precalculus

[valid violet]

yes, you can check your work that way

your teacher's answer key has a typo

it says f(x) = 3 instead of f(x) = -3

[mossy kestrel]

oh really where

i get e.c if we spot any typos

[valid violet]

nice

[mossy kestrel]

thank god

this class is just precalc but its the most failed class at my uni

[rigid sun]

because its abstract

[mossy kestrel]

i just think its poorly presented and taught

its really not that hard though when i reach out to other people except for my teacher

[rigid sun]

nobody easily transitions into thinking in radians and ratios

[mossy kestrel]

none of the notes in class are related to the homework

[rigid sun]

lol

[mossy kestrel]

half of my class was in tutoring yesterday LOL

[rigid sun]

just invite them here

lol jk i'd kms

[mossy kestrel]

LOL i should

i usually try to do stuff with the tutors first before i come onto disocrd

oh lemme add

our quizzess/tests/hw are graded all or nothing

partial credit nonexistent

[karmic wave]

what? How does that work? Miss a minus sign and instant 0 on the entire assignment?

at some point y'all could teach each other

[main geyser]

Could somebody help me to figure out the steps for simplifying these trig functions with trig identities?

I am stuck on figuring out number 17

There is an answer key

I am having trouble figuring out what identities I could use because there is no Pythagorean trig identity for tangent and cotangent

[uncut mulch]

what's happening from your first to second line?

it looks like you squared it properly and then completely wrecked it

[main geyser]

I expanded it and I thought I could factor out tan n from the rest of the expression

[uncut mulch]

but cot^2(n) doesn't have a factor of tan(n)

do you know the relation between tan and cot?

[main geyser]

They’re reciprocals if each other

[uncut mulch]

of but yes

so tan(n)*cot(n) = ?

[main geyser]

1

[uncut mulch]

so you would get
= tan^(n) + 2 + cot^(n)

try continue from there

[main geyser]

Wait don’t you mean cot^(n)

[uncut mulch]

yeh

[main geyser]

Not cos

[uncut mulch]

typo

[main geyser]

Ok

So now would I just break up tan^2(n) and cot^2(n) into sin(n)/cos(n) for tangent and cos(n)/sin(n) for cotangent and then multiply by the LCD?

[uncut mulch]

no

[main geyser]

Since I’m adding them

Oh

[uncut mulch]

note that 2 = 1 + 1

and you can apply the identity used in Q14

identities relating tan to sec and cot to cosec come from dividing both sides of
sin^2(x) + cos^2(x) = 1
by cos^2(x) and sin^2(x) respectively

[main geyser]

Ok I think i got it

Thank you so much

[uncut mulch]

cancel lines on the 1s look like xs

[main geyser]

Oh I see that lol

[uncut mulch]

its pretty obvious that - 1 + 2 - 1 = 0
so you don't really need to indicate that's what you're doing

(also your variable n changed to t)

[tidal sequoia]

why does ln(t) * 9t^8 = t^8ln(t^9)

im so confused

[stuck lark]

$\log(a^b)\equiv b\log(a)$

[obsidian monolith]

RokettoJanpu:

[tidal sequoia]

but you are multiplying the value of ln(t) by 9t^8 I don't understand, you can just have the value go back inside the log after you multiply it? how does that work then

how do I know what b is?

[stuck lark]

you have 9t^8 outside the log, but it seems that you've left the t^8 outside the log and only "brought" in the 9

[tidal sequoia]

so it's just because the constant can go wherever essentially

?

it just reattached to the ln to use that property?

[stuck lark]

no you can bring in t^8 too, your book just chose not to do that

[tidal sequoia]

so I can choose to bring in anything that gets multiplied by a ln/log

?

[stuck lark]

sure

[tidal sequoia]

ok thanks

that's what I wasn't understanding

[stuck lark]

np

[tidal sequoia]

ig for the problem it makes sense they only take the 9, as the rest factors out nicely then

[clever inlet]

7

[serene heath]

"x^2 <-1"

[clever inlet]

think about what that means in terms of absolute values

[serene heath]

[gloomy vigil]

oh..

[clever inlet]

surely what you have now is < 7 no?

oh wait

these inequalities are flipped

which is even more interesting

a number greater than 7 but less than -7

[gloomy vigil]

ok so I understand why the -1 doesn't work out now, but refresh my memory for the uh part here

x^2 > 13

this becomes x > sqrt 13 right?

there's an extra -sqrt13 > x ?

[clever inlet]

yes

graphically

you can look at how the parabola looks

also you really need to split those inequalities

it makes no sense to combine them

[gloomy vigil]

right that's true and makes sense, now i got the proper form i was clueless

[clever inlet]

-7 > x^2 - 6 > 7 makes no sense

[gloomy vigil]

ye lol

x^2 > 13

becomes

x > sqrt13 and -sqrt 13 > x

[clever inlet]

yep

[elfin birch]

if secTheta = 6 does that mean secTheta = 6/1 ?

so r = 1 ?

[clever inlet]

🤔

sure

[gloomy vigil]

that makes sense

[elfin birch]

https://prnt.sc/qvua5q

r = 1 ?

[serene heath]

what is r?

[elfin birch]

radius

[clever inlet]

i mean

sure?

why do you need r though?

[serene heath]

radius of what

[elfin birch]

to find six functions

[serene heath]

just draw a triangle

[elfin birch]

lemme rephrase

is sectheta = 6 does that mean that costheta = 1/6

[gloomy vigil]

i remember seeing some stuff like r before, but my teacher told me to say f that stuff

[clever inlet]

yes

[gloomy vigil]

ye sec and cos are reciprocal
same with sin and csc
and cot and tan

[clever inlet]

pretty much by definition

[elfin birch]

ok dude you dont have to be an asshole

@clever inlet

relax

[clever inlet]

?

not sure where i was being an asshole

[gloomy vigil]

u know what quadrant it's in right @elfin birch

[elfin birch]

yeah 4

because cos < 0

right ?

