precalculus

[hasty wadi]

(;

[calm thicket]

THAT'S THE SPIRIT

I wonder if I should ping sqrt(2), she'll save us 👀

[severe verge]

🤔

[hasty wadi]

@pine kindle only 5 submissions are available

im 4/5

THIS IS THE LAST ONE (::::::::::::

lmao fml

who's this sqrt2 person?

and will they be able to save the day?

WEBASSIGN IS SHIT, BUT IT'S MANAGABLE

[calm thicket]

webassign is bad :c

[severe verge]

how much is this worth? 0.01%?

[grim yarrow]

just put like

[calm thicket]

woog this question is literally 20% of his grade

[hasty wadi]

there are only 11 questions

[grim yarrow]

wait

[calm thicket]

== 1/11*100

[granite stirrup]

9.09090909

[grim yarrow]

no way that's fucking true

[calm thicket]

If he gets this wrong it's 9% of his grade off

[grim yarrow]

20% of your grade on a part of a webassign?

[hasty wadi]

:::::::::))))))))))))

[severe verge]

intriguing.

hi ann

[willow bear]

👀

[grim yarrow]

new epic channel

[calm thicket]

ann save us

[hasty wadi]

i know that once i go to class tomorrow, my teacher is gonna do this fucking question in 5 minutes and put our asses to shame ):

[willow bear]

what's wrong

[calm thicket]

we've devolved into chaos and hopelessness

[hasty wadi]

^

[calm thicket]

part b has stumped us all

[hasty wadi]

LOL

fml

[severe verge]

i suggested an answer, want confirmation or unconfirmation

[calm thicket]

what was your answer

Last I saw from you was the one I got as well (which didn't work)

[severe verge]

arccos(100/L)

[willow bear]

θ = arccos(100/L)

yeah

[hasty wadi]

if this answer stumps ann, were all fucked

[calm thicket]

*we're

[hasty wadi]

no u

[calm thicket]

How'd you get 100/l tho

[vital tartan]

ait ...

[severe verge]

cos

[willow bear]

right triangle

[vital tartan]

20% of his grade?

[severe verge]

=adj / hyp

[vital tartan]

jesus christ

[willow bear]

it's literally just a right triangle jeez

[grim yarrow]

it's not 20%

[vital tartan]

lol

[willow bear]

@pine kindle they say to get it in terms of l

[vital tartan]

tin terms of l but not > in terms of only l

[hasty wadi]

LOL

[calm thicket]

DADE DID WE WIN

[hasty wadi]

i have a "sin-1 function"

[vital tartan]

I've never used webassign before, is it really as bad as you guys say it is?

[hasty wadi]

lemme try this

[willow bear]

do you have cos^-1

[calm thicket]

Repyh, it's worse.

[hasty wadi]

cosine?

i thought i was using inverse sin

[severe verge]

cos^-1

[willow bear]

inverse cosine

[grim yarrow]

lmfao that happened to me once

[hasty wadi]

ahhhhhhh

[vital tartan]

lolol

[grim yarrow]

-0 is different from 0 in certain programming languages

[calm thicket]

Was that a sigh of relief or a scream of terror

[grim yarrow]

it's like signed

signed bit

but you can put it on zero

[severe verge]

cos^-1(100/L)

[grim yarrow]

gross

[severe verge]

or preferably arccos(100/L) for better notation

[hasty wadi]

oh allah, please let this be the right answer to this fucking shit

[grim yarrow]

wait

are you telling me you didn't try that yet

[hasty wadi]

no

[willow bear]

should be

[grim yarrow]

try it

[hasty wadi]

last submission :::::::)))))))))0

[calm thicket]

Here goes

[hasty wadi]

omfg

[calm thicket]

MOMENT OF TRUTH

[hasty wadi]

im scared

[calm thicket]

DUN DUN DUN DUN DUN

THE HYPE IS REAL

[willow bear]

🙏

[grim yarrow]

we're hyping this too much

lol

[hasty wadi]

FUCK YEAHHHHHHHHHHHHHHh

[severe verge]

can u stop with the clickbait and just press it

[hasty wadi]

LETS FUCKING GO

[calm thicket]

YEAAAAAAAAAAA

[hasty wadi]

FUCK YEAH

BITCHES WE GOT THIS SHIT RIGHT BRUHHHHHHHH

[calm thicket]

🎊

[willow bear]

👏

[grim yarrow]

I can't believe you haven't tried that

[vital tartan]

🎊

[grim yarrow]

lol

[willow bear]

[dense terrace]

why is this chat so hyphy

whats going on

[hasty wadi]

THIS IS WHAT FUCKING VICTORY LOOKS LIKE

[grim yarrow]

new epic chat

[vital tartan]

because it took like 1-2 hours to solve a single question

[calm thicket]

now wait not to crash the party

[dense terrace]

rofl

[calm thicket]

but I have no idea still how you got arccos(100/l)

[severe verge]

aye... when will be the day that i fail someones expectations...

