technically 1/1

[tawny creek]

simplfying gives f(x)=1/(x+1)

no

[silver mist]

oh okay

[tawny creek]

you determine the HA by calculating lim f(x) when x -> inf and x-> -inf

both the limits are 0, so y=0 is an HA

[silver mist]

what does inf mean

[tawny creek]

abbreviation for infinity

[silver mist]

oh

What would the range be

and domain

[tawny creek]

domain is R \ {0;1;-1} because the function is only undefined at x=0, x=1 and x=-1

[silver mist]

How would I write that tho

got it wrong

[tawny creek]

i was about to tell a second way to represent it

though, the suggested answer is still wrong (the domain)

[silver mist]

gt it

what about range

[tawny creek]

yep that

[tawny creek]

range is R \ {0} or a different way:

[obsidian monolith]

TargetVN

[silver mist]

What about the limits?

[tawny creek]

its basically just telling you to make a limit statement

for example of the 13rd one:

[silver mist]

How do I do the one with the holes

the limits for that

[tawny creek]

actually to be more precise, i recommend including both positive and negative infinity

[silver mist]

Nah, the other one was the one we use

the one with lim

[obsidian monolith]

TargetVN

[tawny creek]

this is more precise because there are situations where both limits will be different

which creates 2 HA instead of 1 HA as usual

[silver mist]

ohh okay

wait let me check, one second

What would 15 be

[tawny creek]

basically "lim f(x) when x -> somewhere"

for example, the hole at (0;1) would be like

[obsidian monolith]

TargetVN

[silver mist]

Alright, TYSM Target

your goated bro

[tawny creek]

gl

[silver mist]

tyty

@tawny creek

One last question

what about 8 and 10

you said you couldnt see an issue

with what I wrot

[tawny creek]

i regraph the same thing in desmos and it gives the exact graph

[silver mist]

Oh okay

[tawny creek]

so idk what did i miss

[silver mist]

It's alright I'll just submit it

ty tho

[tawny creek]

np

[silver mist]

Are you in the U.S.

[tawny creek]

im in Vietnam

[silver mist]

ohh alr

for me it is 1:14am

so I was gonna say good night

but I guess it would be mroning

or pm

actually

good afternoon

1:14pm

[tawny creek]

yeah its about 1PM here

thx

[silver mist]

alr cya 👋🏽

[raven laurel]

hello guys

[daring vale]

i didnt know that secondary schools did calculus

[winter comet]

wdym?

[daring vale]

like this chanell is meant for secondary school students right?

im like mid way through secondary school and i havent come across it nor have i seen anyone else do it and year 10 and year 11 dont do it and i know cause i saw their curriculam

[winter comet]

i mean this channel is called precalculus

if you want calculus and beyond you can go those channels

[daring vale]

wdym pre calculas

[winter comet]

like #calculus

[daring vale]

pre calc and calc are the same thing

[winter comet]

no

[daring vale]

oh ok

so whats pre calc

[winter comet]

its just a class for stuff before calculus like trig and stuff i dont really know

could be practically anything ngl 💀

[astral apex]

it's a bunch of algebra, exponential functions and logarithms, and trig

meant to prepare you for calculus next

[turbid bloom]

does linear algebra done right provide a full overview of linear algebra

im doing linear algebra on khan academy and it keeps redirecting me to precalculus for parrelelogram rules and stuff

btw what are logarithms used for

[astral apex]

learning linear algebra without knowing logarithms?

not that they’re logically required, just pretty strange

[river drift]

linear algebra done right is usually recommended for a second course in linear algebra. it contains all the necessary material, but a first-time student may find it difficult compared to more introductory-level textbooks like strang or anton

[astral apex]

as for LADR, yes, it’s a full good book, but as mentioned above may be too difficult for you at this time

[astral apex]

they’re the inverse of exponential functions. A lot of things have a logarithmic nature to them, for example our perception of pitch and loudness in sound