[stuck lark]

no

[elfin birch]

oh wait

[gloomy vigil]

i think it's cuz of cot < 0 and your sec is positive which means cos is also positive

[clever inlet]

i mean

[elfin birch]

so it would be in 2

[clever inlet]

you're not wrong

[gloomy vigil]

i think 4 is right

[clever inlet]

just reasoning wise

[gloomy vigil]

"All students take calculus"

" 1 2 3 4"

[clever inlet]

eww

🤢

[gloomy vigil]

since cot is neg given and sec (1/cos) is positive it has to be quad 4

[clever inlet]

this is one of the mnemonics i dislike

[elfin birch]

ahh ok

[gloomy vigil]

😦 it's one that helps me remember @clever inlet do u use anythin to remember it?

[clever inlet]

i mean

you should just understand why it works

[gloomy vigil]

can u tell me why

cuz i dunno

[clever inlet]

cos(t) gives the x coordinate on the unit circle

when you have an angle of t from the positive x axis

sin(t) gives the y coordinate

in quadrant 1, clearly x and y coordinates are all positive

and consequently y/x will also be positive

[gloomy vigil]

oh shit

blowing my mind over here

[clever inlet]

in quadrant 2

y coordinates are positive

x coordinates are negative

[gloomy vigil]

that makes a fkton of sense

[clever inlet]

hence sin(t) is positive

cos(t) is negative

for t between pi/2 and pi

and the ratio y/x would be negative

you can figure out the rest

[gloomy vigil]

yeah i never thought about it like that it makes a ton of sense

[clever inlet]

cause most teachers make you memorise dumb mnemonics

without actually making you understand

[gloomy vigil]

cos is x sin is y, gona be positive at quad 1 all the time, goes for the same shit for the other 3 in opposite ways

yeah i dont know jack nobody teaches me concepts only memorize stuff and now im basically 20 IQ

thx man

[clever inlet]

well

now you know

good job

at least you know now

[gloomy vigil]

😄

so when it comes down to something like this and it asks you to find Domain and Range

since it's abs (2 + 7x)

the domain is -inf to inf because there's no fkery but

the range is [0,infinity) because it's an abs value and can't be less than 0?

[clever inlet]

That's right

Well

Sometimes you need to be more careful

But that's fine here

[gloomy vigil]

i see

[clever inlet]

there's stuff like

e.g.

|x^2 + 1|

where you need to be more careful

[gloomy vigil]

hmm in that case it would be

domain: (-inf,inf)
and range: (-inf,inf)?
cuz of the x^2 making it impossible to be negative

wait no it'd be [1,inf)

[clever inlet]

yep

exactly

[gloomy vigil]

hold on a minute im buggin rn

apparently the answer is [0,inf)

[clever inlet]

for what?

[gloomy vigil]

hm seems like discord is having issue, the |x^2 + 1|

[clever inlet]

Domain is fine

Careful with the range

[gloomy vigil]

yeah im talking about the range

[clever inlet]

rip discord

[gloomy vigil]

apparently it's still [0,inf)

[clever inlet]

it should be [1, inf)

[gloomy vigil]

mathway.com be bugging then

ima check wolfram alpha

wolfram alpha is right ur right [1,inf)

mathway.com buggin smh :p

[clever inlet]

|x^2 + 1| = x^2 + 1 for all real x

[gloomy vigil]

yeah and when x is 0 , 0 + 1 = 1 so min has to be [1,inf) mathway just not perfect

dam discord!

[clever inlet]

i can see it

[gloomy vigil]

oh 😮

[clever inlet]

i mean

you can't see it on discord chat

but you can open it in a new window

[gloomy vigil]

oh gotcha

[clever inlet]

are you having any issues with that question?

[gloomy vigil]

so how exactly are you supposed to be envisioning this

7x^3

7 is positive

x if it's negative makes the equation negative right?

if it's positive the whole thing is still positive

[clever inlet]

firstly, there's a trick with polynomials

but

let's do the proper way first

you're right with that

so consider f(-x)

[gloomy vigil]

7(-1)^3 = 7(-1) = -7

[clever inlet]

we want to consider any arbitrary x

so well

just replace -1 with -

x

[gloomy vigil]

7(-x)^3 = 7(-x) = -7x^3 right

[clever inlet]

^3

-7x^3

[gloomy vigil]

gotcha

[clever inlet]

= -f(x) right?

[gloomy vigil]

oh shit

[clever inlet]

which is the definition of odd

[gloomy vigil]

right there's that whole thing with them

[clever inlet]

for polynomials there's a trick

but i'll let you figure it out

well

"trick"

more of an observation

[gloomy vigil]

f(-x) = f(x) = even

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

if it doesnt fit any of those it's neither

[clever inlet]

yep

exactly

[gloomy vigil]

completely forgot how i was supposed to do that, i was trying to picture how im supposed to envision a full grpah in my brain

[clever inlet]

graphically, they're different types of symmetry

[lofty haven]

anyone know how i can answer this?

[clever inlet]

what have you tried

[lofty haven]

following the sequence in the textbook. I reflect y=√x in the x-axis, and shift it to the left by the units of a

but doesnt the answer actually shift it to the right? Is it the sequence thats wrong?

[proud sparrow]

It's just a reflection across y=a/2

[gloomy vigil]

(brain explodes)

[proud sparrow]

Use the formula provided, what do you have?

@gloomy vigil

[gloomy vigil]

im not exactly sure what it's telling me to do

am i supposed to subtract the values

[viscid thistle]

yes
https://discordapp.com/channels/@me/630835123587383299/737893464716476416

that is what delta means

[gloomy vigil]

ah.. ok i got it thanks

[gloomy vigil]

so -x^2 -8x -3
I gotta make it a quadratic equation first, I assume negative is a no no
x^2 + 8x + 3
to complete the square I do
(b/2)^2

this makes new equation x^2 + 8x + 16 + 3?
er.. hm
then it's (x+4)^2 +3 ?