[dense terrace]

i just finished school

[vital tartan]

neither do I tbh

lol

[severe verge]

T.T

[hasty wadi]

:::::::)))))))

this was fun

[calm thicket]

👍

That's the most fun I've had here in a while

[severe verge]

inverse

[calm thicket]

you mean csc(100/l)

[severe verge]

this is why arccos is better notation

[vital tartan]

no

[willow bear]

@calm thicket cos(θ) = 100/L

[calm thicket]

processing

processing

[calm thicket]

Ohhhhhhhhhhhhhhhhhhhhhhhhhh

[calm thicket]

Wait so is there a general set of rules, I've never seen anything like that

[willow bear]

@calm thicket seen what

[calm thicket]

cos(theta)=100/l

[willow bear]

this is literally the geometric version of cos

...soh cah toa?!

[calm thicket]

OH MY GOD

SO THAT'S WHAT THAT MEANT

All my life I've lived going "I wonder what sohcahtoa was"

"Opposite/hypotenuse and stuff sure, but what does that mean"

and alas

[hasty wadi]

Fml

No lmao

I'm just surprised how fucking long it took us lmao

[calm thicket]

alright let's get the hype train back incoming

oh wait nvm

[grim yarrow]

the hype was the funniest part

so much hype over webassign lmao

[calm thicket]

was just him hyping up a reminder that I wasted my life not remembering sohcahtoa

[vital tartan]

lets move back to #discussion

[calm thicket]

Agreed

[hasty wadi]

That last submission stress bruh

this is one im complicated with for some reason

i got the one before right but not this one

the one before was similar to this

[vital tartan]

what are you looking for?

oh nvm

[calm thicket]

oh my

[hasty wadi]

the altitude

[willow bear]

draw the altitude

it's going to bisect your base

[calm thicket]

cut it in half vertically

[hasty wadi]

its a vertical line

[calm thicket]

length of that line

[hasty wadi]

yeah

down the triangle

[willow bear]

yeah so

h = b/2 tan(θ)

[calm thicket]

== tand(32)

[granite stirrup]

0.62486935

[vital tartan]

tand != tan ?

[willow bear]

tand = tan, degree input

[calm thicket]

tand is in degrees

[hasty wadi]

h = tan(32)/2 ?

[calm thicket]

tan is in radians

[vital tartan]

oh

[willow bear]

@hasty wadi no

b = 2

h = 1 tan(32°)

[hasty wadi]

h=tan theta

[willow bear]

h = (b/2) tan(θ)

it's just that in this case, the length of half the base happens to be 1

[hasty wadi]

wait im writing this down

i'll send it in like a minute

pls tell me if it's okay?

[calm thicket]

okay so not to crash the party again

ann how did you figure that out 👀

does it have something to do with toa

tan(theta)=o/a, solve for opposite?

mk

👍 just checkin'

[willow bear]

what's b

[hasty wadi]

0.62

[calm thicket]

h is .62

b is 2

[hasty wadi]

tan 32

[willow bear]

no why did you use the letter b

it's already taken

[hasty wadi]

oh lmao

[willow bear]

other than that, what you have is correct

[hasty wadi]

dab

[calm thicket]

In soviet russia, you test site

[calm thicket]

=tex \text{Let } a+b=s \text{ and } a-b=d\s=d+2b \implies b = \frac{s-d}{2}\ a+\frac{s-d}{2}=s \implies a=\frac{2s-s-d}{2}=\frac{s-d}{2} \implies a=b??

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[calm thicket]

👀

=tex \text{Let } a+b=s \text{ and } a-b=d\s=d+2b \implies b = \frac{s-d}{2}\ a+\frac{s-d}{2}=s \implies a=\frac{2s-s-d}{2}=\frac{s-d}{2} \implies a=b??

[severe verge]

u have a sign error on the last line @calm thicket

a=(2s-(s-d))/2 = (2s-s + d)/2

[calm thicket]

Oh

xP

[viscid thistle]

How hard is PreCal?

[dense zealot]

Not that hard

U just have to know identities

How to manipulate them

Polar form

Scalars

Vectors

Rectangular form

Limits

Matrices

And that's all

[past jay]

What school did you go to...? We'd have been lucky to go over half that in precal tbh. Actually as far as that goes we haven't gone over some of that in any course, including AP calculus...