[winter comet]

does it cover more material? or is it just the same material but deeper

cuz i havent gotten far but it seems to be just the same material deeper but idk if it does more :l

[river drift]

the main difference is a focus more on proofs than on calculations (although even a more calculation-based linear algebra text has more proofs than e.g. intro calculus)

so it won't really teach you how to do any calculations (it's assumed you know how to do those already), but it will show you how to prove the results that were handwaved in the calculation-based textbooks. and it will also go farther into some of the more conceptual material, but not cover any material of interest only to numerical linear algebra

[winter comet]

yeah

[turbid bloom]

ik what they are just not what theyre used for irl

[silver mist]

wdym

most kids take calc 1 and 2 in 10th

[winter comet]

i wouldn't say most but a lot yea

[silver mist]

yeah a lot

that's what I mean

mb

[winter comet]

most people aren't particularly math people tho

[silver mist]

true

at my schjool tho, most kids take calc 1 and 2 10th

[winter comet]

ah

[cold mica]

can someone give me tips on graphing arccos and arcsin

lwk kinda lazy to actually learn it rn 😿

[novel kindle]

$\forall \phi \in \mathcal{D}, , \lim_{n \to \infty} \int f_n(x) \phi(x) dx = \int f(x) \phi(x) dx$

[obsidian monolith]

SELVATOR

[balmy goblet]

me core

[fading monolith]

?

[scenic turtle]

If I use 4 and 3 in 2πrh it gives 126

Can someone please explain why author chose 5 and 6 specifically

[daring vale]

im in the uk so up to year 11 is secondary school and we dont do calc in secondary school we do it in college and sixthform

[silver mist]

Ohh alr

In the U.S I guess it's diff

For us 9th starts hig school

[vernal path]

in uk middle and high are the same school

[pale shuttle]

This is plug and play tbh, look up properties of exponents and exponent notation to figure out how to apply those fractional exponents to their respective quantities

[manic wasp]

what is sixthform

[dim shale]

put in values and solve

convert everything into conventions

[novel kindle]

1÷3 = 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...

When we multiply it by 3

Equal = 0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999...

which means 1 - 0^+

4÷3 = 1.333333....

[viscid thistle]

hello! does anyone have recommendations on where to go to learn precalc bc and calc bc?

is khan academy reliable? 😭

[simple urchin]

This doesn't sound correct. The average distance from a planet to the sun? Like there are 8 planets from the sun with all different distances, how can there be an average? Maybe I'm reading it wrong.

[winter comet]

not the average of the set of distances of each planet
but the average distance for a planet (the distance varies since orbits are elliptical)

i assume thats what it means

[astral apex]

yes, .9 repeating = 1

it surprises people because they're never told growing up that the same number can have different decimal forms, and it's not so obvious. But it's true

but the only way something like this can happen is with repeating 9s

(In our base 10 decimal system)

for another example, 0.49999... = 1/2

[astral apex]

yes it's fine

[obtuse inlet]

anyone know anything about the general form of a transformed function

[astral apex]

y = a*f(b(x-c)) + d

[obtuse inlet]

Yeah, im just confused with "b"

like for example

[astral apex]

b is the horizontal shrink/stretch factor

[obtuse inlet]

to figure out the value for b its either 1/|b| or just |b|

so if im given say, f(-2x)

and asked to find b

is that 1/|2|

then apply the negative to indicate the reflection?

[astral apex]

well, it's shrinking by 2 and also horizontally reflecting in that case

shrinking by 2 is like multiplying by 1/2 so maybe that's where your 1/|b| is from

it's a shrink if b > 1 and a stretch if 0 < b < 1

[obtuse inlet]

right, and if 0 > b then a reflection is applied

if im not mistaken

what if I was given 1/2f(1/2x) would that be a vertical shrink by a factor of 0.5 and a horizontal stretch by 2?