[viscid thistle]

idk probably

[gloomy vigil]

amen

ok i figured it out, i gotta look ta the (x+4) thing and solve it x = -4, and then substitute -4 as x in the original equation to get that shit, that being said..

why is this a minimum, im stupid

x^2 - 14x + 51
x^2 -14x + 49
(x-7)^2
f(7) = 49 + 51 -98 = 2

[uncut mulch]

you're able to find the location of the vertex but you don't seem to be completing the square properly

[gloomy vigil]

😮

[uncut mulch]

eg for the previous question
-x^2 -8x -3 = - (x^2 + 8x + 3)

you can't just add 16 inside those parentheses as it changes its value

but you can do + 16 - 16

[gloomy vigil]

hm i see so
-x^2 - 8x -3 = -(x^2 + 8x + 3)
Complete square
x^2 + 8x + 16 -16 + 3
(x+4)^2 -16 + 3
(x+4)^2 - 13 ?

[uncut mulch]

don't forget that you still have the - at the front

(that will distribute to both terms)

[gloomy vigil]

hmm wait so would that make it
-(x^2+8x+16) -16 + 3
or would i have to keep the -16 inside the parentheses

wait no

-(x^2+8x+16-16+3)

[uncut mulch]

yes, those would be inside

[gloomy vigil]

-((x+4)^2-16+3)
-((x+4)^2 -13)

ok thanks i think i understand the proper equation like equalization or whatever the term is now

but any idea on why the other question is am inimum

[uncut mulch]

distribute the - sign
then consider the value of -(x+4)^2

[gloomy vigil]

oh wait there's more to this one?

-(x+4)^2 + 13

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooh my god

it makes sense

wait what the heck, is the y intercept the answer?

[uncut mulch]

no

[wide lagoon]

Yo

can you guys help xD

[uncut mulch]

in use atm

[wide lagoon]

im learning propotions even tho im grade 6 and this is like grade 8 or somethingn math

[viscid thistle]

isnt the answer the bottom of the parabola iirc

[gloomy vigil]

bottom of the parabola? was i supposed to graph

[viscid thistle]

no

[wide lagoon]

A basket contains only apples and oranges, and the tatio of apples to oranges is 9:7. IF there are 128 pieces of fruit in the basket, how many oranges?

[viscid thistle]

b-but conceptually thats the minunum

[wide lagoon]

Can someone help? its my first time

[uncut mulch]

why do you think its the y-int?

[wide lagoon]

and can you tell me how you did it

[gloomy vigil]

@uncut mulch it seems it was coincidence i think cuz when i apply
-4 into the equation
-x^2 -8x -3

-16 + 32 - 3 = 13

[wide lagoon]

?

can someone help

[gloomy vigil]

ratio of apples to oranges is 9:7
128 pieces of fruit

[pale kettle]

@wide lagoon Read the rules in #❓how-to-get-help please

[gloomy vigil]

64 = 8:8

64/8 = 8

add 8 and subtract 8

[wide lagoon]

Oh sorry xD

[gloomy vigil]

apples is 72 oranges is 56

[uncut mulch]

but that isn't the y-intercept

[gloomy vigil]

that being said, i doubt i did that correctly

wait whta it's not the y-intercept

[uncut mulch]

y-intercept occurs when x=0

[wide lagoon]

Thanks wrong i think

[gloomy vigil]

ah! that's true wait.. then -(x+4)^2 + 13

[wide lagoon]

Yea that is

[gloomy vigil]

i guess what is the terminology hm

oh it's wrong? oof

[uncut mulch]

in the vertex form:
y = a(x -h)^2 + k
k is the value of the y-coordinate of the vertex

[gloomy vigil]

so y = -1 (a) (x-(-4) (h) ^2 + 13 (k)

so 13 is k

ohhhhhhh

@uncut mulch u make a lot of sense my friend thank you

[wide lagoon]

?

SOoo

Whats the answer

[gloomy vigil]

@wide lagoon A basket contains only apples and oranges, and the tatio of apples to oranges is 9:7. IF there are 128 pieces of fruit in the basket, how many oranges?

hm 9:7
8:8 = 64 each
1/8 of 64 = 8

are u sure it's not 64-8 = 56 oranges

[wide lagoon]

?

can i show you one of the ones my teacher taught

[gloomy vigil]

sure

[wide lagoon]

In a certain system of gears, the ratio of the number of teeth on the first gear to the number of teeth on the second gear is 7:3. If the first gear has 259 teeth, how many teeth does the second gear have?

[gloomy vigil]

259/7 = x/3

I think?

so 777 = 7x

x = 111?

[wide lagoon]

like that

[gloomy vigil]

nice it worked out

[wide lagoon]

But how do i do the orange one

[gloomy vigil]

yeah i dont know the formula i never learned it i just do random stuff like what i said earlier, do u have to submit it online or via paper?

do u use webassign or something like that

[wide lagoon]

IRL

[gloomy vigil]

ah ok 😦 sorry i dont know

[wide lagoon]

kk

[gloomy vigil]

back when i had to do that stuff i would use what i said

[wide lagoon]

i mean im in grade 6

this is like grade 8 or somethijng

firs ttime learning it lol

[gloomy vigil]

yeah ik what u mean my teachers didnt teach me like concepts really well i just had to wing it

[uncut mulch]

9n : 7n
9n + 7n = 16n = 128

[wide lagoon]

i mean i have sat school

[gloomy vigil]

😮

[wide lagoon]

1 hour

its just learning more

@uncut mulch

[gloomy vigil]

ramonov just answered it for u

[wide lagoon]

wdym?

whats the orange then?