But he's right though, precal, or algebra III and trig as it's called in my school, is just essentially more algebra identities, a few introductory concepts and then trig. Most people would probably have more difficulty with the trig than anything else.

Buuut my school doesn't have a great... anything so it may be different elsewhere.

[dense zealot]

Mm I just use aops

Don't care about school :s

[drowsy plaza]

just signed up for their intro to algebra course!

[viscid thistle]

I'm in UTA so yeah

Got my first Pre-cal class tomorrow a bit nervous since math isn't my strongest subject, anddd... I passed the pre req with only a C

[drowsy plaza]

good luck

😃 👍

[viscid thistle]

lol thanks >.<

[dense zealot]

Gl ^^

Just study

Don't try to wing it

[restive phoenix]

I'd put this in memes, but there's no such channel here

[willow bear]

there's #chill

and since you're posting this here i'll point out that when dealing with complex numbers, sqrt(ab) does not always equal sqrt(a)sqrt(b)

[restive phoenix]

Hmmm... I think all possible sqrt(a)*sqrt(b) are roots of sqrt(ab), but not vice versa (edit: nope, I changed my mind, there's a one to one correspondence)

[dense zealot]

Sqrt(ab) is the same as sqrt(a) * sqrt(b) over the reals

U go into imaginary

[restive phoenix]

This image is just for fun though, it's not a question

Actually, nevermind. There's a one to one correspondence for the roots.

[thick raptor]

sighs

[twilit zodiac]

1/n = 0

by definition

[twilit zodiac]

oh with epsilondelta

[grim yarrow]

do you know the archimedean principle?

it says for every real number x, there exists a natural number n such that n > x

[twilit zodiac]

you have to use limit of a sequence proof because x -> inf, or just use definition 1/x -> 0 <=> 1/x = 0

[grim yarrow]

well it would be immediate if you knew that lol

well you can try proving the archimedean principle

and once you know that, apply it to show

for any epsilon

there is a 1/n smaller than epsilon

https://www.screencast.com/t/0jEwaqqQCIR

proof from proofwiki lol

for the archimedean principle

take what as a no

what have you learned about real numbers?

do you know the definition of real numbers? There's multiple but I want to hear what your class gave

OK well it's pretty hard to prove stuff if you don't have a definition for R

are you sure you need to know this for your class?

I'd expect they'd give a definition at leas

just assume the archimedean principle for now I guess

what class is it

[raven creek]

14*P(n, r)=P(n+2, 4)

any1 know

[hexed ermine]

Is that a permutation problem?

[raven creek]

yes

[random jay]

where did you learn how to do that lol

i never learned it in precalc, nor calc nor stats

[candid drift]

Isn't brute force just "guessing small integers and trying until it works"?

[severe verge]

(n+2)!/4! = 14*n!/r!
(n+2)! = 14×4!×n!/r!
(n+2)!/n! = 14×4!/r!
(n+2)(n+1) = 14×(4!/r!)
now check r=1,2,3,4

oh

how does P work

ok

i will restart

[severe verge]

(actually i got distracted

:(

[dense zealot]

@severe verge did u just use "×"

[viscid thistle]

[severe verge]

bedtime :p

[dense zealot]

O

[viscid thistle]

O

[edgy latch]

how did my teacher get these answers

[clever inlet]

the exponent is always 4 right?

it's the base that is changing

[willow bear]

@edgy latch do you know how summation notation works?

[edgy latch]

kinda

[willow bear]

=tex \sum_{k=1}^5 k^2 - k = (1^2 - 1) + (2^2 - 2) + (3^2 - 3) + (4^2 - 4) + (5^2 - 5)

[willow bear]

does this make sense to you?

[edgy latch]

no

oh yeah i do

[willow bear]

okay, which part doesn't make sense?

[edgy latch]

how come if n=3 then theres a 10 at the top? shouldnt it be an 8 at the top

[willow bear]

10 is the last value of the counter used in the summation

it's not how many terms there are

it's where the counter is supposed to stop

[edgy latch]

then why does n=1 end at 8 when the sequence goes up to 10

[willow bear]

in the second version?

it's because the terms themselves are different

=tex \sum_{n=1}^8 (n {\color{red}+2})^4

[willow bear]

so while n runs from 1 to 8, n+2 runs from 3 to 10, as required

[edgy latch]

oh ok thanks

[hoary yoke]

@willow bear Help with the formula pls

its not 1/n

<@&286206848099549185> halp

i cant figure it out

[dense terrace]

same

i cant even see the pattern

[untold wave]

http://oeis.org/search?q=2%2C3%2C4%2C6%2C8%2C9%2C12&language=english&go=Search

[hoary yoke]

dont understand

😐

[willow bear]

neither do i

if some clarification is given about what the denominators are meant to be then i can help

[earnest sable]

looks like 1/2k +1/3k

but not sure

[untold wave]

yeah

[dense terrace]

what is that pattern

[thick raptor]

Hm... is it the harmonic series wihout primes > 3?