[astral apex]

yup

[obtuse inlet]

okay wait I think I understand, to find "b" it's always going to be 1/|b| because 1/1/|2| = 2

so if I had a whole number, like 2 as my "b" then it would be 1/b which in this case is 1/2

just had an insane brain wave oh my god

then my next question, if I'm given a replacement, like y -> 4y can I set it up in an equation format? like 4y = f(x)

then that makes my "a" term = 1/4 so its gonna be 1/4f(x)?

[astral apex]

yeah. In general solve for y and see how the numbers around f(x) end up

[dire harbor]

yo guys

I have ran into a slight conundrum

actually wait this is precalc not calc

wait where is the calc

[river drift]

#calculus

[daring vale]

so ssixth form is like college so year 12 and year 13 but its part of a secondary school years 7 to 11. so same premises same teachers same head teacher and so on.

[willow skiff]

there are also other sixth forms that are not part of a secondary school

sixth forms can be for adults too

[agile nexus]

Organic chemistry tutor is fire tbh

[willow skiff]

yeah

if you want a book try Princeton Review

also there's a huge skill differeence between AP precalc and AP Calc BC

[viscid thistle]

YUHH ive been going through the uh new calculus video playlist rn 😭 💀

[viscid thistle]

oop-

[viscid thistle]

OKII thank you

[agile nexus]

yeah he's a W

[viscid thistle]

FR

[formal wren]

How?

[winter comet]

at theta=0, what is the displacement from the ray it creates to the x-axis?

[formal wren]

Wdym?

[winter comet]

you understand that the ray they call P starts at the positive x-axis and rotates around counter-clockwise right?

[formal wren]

Why counter clockwise

I did it clockwise

Oh wait

Mb

Yeh ur right

So like how do I interpreters graph works

What do the graphs mean

[winter comet]

for every theta, there is a ray P that has a distance y from the x-axis and a distance x from the y-axis

[winter comet]

so these graphs are what the y-values are per theta

is this makin sense or naw

[formal wren]

Yess

I seee

So it would be 1

?

[winter comet]

what would be 1?

[formal wren]

Y and X

[winter comet]

x and y vary

like for this angle, x is much smaller and y is much bigger...

[formal wren]

Ohhhh

[formal wren]

I c

I was used to that angle that’s always 1

[winter comet]

i mean the radius is 1...

[formal wren]

Wait it’s always 1 right?

[winter comet]

for this circle the radius is always 1 yes

based on the possible answers

[formal wren]

Got u

[winter comet]

so anyway

when theta is 0, do you know what y is?

[formal wren]

Ermmmm

0?

[winter comet]

yea

[formal wren]

I think

[winter comet]

what about when theta is pi/2 ?

[formal wren]

Wait how

I guessed

Isn’t theta the right angle plus the extra part in the second part of the circle

[winter comet]

when theta is really small, y is really small
(and when theta is 0, y is 0 and x is 1)

[formal wren]

R u taking tangent of it?

[winter comet]

no...

like here, y=0 because theta=0

the ray IS the positive x-axis when theta=0

[formal wren]

Oh is theta that tiny red angle?

[winter comet]

yeah

well i mean

[formal wren]

But in the picture

It’s large

[winter comet]

its a variable angle

you can make it however big you want, and it will have a corresponding y-value and x-value

[formal wren]

Ohhhh ok

But like

If it’s an angle

Why wouldn’t it be like 125 for example

[winter comet]

it can be

[formal wren]

So how is y=0

[winter comet]

y=0 when theta=0

[formal wren]

Is that a common rule?

[winter comet]

when theta = 125 degrees, y is something different

[winter comet]

are you familiar with sine and cosine?

[formal wren]

Yes

[winter comet]

y = sin(theta) for a unit circle, and x = cos(theta)

[formal wren]

Yes

[winter comet]

for theta starting at the positive x-axis

[formal wren]

OHHHH like the side values??