[gloomy vigil]

9n is apple 7n is orange

[uncut mulch]

that would be an idea of where to start

[wide lagoon]

56?

[uncut mulch]

9n and 7n represent the number of apples and oranges
and they are still in the ratio 9:7

[gloomy vigil]

nice

[wide lagoon]

So N is 8?

[uncut mulch]

lowercase n but yes

[wide lagoon]

possible to show me how?

[uncut mulch]

16n = 128
n = 128/16 (from dividing both sides by 16)

[gloomy vigil]

damn that's awesome

[wide lagoon]

how did you get 16

[gloomy vigil]

9n + 7n

[uncut mulch]

9n and 7n represent the number of apples and oranges
and they are still in the ratio 9:7

their total is 9n + 7n = 16n which is also given as 128

[wide lagoon]

Ahh

[gloomy vigil]

im lowkey losing my mind rn so im probably never gonna forget what was said today

feelsgoodman finally learning

oh crud ive hit another roadblock

y=7x^2 + 42x + 65

y=7x^2 + 42x + 441 -441 + 65

[uncut mulch]

consider:
7x^2 + 42x + 65 = 7(x^2 + 6x) + 65

[gloomy vigil]

O_O

7x^2 + 42x +65 = 7(x^2 +6x) +65
OH GOD
7(x^2 +6x + 9 - 9) +65
7((x+3)^2 -9) +65

[uncut mulch]

similar to before,
distribute the 7

[gloomy vigil]

so 7(x+3)^2 -63 + 65
y = a(x-h)^2 + k
y = 7(x-(-3))^2 + 2
k is 2

[uncut mulch]

yes

[gloomy vigil]

YEEEEEEEEEEEAH

feeling like a little kid again

[uncut mulch]

aren't they teaching you this in class?

[gloomy vigil]

my situation is kind of rough, i havent done math in like 6 years and im taking calc rn so im going off of stuff from memory

[uncut mulch]

ah

[gloomy vigil]

im sure u noticed that i confused something for the y-intercept

so u can tell that im kinda (yikes)

[uncut mulch]

you'll be fine. you're getting these concepts quite quickly

[gloomy vigil]

❤️

hmmm "Determine the domain of the function f(x) =x^(7/2)

x^(7/2)
= 7 sqrt x

[clever inlet]

hmm

[gloomy vigil]

er that is not what i meant in terminology

[uncut mulch]

that doesn't mean what you probably think it means

[gloomy vigil]

7superscript or whatever sqrtx?

yeah that

[uncut mulch]

yeh its not that either

[gloomy vigil]

oh

[viscid thistle]

isnt it sqrt(x^7)

or sqrt(x)^7 idk

[uncut mulch]

^

[gloomy vigil]

ahhh

sqrt(x^7)

i see

so that's why the domain has to be >= 0

[viscid thistle]

you could literally divide 7 by 2 and get 3.5 which is x^3 * sqrt(x)???

[gloomy vigil]

wait what O_O

[viscid thistle]

i have no clue

maybe its true

i know x^3.5 is correct

[gloomy vigil]

if true that is some big news right there

altho it wont work to my problem i guess cuz if x^3.5 that means all real numbers would be the domain right

[viscid thistle]

huh thats true

[gloomy vigil]

altho I guess technically speaking writing it as 3.5

is the exact equivalent as 7/2 which forces u to take

the sqrt (x^7)

[viscid thistle]

but not really because thats like saying x^1/2 is for all real numbers

[gloomy vigil]

yeah

[uncut mulch]

still issues with -ve numbers

[gloomy vigil]

i see i see

so 0 can't be raised to a negative power huh

0^-1 = 1/0^1 = 1/0

[viscid thistle]

when dividing by zero some equations just say that it equals some limit for continuity purposes

[gloomy vigil]

think my brain just dipped in some lava

[viscid thistle]

but the meaning is ambiguous

[fleet yew]

-ve

?

[gloomy vigil]

negative

i believe @fleet yew

[fleet yew]

Thats weird

Why not just say negative

[gloomy vigil]

shortcuts

:p

[fleet yew]

It really doesnt save any time

[uncut mulch]

+ve and -ve are generally accepted as abbreviations

[fleet yew]

Considering you have to move you hands away from the letters on the keyboard and look for the minus or plus sign

You also gotta press shift too

[uncut mulch]

keypad

[gloomy vigil]

lol

[uncut mulch]

laptop users

[fleet yew]

Still you have to move your hands out of typing position

Actually wastes time

[gloomy vigil]

that probably depends on the typist's speed tho right

[fleet yew]

If you're above about maybe 30 wpm then yeah you're wasting time

[gloomy vigil]

I just got to this problem and i have to say, what on EARTH IS TRANSCENDENTAL BRO?

WE ENTERING LIKE 4TH DIMENSION IN MATHEMATICS OR SOME SHIT?

[fleet yew]

Think about it

Pi for instance is transcendental

[gloomy vigil]

O_O

[uncut mulch]

wtf is that question...

[viscid thistle]

is it synonymous with irrational

[gloomy vigil]

I need to learn up definitions ASAP

[viscid thistle]

because irrational is not on the list

[fleet yew]

No @viscid thistle

[clever inlet]

pretty ehh question

[fleet yew]

Irrational doesnt really apply to functions

And irrational does not mean transcendental

[gloomy vigil]

the answer to the problem was polynomial but reading the word transcendental spooked me

[clever inlet]

does Transcendental apply to functions either though

[uncut mulch]

there's more than 1 correct answer

[gloomy vigil]

wait what there's more than 1

Nice.

the systems busted!