[untold wave]

sounds about right

no its probably what dusty said

[earnest sable]

doesn't look like any pattern to me

[thick raptor]

Oh, that makes more sense

[untold wave]

sum of 1/2k + sum of 1/3k

[thick raptor]

No

[dense terrace]

no

[earnest sable]

but thats just an intuition

[untold wave]

actually

[earnest sable]

you cant assumethat

[dense terrace]

it includes 1/6

[thick raptor]

2k can't be equal to 3k

[dense terrace]

and 1/12

[untold wave]

1/2^k+1/3^k

[thick raptor]

No, it includes 12

[earnest sable]

but you still don't know whats after the ...

[untold wave]

so its what oeis says

[hoary yoke]

its all 2 and 3s

:/

[untold wave]

1/(2^i*3^j)

[earnest sable]

so we need more detail on the éroblem

problem*

[hoary yoke]

no more details dusty :d

ifnd the sum is all it says

[untold wave]

=tex \sum_{i,j\in\mathbb{N}}\frac{1}{2^i3^j}

[thick raptor]

_> beat me

[hoary yoke]

but to what

[dense terrace]

that doesnt look right

[thick raptor]

I'd rather write $$(i,j)\in\Bbb N^2$$ tho

[hoary yoke]

no it is right

[dense terrace]

its gonna be infinity

[thick raptor]

Why?

[untold wave]

Same thing

[hoary yoke]

they are natural numbers

UGH

[dense terrace]

then what about duplicates

[hoary yoke]

its damaging my brain

[thick raptor]

What about what duplicates?

[earnest sable]

let's try that and see if we get the initial sum

[hoary yoke]

wait

[dense terrace]

nvm it wont give duplicates

[hoary yoke]

it can include 0

[willow bear]

solarkoid, the only correct answer to that picture you posted is "Question not well-posed."

[thick raptor]

Yeah

[earnest sable]

lol

[willow bear]

that's it.

[thick raptor]

And that too lol

[hoary yoke]

thats literally wat it said

and note:

[willow bear]

the question is poorly worded.

[earnest sable]

tell yourteacher mathematicians don't use dots

[thick raptor]

@willow bear what words?

=)

[earnest sable]

thats why sigma was inventd

[hoary yoke]

note: The terms are the reiprocals of pos. integers whose only prime factors are 2s and 3s

thats it

[untold wave]

Meh dusty id say dots are fine if the pattern is clear

Ah well so you're given the pattern!

[thick raptor]

@hoary yoke k then

[untold wave]

That's an important note!

[thick raptor]

@untold wave meh to ...

[hoary yoke]

Wait

[earnest sable]

well its what i said in the beginning then

1/2k +1/3n no?

[hoary yoke]

ill try this one

[untold wave]

No its what i said

[earnest sable]

ok

[hoary yoke]

pls someone put sigma

with bottom of 0 to infity

[thick raptor]

=tex \sum_{(i,j)\in\Bbb N^2}\frac1{2^i3^j}=\frac1{(1-\frac12)(1-\frac13)}

Sad

[earnest sable]

i think its two sums

[willow bear]

note: The terms are the reiprocals of pos. integers whose only prime factors are 2s and 3s

right

[hoary yoke]

pls sigma from 0 to infinity

[earnest sable]

cuz theres only one 1

[untold wave]

SPOILER

[thick raptor]

Oh

=(

Sry

[earnest sable]

@thick raptor he said prime factor

doesn't that mean 2 times something

[thick raptor]

And what about it?

[hoary yoke]

=tex \sum_{n=0}^{\infty} \frac {1}{2^n}

ugh

[willow bear]

^

[thick raptor]

=tex \sum_{i=0}^\infty\sum_{j=0}^\infty\frac1{2^i3^j}

[hoary yoke]

exactly what i wanted to post

yep

i think thats it

so we have to find 2 sums and multiply it to each other?

got sum of 3

was right

its 3

😄

[thick raptor]

Yes, you can find the sums separately and multiply the results

And yeah, it should be 3

[edgy latch]

How do I do this

[willow bear]

do you know how nPr is defined?