Outside*

[winter comet]

wdym

[formal wren]

I think I get what u mean

Like the unit circle

Cis and sin values

When theta is 0

Cos and sin is 0

[winter comet]

when theta is 0, y= sin(theta) = sin(0) = 0
but also when theta=0, x = cos(theta) = cos(0) = 1

x is the horizontal length and y is the vertical length here

[formal wren]

Why is cos x 0=1

[winter comet]

i mean can see that when theta is 0, the horizontal distance is 1... from the picture...

and the vertical distance is 0 :l

[formal wren]

Ohhhhp

I see

Continue

[winter comet]

its like an infinitely small triangle but the height of the triangle is 0 so XD

[formal wren]

I seee I though the p line is what we was talking about

[winter comet]

ahh nono yea thats the radius and its always length 1

[winter comet]

do you know what y is when theta=90 degrees?

[formal wren]

1

[winter comet]

yeah

[formal wren]

Alr so

I get that

How do I get the graph

[winter comet]

so we know when theta=0, y=0 -> (theta,y) = (0,0)
and when theta = 90 deg = pi/2 radians, y =1 -> (theta, y) = (pi/2, 1)
right?

[formal wren]

Yes

[winter comet]

does any y-theta graph look like it has both of those points

[formal wren]

Has points (0,1)

[winter comet]

or better yet, does one look like a sine wave :P

[formal wren]

And ?

What other points

[winter comet]

(0,0) and (pi/2,1)

[formal wren]

Is this just pi/2

What’s the 1

OHP

WAITP

NVM

[winter comet]

when theta = pi/2, y=1

yea

[formal wren]

it’s a coordinate

[winter comet]

mhm

[formal wren]

Gotta

Ok soooA has it

What would I write for explaining

Why the other graphs are wron

g

[formal wren]

?

[winter comet]

yea

[winter comet]

uhh

you could say when theta is pi/2, y is 1 and none of the graphs besides A has this attribute? or something idk

[formal wren]

Ohhh ok tysm

Wait

[formal wren]

Sorry

Why did we choose pi/2

Out of the other points

[winter comet]

pi/2 radians is 90 degrees, kind of an arbitrary choice but easy to work with
I kind of specifically picked it because i could see the other graphs didn't have it

[formal wren]

But graph d has it?

[winter comet]

at pi/2, y is 0 for graph d

[formal wren]

Oh yeh right

Thank you

[formal wren]

@winter comet help

[grizzled bolt]

Hello

[willow skiff]

you can just plot y = cos(x) on Desmos to find out the shape of the graph

go back to your notes to find out what cos(theta) represents on the unit circle

is it x or is it y

[valid mason]

im just reading through a textbook, but shouldn't this be equal to 80? because it didn't take the absolute value of -13

[fathom sphinx]

Can i express the range as an inequality?

[willow skiff]

you can't because the domain is not continuous

so the range of the function would just be individual y-values in a set

[fathom sphinx]

Ah so if it was continuous it wouldn't have a restriction?

[willow skiff]

yeah now you would be able to use an inequality

[fathom sphinx]

ah i see

thanks @willow skiff

[willow skiff]

yeah so like there's a difference between range and codomain

at high school level there's no need to introduce the idea of a codomain, cause the domain is implicitly assumed to be R

unless there's info that says otherwise in the question

no worries!

[fathom sphinx]

i wish they had ''codomain'' at the high school level

😔

[whole void]

@willow skiff Can u explain codomain a tiny bit and its use? I don’t get it exactly

[muted hinge]

There's no absolute value they just used square brackets to distinguish from the other brackets

[valid mason]

pfft lmao, completely overlooked that i will make sure i use my glasses next time thanks

[willow skiff]

properly speaking, a function contains three parts: the domain, the codomain, and a relation between the domain and the codomain

in high school or below you omit the first two

but if you've seen $f: \mathbb R \to \mathbb R$ for example, you know that codomain = domain = R

[obsidian monolith]

south

[willow skiff]

we also could have $f: \mathbb Z \to \mathbb Z$

[obsidian monolith]

south

[willow skiff]

in other words, we define the set of the function's possible outputs in the function definition

that set is the codomain

[whole void]

Yeah. Is there anything like important about the codomain? I understand there are differences between the range and the codomain clearly but still

[willow skiff]

no

[whole void]

oh? so whats the point of specifying the codomain? why not just say f(x) is a function defined on the reals ...