[uncut mulch]

but polynomial is probably the one they want

[clever inlet]

i guess it depends which algebraic you mean

[viscid thistle]

seems like a blanket term for non polynomial numbers

[uncut mulch]

polynomials are also rational functions

[clever inlet]

that's true

[fleet yew]

Like the pythagorean constant is irrational but not transcendental

[gloomy vigil]

O_O

[uncut mulch]

overall horrid question

[fleet yew]

I think algebraic refers to basic operations

[gloomy vigil]

this answer was algebraic

[fleet yew]

Like excluding things like trig functions etc

[clever inlet]

wtf

so they're going by that meaning of algebraic

[fleet yew]

Algebraic means +-×÷^ and sqrt iirc

[uncut mulch]

well at least in this case its definitely none of the other 3

[clever inlet]

then surely the last one is equally as algebraic

[gloomy vigil]

o_o.

[fleet yew]

Polynomial is the only logical answer for the last one imo

[viscid thistle]

algebraic?

[fleet yew]

I mean a polynomial is algebraic in the same way a square is a rectangle

[gloomy vigil]

@viscid thistle ye

weird sets of questions, ive done like 9 of them mand they were all polynomials or algebraic

where's the love for rational or transcendental

[heady harness]

Sorry, I am not here to answer the question, but I do have one, relating to this one. What does it mean for a polynomial to be transcendental?

[gloomy vigil]

That my friend is a fantastic question!

I hope someone can answer that lmao

[uncut mulch]

https://en.wikipedia.org/wiki/Transcendental_function

[fleet yew]

Something like log or exp

[heady harness]

oooohhhhhhhh

[gloomy vigil]

ooh

[heady harness]

I thought it was like a transcendental number

okay

[gloomy vigil]

i thought transcendental was some like infinity type stuff

[fleet yew]

Exp specifially means e^x

Yeah you're actually right

About infinity

[gloomy vigil]

O_O

[fleet yew]

Specifically not being represented in a finite number of algebraic operations

[heady harness]

so essentially not algebraic, right?

[gloomy vigil]

x^-1 and 1/x^-1
both of their domains are (-inf,0)U(0,inf) ?

[clever inlet]

yes

the second one is kind of interesting

[fleet yew]

That second equation is just x lol

[clever inlet]

it behaves like x

for all x except x = 0

[fleet yew]

Technically for x!=0

But no one cares because you can just take the limit

[gloomy vigil]

wait what

oh shit ur right it really is just x

[clever inlet]

1/x^-1 simplifies to just x

but domain is taken before simplifications

[gloomy vigil]

ah right

[clever inlet]

or i should say

you should keep the domain across simplifications

[fleet yew]

0/0=1 so it's all good

[clever inlet]

[fleet yew]

Yeah think about it

Lim as x->0 Sinx/x

[clever inlet]

[fleet yew]

Lim as x->0 x/x

[clever inlet]

x^2/x

[fleet yew]

Thats not 0/0

Thats just x

[viscid thistle]

[clever inlet]

[fleet yew]

You have to simplify the expression before taking the limit

[clever inlet]

[fleet yew]

Lim as x->0 tanx/x

[fleet yew]

Im telling you man 0/0 is 1

[clever inlet]

sin(x^2)/x

[heady harness]

1x = 2x; divide each side by x
1 = 2

[viscid thistle]

thats a massif sigmy boi

[hallow flicker]

Can someone create a formula for this

[viscid thistle]

wdym a formula

it is a formula

[gloomy vigil]

i wish i even knew what i was looking at LOL

[viscid thistle]

LOL

[fleet yew]

Why do you have two indexes

[viscid thistle]

im sorry i couldnt help it

[gloomy vigil]

u could tell me that's the DNA strand genome or something for coronavirus

and id believe u

[fleet yew]

Its not scary lol its just greek

[viscid thistle]

yeah you gotta learn greek first

[fleet yew]

That weird E looking thing is called a sigma

[viscid thistle]

it means sum

[fleet yew]

I swear im not trying to prank you

[gloomy vigil]

u mean like summa cum laude?

[viscid thistle]

yeah

[fleet yew]

Its actually called sigma

[viscid thistle]

exactly

[gloomy vigil]

hm sigma

[viscid thistle]

it means sum

[gloomy vigil]

sounds a lot like ligma..

[hallow flicker]

Did you guys figure it out

[fleet yew]

Its not some sort of immature joke ninja would make

[hallow flicker]

I was thinking of using this

[viscid thistle]

i dont understand amd is right why the fuck does it have two indexes

is it a double sum

[hallow flicker]

Ok so o wanted to use the formula at the start but the thing that being multiplied if changing

[fleet yew]

So lemme get this straight

This series is

0+3+8+...

Or am i interpreting this wrong

[hallow flicker]

Let me see

But can you make a general formula?

[fleet yew]

I dont see why youd need to with so few terms

Also this makes no fucking sense

[gloomy vigil]

is this a precalc question btw, cuz i think i wouldve printed this out and given it to my teacher if i saw something like it

[fleet yew]

Do you mean like the sum of a sum or something

[hallow flicker]

0 plus 4 plus 10 plus 18 and so on

Ok let me write it again

[viscid thistle]

voltage are you as bored as me

[gloomy vigil]

@viscid thistle yo what did u eman by like 2 index and stuff

[viscid thistle]

cuz it must have taken a lto of effort to find that meme

[gloomy vigil]

no bro im sufferin rn

[viscid thistle]

and copy and paste it in here

from what?

[gloomy vigil]

from lack of knowledge

[viscid thistle]

oh

read wikipedia?

[gloomy vigil]

i need like 5% of you guys combined IQ, no but real talk is that actually precalc (this number is probably like infinity)

cuz im scared for my next class if it is

[hallow flicker]

Ok this

[viscid thistle]

wonderful

[gloomy vigil]

id cal that abstract art of the highets level right there

[hallow flicker]

Bruh this question is kinda hard

[fleet yew]

that is much more pleasant

[viscid thistle]

yeah

it is art

boy i love greek numerals

[hallow flicker]

If you guys can solve it then can you make a more general formula?