[edgy latch]

Yeah

N!/(n-r)!

[willow bear]

=tex 14 \frac{n!}{(n-3)!} = \frac{(n+2)!}{(n+2-4)!}

[willow bear]

=tex 14 \frac{n(n-1)(n-2) \cdot (n-3)!}{(n-3)!} = \frac{(n+2)(n+1)n(n-1) \cdot (n-2)!}{(n+2-4)!}

[willow bear]

is this clear?

@edgy latch

[edgy latch]

How did you get the right side

[willow bear]

...you understand what i did on the LHS, but not the RHS?

[edgy latch]

Yeah

[willow bear]

=tex (n+2)! = (n+2) \cdot (n+1)!

is that clear?

[willow bear]

@edgy latch

...

[edgy latch]

I had a guest speaker so I couldn't use my phone

I figured it out tho

[inland forum]

need help with finding the max value of a function

y=-x(x-2)^4(x+3)

i keep getting 337, however desmos shows 550

[neon compass]

=tex -x(x-2)^4(x+3)

[inland forum]

i used the vertex and subbed it into the equation

the x value of the vertex

[willow bear]

what vertex

[inland forum]

sorry, i found axis of symmetry

and i subbed in the x value

into the equation

to try and find the max value

[willow bear]

axis of symmetry??

[inland forum]

yea

of the parabola

[willow bear]

this is not a parabola, though

[inland forum]

i know

but the left side

[willow bear]

left side?

[inland forum]

i did -3 + 0 /2

[willow bear]

...why

[inland forum]

got -1.5 as my axis of symmetry

what do you mean lol

[willow bear]

this graph does not have an axis of symmetry

[inland forum]

ok well how can i find the max value then

[willow bear]

take the derivative, set to zero

[hoary yoke]

ok imm done with this

i dont understand sinusoidal graphs and now this

is there a way to solve arccos(x) by hand?

without calc

[willow bear]

what do you mean by solve

[hoary yoke]

like calculate without calculator

[willow bear]

no, there's no easy way to find the arccos of an arbitrary number w/o a calculator

[hoary yoke]

😭

i have arccos(-13/20)

[willow bear]

best i can tell you about that is that it's gonna be greater than 2π/3 (= arccos(-1/2))

[hoary yoke]

2.28

:/

[willow bear]

== acos(-13/20) - 2*pi/3

[granite stirrup]

0.18398566

[willow bear]

0

so my point stands

i mean obviously there are some nice values

arccos(0) = pi/2, arccos(-1) = pi, arccos(1) = 0

basically, all the easy angles, just with the notation turned around

[hoary yoke]

ok

another question

how can i graph sinusoidal function with its equation

i always get it wrong

by equation?

i know midline, period, amplitude and i can find highest point and lowest point

Period is 20

Amplitude is 2

midline is 7 or -7

not now

it is interactable graph

cant remember

midline is absolute value or not

ok

midline minus the amplitude is the lowest point right?

got it wrong

OMG

god i thought i set the minimum point

still ok doe

but its still wrong

this is all y values

how to figure x values

yes

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+sin(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hoary yoke]

oh

it worked

😐

how to get that it goes down then up

😐

wtf

ok

sin at 0 is down to up

and from 0 its up and down

got it

could u plot cos too?

pls

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+cos(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hoary yoke]

ok so cos goes up as it approaches 0

and goes down from 0

[hoary yoke]

ok

period is 2

amplitude is 3

midline is 2

Extremum point is 5

Lowest point is -1

lol

ill try one on khan now

ill try 😄

thanks

[viscid thistle]

@hoary yoke if u need more help u can ask me

this is one of the thing i know how to do anyway,

[hoary yoke]

lol

[viscid thistle]

Find the following trig ratios by drawing the terminal and finding the reference angle: sin(235degrees) can someone help me with this, its pre calc 12

[willow bear]

do not spam your query across multiple channels.

[viscid thistle]

Can anyone help me with the above ^^ it's probably hella simple

[dense zealot]

I already told u

[viscid thistle]

Oh did you? Didn't see it, kind new to discord

[dense zealot]

Ok so

the reference angle is just

235-180

= 55°

[viscid thistle]

Right, got that part

[dense zealot]

And what do u mean by terminal angle

I know what terminal sides are....