[willow skiff]

what you said means that the domain is the reals

the codomain could be anything, as long as the range is a subset of the codomain

[whole void]

yep

[river drift]

when we are defining functions formally, we always have to specify the domain and codomain as part of the definition of the function

and it's much easier to say "this outputs real numbers" than try to figure out the range

[astral apex]

it's useful to have the concept of a function being "onto" or not. Without codomains, every function is onto its image set (aka range), and the concept disappears

[turbid saffron]

how does one express 3^2^4^5 as a single power?

[astral apex]

do you mean ((3^2)^4)^5 or 3^(2^(4^5))?

if you came across it and it looked like this:

$$3^{2^{4^5}}$$

[obsidian monolith]

ManifoldCuriosity

[astral apex]

then you work your way from the top down

a largish sort of number

writing it as a single power isn't very practical because 4^5 = 1024 and 2^1024 is kind of large. That's the number that's the single power you'd put on 3

2^1024 has 309 digits

[opaque loom]

3^30

powers multiply dont they?

[gleaming crest]

Not if it's written like above

If it's (3^2)^4)^5 then yes

[faint atlas]

help

i cant work it out

please just help

[grim bolt]

try using summations

and stirling's approximation

i've seen this exact question before

so i know the answer is e^x

[winter comet]

<@&268886789983436800>

again?

😭

[safe basin]

some persistent ahh mf

[winter comet]

fr

[scarlet wyvern]

how would i solve this? I originally squared both sides but i realized that ruled out the possibility for a negative solution

and i cant think of another way to solve problems like it without squaring both sides

[whole void]

what?

did it get deleted

[winter comet]

some guy that was spamming a scammy-looking link over and over

yeah

i mean like

he'd get banned and then another would repost

💀

did it like 3 times lol

[whole void]

know the tangent half angle

[scarlet wyvern]

is that another trig identity

[whole void]

yes bruh

[scarlet wyvern]

mb my teacher only got us to the sin sq cos sq = 1 identity so far

[kind glade]

Hey I've been having difficulty trying to deduce the solution to these answers

It's hard for me to find a specific video

Or I just didn't understand the video

Can someone please tell me how these answers are derived or show me video that can guide me

Can someone explain question 1 if possible

[waxen vale]

For trig identities, you typically only want to work on one side at a time

[whole void]

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

[obsidian monolith]

hockeydude85

[whole void]

thats like the most basic possible identity. hopefully u will still get there

[solar olive]

$\frac{1-\cos x}{\sin x} = \tan \frac{x}{2}$

[obsidian monolith]

impract1cal

[unreal ridge]

any1 know how to solve this only using pythag identities?

would greatly appreciate it 🙏 (please ping if u manage to solve it)

[solar olive]

$\frac{2\tan x}{1-\tan^2 x} = \frac{2 \tan x}{2-\sec^2x}$

[obsidian monolith]

impract1cal

[scarlet wyvern]

@unreal ridge

in the same struggle boat with the only pythag identities 🙏

[unreal ridge]

ty

im looking through it rn

[unreal ridge]

😭

quiz tmr and teacher was absent today for me

[fathom sphinx]

where does ''the 2 in (k+2) come from ;-;

[fading monolith]

When you sum k(k+1)/2 + (k+1)

The numerator turns into k(k+1)+2(k+1) if you factor (k+1)(k+2)

[acoustic leaf]

Is this correctish

[inner topaz]

looking correct

put limit before sigma though

[whole void]

No. That sigma symbol is drawn too poorly

[safe basin]

Blud got the ECG signal sigma

Js draw an M sideways bro 😭

[winter comet]

<@&268886789983436800>

[raven laurel]