[viscid thistle]

wdym more general

[hallow flicker]

And also this should have a solution

[viscid thistle]

you want us to sum it?

[gloomy vigil]

this reminds me of like a sphinx riddle

[hallow flicker]

Like use the variables instead of numbers

[fleet yew]

he means an explicit formula

that second one is literally 0 + 1 + 2

come up with an explicit formula for the first one

also why did you write B=2+3

[viscid thistle]

oh uh 3 + 4 + 5??

why is this a thing

[fleet yew]

as opposed to B=5

[viscid thistle]

i presume because 2 is the same as n

the functino could be defined as a recursive relation instead of a sum

[fleet yew]

(3+4+5)(0+1+2)

if i'm reading this right

[hallow flicker]

its a z

you choose the variable

[fleet yew]

that makes much more sense

cross your z's kid

it is worth it believe me

[gloomy vigil]

lol

[hallow flicker]

wait hold on what if i do this

[fleet yew]

i learned that in physics class

[hallow flicker]

like 0 times 3 plus 4 times 1 plus 5 times 2 plus 6 times 3 and so on

[gloomy vigil]

yo, how is this wrong!
quadrant 1

cot = c
tan = 1/c
tan = sin/cos
cos = c?

[clever inlet]

a/b = c/d

does not necessarily imply

a = c

b = d

[hallow flicker]

guys helpe solve my quetsion first

shouldnt this be asked in trig

[clever inlet]

there's a formula for summing consecutive integers

[gloomy vigil]

wait this is trig?

[viscid thistle]

yes

what does cot mean

[fleet yew]

1/cos(theta)=c

1/c=cos(theta)

[hallow flicker]

bruh

i need help with this qustion

[gloomy vigil]

yeah answer his question ^ mb

thx for responding

[hallow flicker]

its not as simple as taking the sum of the b then multiplying it with the sum of the n

[fleet yew]

the second sum has a pretty simple formula

(z^2+z)/2

[viscid thistle]

cos = sin(theta)/c @gloomy vigil ?

there is probably a way without the sin

[gloomy vigil]

@viscid thistle I legit JUST got to that conclusion after googling

lmao

yeah it seems it's like cross mulitplication is the answer

cot(theta) = cos(theta)/sin(theta) = c/1
cos(theta) = sin(theta)*c wait nevermind u said divided by c.

[viscid thistle]

yeah since we flip/invert sin/cos and mult by sin

there is definitely (?) a way without sin though

[fleet yew]

@hallow flicker i think i got it

[viscid thistle]

actually maybe not

[gloomy vigil]

@viscid thistle ud be right, cuz it doesnt take sin going in

[viscid thistle]

since inverting cot requires a periodic function

[fleet yew]

$(\frac{(z+3)^2+(z+3)}{2}-6)(\frac{z^2+z}{2})$

[obsidian monolith]

AMD:

[viscid thistle]

sqrt((cot(theta)x)^2 + ((1/cot(theta))y)^2) = 1 and we are solving for y

good luck

[gloomy vigil]

my brain cells are screaming at me

[viscid thistle]

fuck i messed up

you see i dont know math

[fleet yew]

where'd anime kid go

[gloomy vigil]

now we are speaking the same language

[fleet yew]

i got his formula

[gloomy vigil]

@hallow flicker yo AMD got ur form!

[viscid thistle]

[gloomy vigil]

ok so

im on attempt 8

i got it wrong 7 times

[viscid thistle]

you could probably rearrange that by completeing the square

[gloomy vigil]

hmm completing the square

can i try hollywood squares?

[viscid thistle]

idk man

[fleet yew]

cot(x)=cos(x)/sin(x)

[gloomy vigil]

im honestly really saddened that cos(x) wasnt c

that was like a betrayal you know what i mean?

[fleet yew]

isn't it just c sin x

[gloomy vigil]

i tried that

didnt work seems to not accept sin

[fleet yew]

why not

i mean that is the right answer

maybe you didn't type it in right

[clever inlet]

• multiplication?

[viscid thistle]

maybe your keyboard is greek

[gloomy vigil]

i tried it again

[clever inlet]

ok

[gloomy vigil]

if i have to put the * and it's right im gonna have world war 3 in my brain

but i think it's saying i cant use sin

[uncut mulch]

without trig functions probably

so draw a triangle

[gloomy vigil]

hmmm

so to draw that triangle. i gotta put that in quadrant 1

[clever inlet]

actually

[gloomy vigil]

cot is cos/sin, and is equal to c

[clever inlet]

cos(t) = cot(t) * 1/csc(t) right?

and then spam some pythagorean identities or something

[viscid thistle]

hm

it says its les than pi/2

could you find theta under that assumption

[fleet yew]

$\cos(\theta)=\frac{c}{\sqrt{1+c^2}}$

[obsidian monolith]

AMD:

[viscid thistle]

yay

[gloomy vigil]

is that the answer

because if it is, what the FK

[clever inlet]

pythagorean identities probably

[fleet yew]

no they'll just want that ratio ig

[gloomy vigil]

ima submit it and c

[viscid thistle]

1+c?

oh

nbm

[fleet yew]

1^2=1

[gloomy vigil]

feelsgoodman

no but how the hell did u do that

[fleet yew]

ok

so basically there are these things called right triangles

[gloomy vigil]

O_O

[viscid thistle]

👀

[fleet yew]

draw a right triangle in quadrant I of the unit circle with some arbitrary angle theta

[gloomy vigil]

so far so good

[fleet yew]

cot(theta)=cos(theta)/sin(theta)

and cot(theta)=c

[gloomy vigil]

yep yep

[fleet yew]

therefore cos(theta)/sin(theta)=c

which implies

cos(theta)/sin(theta)=c/1

[gloomy vigil]

right

[fleet yew]

so cos theta is the horizontal part of the right triangle

[viscid thistle]

(x/y)/(1 from x/y) and so we normalize x??? where x = cos idk

[fleet yew]

sin theta is the vertical part

[gloomy vigil]

SOH and CAH

so sin is 1 and cos is c on the triangle?