[viscid thistle]

It just means the terminal arm

like if you were to draw 235

degrees

the terminal arm is in the 3rd quadrant

The question is asking for the trig ratios though, was wondering how to get that without the ref angle forming a special triangle

[dense zealot]

well

For the question

If they want u to use trig ratios

U have to find the angles

[viscid thistle]

The question is just word for word "Find the following trig ratios by drawing the terminal and finding the reference angle: (Hint: If the degree symbol is not shown, assume measure is in radians) a) sin(235degrees)

I know the part about drawing 235 degrees and finding the ref angle of 55

but yea I got no idea how to get the trig ratios out of that if it's not giving me a ref angle i can use from a special triangle

another question is cos(-11.23)

[dense zealot]

?

55,90,25

Mmm

[viscid thistle]

by trig ratio it means like sin235 = y/r and we're finding the y and r, not the angless at least what I thought

[dense zealot]

Ohhhh

For that

Would u be allowed to cheat and use sum and difference identities? :P

[viscid thistle]

probably not lol

is there not any simple method im forgetting if u cant make a special triangle?

[dense zealot]

Mm

When it says trig ratio

Does it want a straight up a/b

Or sin235° = tan235°*cos235°

[viscid thistle]

I asked someone and they think it just means I should write the answer as sin(55°) = 0.82

-sin(55°) = -0.82

or

sin(-55°) = -0.82

Is there any specific way it should be written

or does either work

[dense zealot]

And sin(180-x) = sin(x)

[ebon silo]

I'm checking an answer for a friend and don't know what class this is for
it's a problem relating to sigma-notation sums and being equal to their terms
should I put it here or in #calculus ?

"
Which of the following is equivalent to sum((x-1)^2)
a. sum(x^2) + 2*sum(x) + sum(1)
b. sum(x^2) + sum(2x)
c. sum(x) + 2*sum(x) + sum(1)
d. sum(x^2) + sum(x) + sum(1)
"

and sum is just over some interval, any values that are defined will work

problem says it's A but I can't figure out how that works of if it was a mistake

[boreal shell]

(x-1)^2=x^2-2x+1 right?

[fringe stream]

definitely seems like a mistake.

it should be - 2*sum(x).

[hoary yoke]

ok

so this graph is transformation of sin(x) graph

so. i tried but couldnt

[hoary yoke]

<@&286206848099549185>

Horizontal shift and vertical shift

amplitude is 5

ye so a is 5

i just need b

i can never find it

yes

:/

Horizontal stretch

5.5 pls 2.5?

so period is 8

but sin period is 2pi right?

2pi times what is 8?

NO

SORYY

2PI/X IS 8

pi/4

ugh

so c is pi/8

b is pi/4

c is pi/8

-pi/8

:/

wat to do

graphing is hard

no

khan

😐

well it will be done soon

:d

we will learn trig identities and done

no

[hoary yoke]

no

amplitude is 2pi/b

ye i kno that 😄

but what do you mean NEGATIVE

👀

it will go 3 by left

but on cos its right

since cos is negative function?

[hybrid charm]

Even function

[hoary yoke]

ye nick about that

thanks for reminging

:/

how can i tell even, odd or neither function

[hybrid charm]

:-\

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+cos(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hybrid charm]

f(x)=f(-x) for all x is even

[hoary yoke]

ye

so sin is off

odd

[hybrid charm]

f(x)=-f(x) is odd

[hoary yoke]

;/

[hybrid charm]

☹

[hoary yoke]

ok so like for function y is x

[hoary yoke]

or y is -x

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+sin(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hoary yoke]

😐

brain.exe stopped responding

it will be -sin(x)

wont it?

😐

brain.exe crashed

[hybrid charm]

Sin(-x)=-sin(x)

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=plot+y+%3D+-x
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hoary yoke]

ok

we should stop this

😐

[hybrid charm]

:-(

[hoary yoke]

Can you tell me what is intersection point on midline for cos(x)

i cant remember

like was it (pi/2;0)

my answer above

was wrong

ye

period

ok so like i got it right half

bcs i got wrong b

i messed up c

[hoary yoke]

cough

[calm whale]

eh

[hoary yoke]

WHY OVER 2

[calm whale]

2pi/b=period ?

[hoary yoke]

yes

[calm whale]

ooo yes

woah!

[hoary yoke]

ye WHY TIMES 2

why not times 4

it is 1/4 of the actual periof isnt it

:/

bcs 1/4 of the period

what you drew

the top blue line

[granite stirrup]

Query made by @pine kindle
Data sourced from Wolfram|Alpha: http://www.wolframalpha.com/input/?i=+plot+sin(x)
Do more with Wolfram|Alpha Pro: http://www.wolframalpha.com/pro/

[hoary yoke]

ye thats 1/4 of the period

yes

?