Guys i got a 65/100 on my vectors and law of sines/cosines quiz

[sturdy hound]

what topics does this question cover and also does anyone know where i can find more practice questions like these

[sturdy hound]

its ok i also did bad on my recent test

luckily my teacher is super nice tho so i can do reassessments

[raven laurel]

i cant.my friend got a 27/100 tho LOL

[raven laurel]

what did u get

[sturdy hound]

oop

[sturdy hound]

77.5%

[raven laurel]

BRO THATS SO GOOD

ID KILL FOR THAT SCORE

[sturdy hound]

uhh idk abt me tho 😭 bc everyone else in the class did so much better

[sturdy hound]

maybe ur tests are way harder

[raven laurel]

how much is a A in ur class

[sturdy hound]

93 percent

we have A+'s tho from 96.5% and up

or 97% i think

[raven laurel]

for us a A is 87 percent and he rounds up lol

[sturdy hound]

WOAH

lucky

[raven laurel]

so 77 is really fckiong good

[raven laurel]

he gives us the hardest shit

[sturdy hound]

makes sense

[raven laurel]

no lucky

[sturdy hound]

oof

[raven laurel]

what topic u doing rn?

[sturdy hound]

vectors and matrices

[raven laurel]

i am starting partial fractgions

[raven laurel]

thast the test i got a 65 on

[sturdy hound]

oh💀 i hope i do good

[sturdy hound]

idk what that is yet

[raven laurel]

hard shit

[sturdy hound]

oh no

anyways i gotta study tho but also if u can find any practice problems liek this id aprpeciate it

[raven laurel]

LMAO thats the hardest type of problem

do u know how to do it?

[sturdy hound]

not really

my teacher always pulls out the problems we've never seen before to test our "application"

😔

[raven laurel]

when your teacher doesnt talk about it and puts it on the test its pretty fucking hard

[sturdy hound]

fr

like im not that intellligent im jsut good at memorizing

[raven laurel]

so true

[thick ridge]

can someone help me out with some precalc i gotta do?

i got a test tmr to study for

[sturdy hound]

what topics is it on

[thick ridge]

trigonometric identities in precalc

that should give you a basic idea

[sturdy hound]

i dont think i got to that unit yet 🙁 idk what im doing is just reviewing a ton of review problems online cuz it will help me get more experience

and i think urs might be more memorization? so maybe make a quizlet and then review that too

sory cant be of much help

[raven laurel]

i did this chapter alr whhat u need help with

@thick ridge

[scarlet wyvern]

ima be honest trig identities are a lot of intuition unless you wanna have like 15 steps

so a lot of practice

idk if you can do that in the time you have tho 😭

[thick ridge]

sorry was doing my laundry

[thick ridge]

omfg thats all it feels like

[scarlet wyvern]

yea you kinda need to just feel whats right

and go with your gut

ig its just pattern recognition

[thick ridge]

if you dont somehow decide to go down the right path by luck or have like vision into the future, it feels like ur done lmao

[scarlet wyvern]

usually most methods can lead you to the right answer

it's just that some are a bit more tedious

like sure you could convert everything to sin and cos but knowing some identities and tips&tricks help save time and effort

[thick ridge]

memorization is a small part compared to what feels mostly like logical thinking

[raven laurel]

what i used

is convert everything into cos and sin

and use identites from there

[scarlet wyvern]

this will work fine it's just more steps

i guess its like the most reliable method

[raven laurel]

thats how i did it lol

[raven laurel]

ye

[thick ridge]

how would you do it hub?

[scarlet wyvern]

intuition 😭

[thick ridge]

ah

[scarlet wyvern]

like honestly whenever i see a problem

[thick ridge]

so im cooked

[scarlet wyvern]

my first thought is like

okay whats the least amount of brain power i can use to condense this all

so like if its easy enough just multiple fractions to get the same denominator and then use identities

[thick ridge]

i think what really fcks me is just mid test, ill get tunnel visioned

[scarlet wyvern]

converting to sin and cos is my last resort

[scarlet wyvern]

just convert it all to sin cos

it'll 100% lead you to the right answer

it's just annoying

[thick ridge]

can you give me a really annoying one to solve by just converting to sin and cos?

so i can practice?