[fleet yew]

vertical is 1, horizontal is c yes

[gloomy vigil]

and then pythagorean 1^2 + c^2 = hyp

[fleet yew]

yes

i think you've got it lol

just one more step

[gloomy vigil]

1 + c ^2 = hyp

and since it's asking for cos, it's c/(1+c^2) but it's sqrt cuz that was supposed to be sqrted b4

holy fuck

[fleet yew]

dude in all honesty i hate that question

it is worded weird

[viscid thistle]

whats hyp

[gloomy vigil]

hypotenuse

[viscid thistle]

oh

[gloomy vigil]

and fk this question lmao

[fleet yew]

i don't blame you for taking 8 attempts because it really was not a good question lmao

[gloomy vigil]

this discord is a blessing

yeah i also kidna double clicked

i tried a few guesses from here without reading the feedback

and it was like that one that said u cant use sin or whatever

so im like "shiiiiit"

but the homework shit is worthless in points anyway, in eed to understand what im doing and pass the exams

thanks for the help in understanding what i need to do

[fleet yew]

that's the spirit man

so many people just want the answers

and then come test time they fail miserably

[gloomy vigil]

if my brain could google it automatically i would just want the answers, unfortunately life ain't that gifted!

lmao

gotta understand asap

[viscid thistle]

why does 1 from cot equal hyp?

[fleet yew]

?

[viscid thistle]

oh

hm idk i intuitively get it

wait what

cot changes over delta but hyp is always the same?

[gloomy vigil]

cot = cos/sin = c/1

sin = 1 cos = c hyp = 1^2 +c^2

a^2 + b^2 = c^2

cos = c/sqrt (1 + c^2)

yo i just realized u said delta, what the hell is that

[viscid thistle]

oh i meant theta

[gloomy vigil]

oh

[viscid thistle]

but same thing

[gloomy vigil]

it's all greek to me

yeee boi

tiime to apply some of htat learned knowledge

so it's sqrt 24... cos should be sqrt24/5

but i just realized it says 2theta..

this isnt one of those double angle formulas or something right..

[fleet yew]

Find theta first

This is really simple if you dont overthink it

[gloomy vigil]

hmm

[fleet yew]

It wants an exact answer

Dont use a calculator

[gloomy vigil]

i kinda gave up on that one for now cuz of the time but

the good news is

I went further and did this one

in like 10 seconds flat

that felt good lol

alright my time limit hit, time to go back and do that problem

im supposed to find theta?

O_O w0t

cos2theta = cos^2 theta - sin^2 theta

isnt it like

Cos2theta = cos^2 theta - 1/25

[fleet yew]

If sinx=1/5

How do you get x

By itself

[gloomy vigil]

oh shit arcsin

x = sin^-1 (1/5)?

[fleet yew]

Yeah

Now plug that in

If x = sin^-1 (1/5)

Then cos(2x)=

?

[gloomy vigil]

oh.

23/25

[fleet yew]

Wow lol im surprised thats such a nice number

[gloomy vigil]

you know

im banging my head on my desk rn

cuz i actually solved this rpoblem correctly

but i didnt submit it on time by 1 second

[fleet yew]

Bruh

[gloomy vigil]

i shouldve avoided that meme

[fleet yew]

Which meme

[gloomy vigil]

somethin pregnancy or whatever

lmao

wouldve had 1 extra second of learnin

oh well good stuff tho now i know two ways

to do that problem

[fleet yew]

Its ok

People make mistakes

[gloomy vigil]

ye also good taht homework is kinda on the low end of the grading spec

[fleet yew]

Thats why pregnancy happens

[gloomy vigil]

lmaoooo

no kidding

[fleet yew]

If it weren't for mistakes humanity wouldn't exist imo

[gloomy vigil]

appreciate all the help im probably gonna become a regular on this discord, i didnt expect so many good people helping out maybe one day ill get to 5% of you guys level

a man can dream right?

true humanity is a mistake in of itself, but that is why it's also the paradox/contradiction of perfection

how can something so beautiful be so ugly at the same time

[fleet yew]

Imagine if your dad didnt accidentally nut inside ur mom

[gloomy vigil]

lowkey half of divorces that would've happened get stopped because of accidental nuts

the other half happen because of them though

[fleet yew]

Children are a blessing and a curse

You're onto something

The duality of man or some shit

[gloomy vigil]

now if only i could apply that to like that sigma question earlier that one guy posted

was that a precalc question

because i never seen anything like that in my entire life

[fleet yew]

Kinda but not really

I learned sums in alg2

But we didnt do much with them

[gloomy vigil]

whattt that was in alg 2?

[fleet yew]

Just learned how to type em in the calc

I mean its not that hard lol

[fleet yew]

Just use that brain of yours and stop going on 9gag

[gloomy vigil]

the truth hurts but so does not knowing math for later so ill take that advice

i hope to get more questions like that transcendental crap from before, that'd be nice

[fleet yew]

Heres an example

[gloomy vigil]

logs and exponents right

LMAO

bro women don't even fit on the equations in math dude

[fleet yew]

This is what happens to your brain when you use 9gag

[gloomy vigil]

sin(woman) = no sin (man)

a man without sin is equivalent to a woman with sin

this is why men go to jail over false rape accusations

thanks im a lawyer

[fleet yew]

Just do what mike pence does

Dont talk to women

[gloomy vigil]

lmao

[fleet yew]

No one will ever accuse him of rape

[gloomy vigil]

pence also means

the man's size is probably incapable of causing penetration

as a result even if they did accuse him, they would fall back to the same limit of which sin(women) = no sin (man)

[fleet yew]

I dont understand your logic here

[gloomy vigil]

that's the beauty of it

[fleet yew]

Women arent evil lol

I mean not all of them

You can't make sweeping generalizations

[gloomy vigil]

of course that is absolutely correct but it's not the women that is being talked about in the equation

it's the man

an innocent man is equivalent to a woman that has sinned infinitely

[fleet yew]

Man sins just as much as woman

[gloomy vigil]

!