;/

but no

its not

thats 1/8 of a period

or no

it is

:/

ugh

ok ill tell you

i thought from pi to -3pi/4 was 1/4 period

and it SHOULD be 1/4

bcs full period is 2 curves

i think i didnt understand periods well

:/

full curve is 1/2

of period

oh shiet

omg

most of it is done

i just wonder

will it go LEFT by 3pi/2

or RIGHT by 3pi/2

@willow bear

since it is negative 3pi

[willow bear]

i mean you could say it'd "go right" by that much

or you could rewrite sin(2x - 3π) as -sin(2x)!

[hoary yoke]

ye it went right

😐

but i still did it wrong

"managed" to do it

[dense zealot]

Hi!

Can u like take a pic

So

U just multiply numerator and denominators

U get tan/tan

[calm whale]

which is like 1

[dense zealot]

Which simplifies to 1

[calm whale]

🥇

[dense zealot]

You can also see that u can cross simplify those two things

[calm whale]

{sin/cos}/{sin/cos}

🤔

[dense zealot]

yw

[viscid thistle]

someone please help me

[clever inlet]

Ok

So you have 3 roots right?

[viscid thistle]

yea

[clever inlet]

So you know like how you can write it as a(x-r1)(x-r2)(x-r3) right?

[viscid thistle]

oh yea

[clever inlet]

Solve for a so that it forces the cubic to pass through that point that isn't a root

[viscid thistle]

k hold on

how

i cant

[willow bear]

what've you tried so far?

[viscid thistle]

i just did the 0 = a(-4)(-2)(3)

[willow bear]

huh? where'd you get that from

[viscid thistle]

idk tbh

just pulled it outta my ass

desperate attempt

[willow bear]

well there's your problem eh

okay

[viscid thistle]

yea my problem is no idea

[willow bear]

so as kangaroux said

the polynomial's three roots are known, so we can write it as $$y = a(x+4)(x+2)(x-3)$$

[willow bear]

is that clear?

[viscid thistle]

yea

got that

oh wait i need to use the (-1,-36) in that formula?

[willow bear]

and we know that when x = -1, y = -36

yes indeed, that's how you solve for a

[viscid thistle]

im such an idiot

thank you so much

[willow bear]

do you require any further assistance?

[viscid thistle]

nope got it

D value is straight forward

[willow bear]

ok

[viscid thistle]

thanks

this feeling is great

when you solve something

[viscid thistle]

can someone help me with this quesiton

i don't know how to do this

[willow bear]

try finding explicit formulae for f and g

[viscid thistle]

how do i do that

i thought absolute value graphs couldnt be negative

[clever inlet]

well

you could have a transformation

such as

-|x|

[viscid thistle]

oh right

a reflection

[clever inlet]

yeah

i don't know terminology

[viscid thistle]

it's alright haha

it's different for both canada and usa

but i mean a reflection is a transformation so you are right

[clever inlet]

maybe

anyway

do you know how to approach the question from here?

[viscid thistle]

hmm

let me try

one sec

no i dont

[clever inlet]

well

if you are trying to find the explicit formulas

have you found those?

[viscid thistle]

yea

-|x| + 2 and -|x| + 4

[willow bear]

now can you multiply these?

[viscid thistle]

i forgot how to multiply absolute values

let me watch a real quick vid

[willow bear]

...

[viscid thistle]

i don't know how to multiply these 2 functions

[willow bear]

does "distributive property" ring any bells

[viscid thistle]

yea that's what im trying

[willow bear]

(2 - |x|)(4 - |x|) = 8 - 6|x| + x^2

[viscid thistle]

okay

[willow bear]

= (|x| - 3)^2 - 1

[viscid thistle]

wait

how did you simplify that

[willow bear]

completing the square

is a thing

[viscid thistle]

i have never done that with absolute value functions

i'll ask my teacher about it

but anyways

what do you do after

[clever inlet]

well

it's in completed square form

you have minimums of -1

[viscid thistle]

oh my god

thanks

oh my god

the completing the square wasnt even necessary

i just had to graph it

but i was too blind to notice the range

[clever inlet]

i think completing the square probably is somewhat useful

cause like

it behaves like (x - 3)^2 - 1 for positive values of x

and

(-x - 3)^2 - 1 for negative values of x

it's in nice graphing form

[viscid thistle]

i see

[viscid thistle]

bit stressed

diploma on thursday

[languid wind]

how would i solve 2^(x+3) = 3^(2x-1)?

[dense zealot]

So mean

Logarithms suck

And memorizing all those rules

[thick raptor]

@dense zealot the key is to memorize basic integral rules and use integral definition of logarithms.