[scarlet wyvern]

yea one sec

ill give you one from my test review

[thick ridge]

cuz i feel like my issue with doing that route is then my algebra is a whole cluster fuck of random stuff

and i have no idea how to solve it all

[scarlet wyvern]

when i do basic algebra i turn my brain off and write bigger

cause im pretty confident in my ability to do alg 1

so as long as i dont go blind i can just do it

[thick ridge]

alright one sec

[thick ridge]

are these parathesis or brackets

cuz idk what brackets mean

[scarlet wyvern]

brackets are just parenthesis

[thick ridge]

oh ok

[scarlet wyvern]

but sometimes it's hard to tell when you have too many parenthesis

so brackets make it easier to see

wait idk if youre doing verifying trig identities

if you are heres another problem

[raven laurel]

@scarlet wyvern my teacher is a bitch so he will say verify if possible to throw us off

[scarlet wyvern]

yo thats actual torture lmao

[raven laurel]

i know 😭

[scarlet wyvern]

our teacher doesnt give us problems that cant be verified

[raven laurel]

lucky

[scarlet wyvern]

what are those steps 😭

but yea answers right

[thick ridge]

i turned everything into sin and cos like you said 🥲

[scarlet wyvern]

it's just hard to follow

idk what leads to what

i just see a big circled 1

[thick ridge]

im confused at what the answers supposed to be

[scarlet wyvern]

you're just trying to prove they're equal

also when you verify you typically only change one side of the equation

[thick ridge]

oh

[thick ridge]

ah, my teacher doesnt really make us do any verify problems

[scarlet wyvern]

its good practice

[thick ridge]

ig so

[scarlet wyvern]

its just simplifying

but its more demanding

[thick ridge]

the most we’ll have to verify is if an answer is an actual answer (like in those weird ass algebra 2 units where some answers were fake)

[scarlet wyvern]

i kept forgetting to do that

[thick ridge]

oh this ones a bitch 😭

[scarlet wyvern]

yea ima be honest i got tunnel visioned

[thick ridge]

can you give me just the first step?

like just the first one?

cuz i have genuinely no idea how to solve it

[scarlet wyvern]

turn 1 to cos^2/cos^2

for the first fraction

[thick ridge]

i did that

[scarlet wyvern]

second fracation turn 1 into the pythag identity

sin^2+cos^2

[thick ridge]

but at least i know im on the right track

my algebras shit, am i allowed to do this?

[scarlet wyvern]

yea

[whole void]

u need to have an argument for sin not just sin

But yes of course multiplication works like that …

[thick ridge]

this is where im at rn

i got no idea where to go from here

[scarlet wyvern]

i have no clue where youre at

[thick ridge]

the thing circled

[thick ridge]

this question

[scarlet wyvern]

yea i just have no clue what you did to get there

[scarlet wyvern]

you did this step wrong

well technically before that step

from here to the next step

tip for fractions like these:
(a/b)/(c/d) is just (a/b) x (d/c)

[thick ridge]

like this right?

[scarlet wyvern]

you cant write that cause thats not correct

but if you omit that step then yea its right

[thick ridge]

ykim i was just visualizing keep change flip

[scarlet wyvern]

if its just aid then put it as sidework not an arrow cause that indicates it's a step

[thick ridge]

the “2cos^2 - 1” is pissing me tf off cuz i cant factor it for shit 😭

[thick ridge]

can you give me a tip to go from here?

[scarlet wyvern]

yea uh

you did too much

idk where you went wrong but something went wrong

[thick ridge]

😭

[scarlet wyvern]

i need to goto sleep so ill just send my solution

[thick ridge]

ok

[thick ridge]

damn youre smart