[fleet yew]

Just in different ways

[gloomy vigil]

indeed

sin(aphrodite) = cos(marriage papers)

Q.E.D. = divorce

@fleet yew remember that 23/25 beautiful number

this was the next question

some scary stuff

[fleet yew]

Those are both relatively beautiful imo

Any rational is beautiful

[gloomy vigil]

😦 oh man

[fleet yew]

Especially in trig

[gloomy vigil]

how much of this do u think exists in calc

[fleet yew]

Trig stuff never goes away

[gloomy vigil]

damn u world!!!

[fleet yew]

It gets even harder and more important

In fact trig is essential for complex numbers

[gloomy vigil]

oh boi

sounds like fun

lol

[fleet yew]

It is

Just wait until you learn about the reimann hypothesis

[gloomy vigil]

u mean this ?

[fleet yew]

No that game sucks

[gloomy vigil]

lmfao

[fleet yew]

I didnt like it

[gloomy vigil]

when i hear reimann hypothesis if i ever do in class ill be pinging u

hard

[fleet yew]

It wont be for a long while

[gloomy vigil]

is it like rocket science discrete math type of stuff

[fleet yew]

Maybe till college even

No its intense pure math

[gloomy vigil]

man how the fk did people invent all this math bro

it's one thing to learn it, another thing to learn it without learning it

[viscid thistle]

Because they were smart

[gloomy vigil]

they were smart, yeah right bro what kind of drugs did they shoot up into their brain bro

[viscid thistle]

they were geniuses and spent their entire lives on it

[gloomy vigil]

archimedes probably like did a breakdance on his brain until a concussion gave him supergenius intellect

[viscid thistle]

The capability of the human brain is truly amazing

[gloomy vigil]

it really is

[viscid thistle]

What grade r you in?

[fleet yew]

[viscid thistle]

Feynman himself wasn’t any genius but he was able to be a pretty good physicist.

[gloomy vigil]

technically 13th

lol

[viscid thistle]

I’m in 11th grade (USA)

[fleet yew]

Imo there is a genetic component to intelligence

[gloomy vigil]

i probably shouldve taken physics

[viscid thistle]

whoa

u old

Nah as long as ur brain is at least average with hard work and patience u can be very good in physics

i just wanted to insult your age

[gloomy vigil]

how old are u @viscid thistle

[viscid thistle]

so i could feel better about myself

Feynman wasn’t a genius and he became a pretty good physicist so

look fren if i told you my age then i would stop being my age

[fleet yew]

Feynman was a genius

[viscid thistle]

its happened to all the ages ive been

[fleet yew]

How dare you

[gloomy vigil]

who the fk is feynman

feignman?

[viscid thistle]

Lmao u don’t know how Feynman is?

Look him up

[gloomy vigil]

feynman might as well be kim jong uns 3rd brother

[viscid thistle]

https://en.wikipedia.org/wiki/Richard_Feynman

[gloomy vigil]

hmm

oh shit

[viscid thistle]

he has a pretty big forehead

[gloomy vigil]

i know that guy

[viscid thistle]

if you know what i mean

Feynman was just pretty curious and interested in what he wanted to learn

[fleet yew]

I hate it when people say shit like oh albert einstein failed math class as an excuse for being dumb

[gloomy vigil]

yeah no he didnt fail it, he was busy nutting all over himself when he figured out e=mc^2 in 2nd grade

[viscid thistle]

Lol

I heard he made his own proof for the Pythagorean theorem when he was a kid

[gloomy vigil]

now if only i could solve how to rig the lottery..

[viscid thistle]

Or he figured out a proof when he was a kid somethin like That idk

i hate it when my illiterate teachers say that math is bad

[gloomy vigil]

math is bad, when i dont understand it

math is good, when i do.

😄

[viscid thistle]

yeah tahts why theyre illiterate

[fleet yew]

Your teachers say that?

Which ones

[vernal moon]

wassup guys

[viscid thistle]

My us history is so smart in historical and business stuff but he sucks at math and science

[fleet yew]

It's all the fucking liberal arts teachers all like "OMG i suck at math"

[gloomy vigil]

he used up his nen potential in the history but gave up on math and science

[fleet yew]

Normie teachers i swear

[viscid thistle]

Ye ig

uhh well my religion teacher seems to hate math and my french teacher said that if you like conjugating verbs you must like math because you plug stuff in and then my biology teacher said that the directino of dna (antisymmetric) is very mathematical

stuff like that

[gloomy vigil]

bro religion?

[viscid thistle]

I’m alright at history and I’m pretty good in language arts and I’m amazing in math and science

At least that’s how I rate myself

[gloomy vigil]

i wont make the joke but u know religion vs science

lol

[viscid thistle]

idk its what made me like math though

[fleet yew]

I love math but conjugation is retarded

[viscid thistle]

I was graphing trig functions

[fleet yew]

French is the opposite of any sort of logical process

[viscid thistle]

And damn they were sexy

oh

[gloomy vigil]

😮

[viscid thistle]

wow how did you gueess i was taking french

and wdym

[gloomy vigil]

bonjour

[viscid thistle]

conjugation is very easy its intuitive

@gloomy vigil r u french

[fleet yew]

You literally just said it lol

[gloomy vigil]

hell no

that's the only word i know