[dense zealot]

I'll

Ik*

[thick raptor]

Nah

[viscid thistle]

man I get help for this question

may*

[willow bear]

if sqrt(f(x)) is never greater than 9, what can you say about f(x) itself?

[viscid thistle]

it's never greater than 81?

[willow bear]

bingo

that alone lets you identify the point which cannot be on the graph of f

[viscid thistle]

you're actually a genius

i hope one day, that i will be in your spot helping others 😃

can someone explain this to me

it says the answer is B but i do not know why

[willow bear]

do you know what "inverse of a graph" means

[viscid thistle]

yea

switching the y and x

[willow bear]

so why don't you do that to each of these graphs

you know how to rest if a graph corresponds to a function, right?

[viscid thistle]

yea

if it has its own value

[clever inlet]

each x only gives one y value right?

[viscid thistle]

right

[willow bear]

if it has its own value

...

[viscid thistle]

haha sorry 😅

[willow bear]

@clever inlet yes

i mean, what i had in mind was the graphical version of this

the vertical line test

[clever inlet]

yeah

[viscid thistle]

i dont understand how i switch the x and y when there are no points

[willow bear]

which, if the axes are relabeled, becomes the horizontal line test

you don't really need to redraw anything

you can just relabel the axes

[viscid thistle]

what do you mean by that

[willow bear]

the axes are labeled x and y there

switch those labels around

[viscid thistle]

mhm

that's kinda like rotating it clockwise 90 degrees

[willow bear]

not really, since there'd also be a flip involved

[viscid thistle]

oh

after i label the axis i do the horizontal line test?

[willow bear]

yes

(because a better but less catchy name for it would be "parallel-to-y-axis-line test"

[viscid thistle]

im kind of confused

i relabel the axis and then do the horizontal line test

oh wait

graph 2 and 4 dont pass the horizontal line test

[quartz garnet]

Indeed they don't

If a graph passes the horizontal line test

it always has an inverse

[viscid thistle]

it always has an inverse that's a function?

[clever inlet]

yes

[viscid thistle]

oh

so what's the point of relabelling the axis

i just have to do the horizontal line test that's it

[willow bear]

so that the graph will become y = f(x) rather than x = f(y)

merely a cosmetic thing, i guess

[viscid thistle]

oh so it isn't necessary

[viscid thistle]

how would i do this

[willow bear]

these are both linear

find formulae for each

subtract them

[viscid thistle]

how do i find the formulae if it has a specific range

[willow bear]

do you not know how to find the equation representing a given line

[viscid thistle]

oh wait

y = mx + b

[willow bear]

yeah can you find m and b for both of these lines?

[viscid thistle]

yea

[willow bear]

well do that

[viscid thistle]

i subtract the two equations and i get y = 4.5x + 3

[willow bear]

i'm going to trust you on the arithmetic there

so now, you know that x is between -2 and 2, according to the graph

[viscid thistle]

o

[willow bear]

can you find what interval y must be in, based on that?

[viscid thistle]

yea

-6 < x < -12

ah got it

thanks!

[willow bear]

...uh

[viscid thistle]

less than or equal to

[willow bear]

not only is that inequality, the way you wrote it, always false

how did you get those numbers in the first place?!

-12?!

[viscid thistle]

oh whoops

WHOOPS

-6 < y < 12

there we go

sorry 4:05am and super tired

but math diploma is tomorrow

and i need atleast 90 :((

this is how i did during the course

[dense zealot]

Rip that trig quiz

[signal mesa]

can anyone help me find the intercept of (-x+2)/7 and sqrt(x)/2

[willow bear]

the intersection points of these?

[signal mesa]

ah yes

[willow bear]

=tex \frac{-x+2}{7} = \frac{\sqrt{x}}{2}

[signal mesa]

yes

[willow bear]

make a substitution

u := sqrt(x)

[signal mesa]

and then x becomes sqrt(u)?

[true vigil]

no, if u = sqrt(x), u^2 = x

for positive x

[signal mesa]

thanks i figured it out <_<

[viscid thistle]

this means the inverse of the graph right?

[calm whale]

probably yes

[viscid thistle]

if a function is reflected over the y = x its the same as the inverse?

[calm whale]

reflected upon the x-xis 🤔

[dense zealot]

Ya

[calm whale]

or the y=axis

I'm confused

[dense zealot]

It doesn't have an inverse tho

Doesn't pass horizontal line test

[viscid thistle]

ah kk

[calm whale]

it dont?

[viscid thistle]

all invariant points are found on y = 0 and y = 1

for an inverse

[dense zealot]

@calm whale bakabakabakabakabakbakbaka