geometry-and-trigonometry

[little osprey]

that question came up in my exam

[pastel anvil]

the general formula uses theta so its confusing

[dry glen]

lol
@little osprey your f*cking pfp made me shit my pants

that question came up in my exam
@little osprey you do IB?

[little osprey]

Yeah

[dry glen]

the general formula uses theta so its confusing
@pastel anvil I getchu

[little osprey]

Wait you too?

[dry glen]

I'm solving past papers before I start IB1

[little osprey]

Oh ye, youre M22 too

[dry glen]

trying to get through 75% of the syllabus

you're M22?

[little osprey]

ye

[dry glen]

how come it came up in your exams already?

[little osprey]

MYP exams

for trig

I didnt know this was a past paper question

[dry glen]

what the hell

[little osprey]

did you do MYP?

[pastel anvil]

1/2 ( (α -sinα) * (2r)^2 + (θ - sinθ) * r^2 )

[dry glen]

they are really working you then

[little osprey]

what paper was this from

[dry glen]

yea did MYP 2 3 4 5

[little osprey]

ohh nice

[dry glen]

what paper was this from
@little osprey idk acc

[pastel anvil]

$1/2 ( (α -sinα) * (2r)^2 + (θ - sinθ) * r^2 )$

[somber coyote]

Seagull:

[dry glen]

it's a compilation

woah

[pastel anvil]

yes the robot is working

[dry glen]

I'm confused about the formula

[pastel anvil]

ok

[dry glen]

especially the theta minus sin theta one

i get the 2r^2 part

[pastel anvil]

u can derive it

[dry glen]

oh

[pastel anvil]

it makes sense once u derive it

[dry glen]

(2r)^2 * (a/360) - 2rsin(a)

Is this correct tho

for the bigger circle

[pastel anvil]

which forula is that

[dry glen]

$(α /360) * (2r)^2 - 2rsinα)$

[somber coyote]

+C:

[little osprey]

Are you doing AA HL?

[dry glen]

so a is the angle

Are you doing AA HL?
@little osprey mhm take this to DM tho

rn I'm tryna do smth

a is the angle in degrees

I divide that by 360

to get angle of sector

[little osprey]

fair my b

[dry glen]

then I multiply that by the area of circle

take out the area of the triangle 2rsina

is that fine?

oh I get it

[pastel anvil]

its in radiants tho

[dry glen]

if α is in radians

I can take out the 360

[pastel anvil]

ya its in radiants

[dry glen]

so

$(α) * (2r)^2 - 2rsinα$

that's the area of the smaller sector, right

[somber coyote]

+C:

[upper karma]

Here’s a challenge— try to derive that formula.

[dry glen]

what's the formula again?

I thought you were gone xDDD

[pastel anvil]

well he came back

💥

[upper karma]

Well I decided I would be a couch potato 🥔

[pastel anvil]

magic

[upper karma]

maths is fun but I have a head cold and there’s nothin else for me to do

[dry glen]

damn

so what about the other one

the same?

[pastel anvil]

im confused srry

[dry glen]

so I thought it was area of circle

times angle in radians

minus the area of triangle

[pastel anvil]

yeah

which is this:

[dry glen]

this?

[pastel anvil]

1/2 ((θ - sinθ) * r^2 )

[upper karma]

How about stop deb8ing Over the formula and find it yourself

draw a diagram and proceed

[pastel anvil]

this represents the sector minus the triangle

[dry glen]

I already got the answer

but

still don't know how to derive the formula

nvm got it

was just confused with sin(thetha)r^2

but that's just part of 1/2absin(theta)

why does the 0.5 go for theta times r^2 (area of circle times angle)

[pastel anvil]

cuz its area of circle times half the angle

[dry glen]

why is it half the angle?

[pastel anvil]

magic

[dry glen]

i thought you could multiply by the angle in radians

cut the bs xD

I know your ways

now tell me your ways

[pastel anvil]

i have no idea how they got the cirlce area formula

[dry glen]

oh

well there goes my answer xD

[dry glen]

ohhh

that formula

I see

[arctic vortex]

sorry for interrupting u guys but how do i solve this

i used lateral area for the cylinder

idk what to do for the cone

[dry glen]

the cone

you have a formula

[pastel anvil]

what did u get for the cylinder

[dry glen]

height times smth smth

1/3 height

times radius of circle squared I think

[arctic vortex]

i got 829.38 for the cylinder

i think its b

[pastel anvil]

thats volume

+C thats volume formula

[dry glen]

oh I'm dumb xD

OKAY OKAY CHILL

I FORGOT

hehehe

[pastel anvil]

Lol

srry

[dry glen]

surface area is angle times slant length

[pastel anvil]

[dry glen]

what

[pastel anvil]

thats me

im the cat inside the emote

[arctic vortex]

why areu crying

[pastel anvil]

this math is too beautiful

im crying of hapiines

[arctic vortex]

o

[pastel anvil]

so anyways

[dry glen]

bruh

[pastel anvil]

wat

[dry glen]

BRUH

nah it's okay

I understand

[pastel anvil]

whats bruh mean

[arctic vortex]

oh

i got it

[pastel anvil]

🦾

[arctic vortex]

is tihs correct

[pastel anvil]

yea

[dry glen]

yea

[upper karma]

How y’all doin

[pastel anvil]

did u use the congruence theorems

[upper karma]

Hmm nvm looks like progress

[dry glen]

yea

so

there's another question

I need to show that alpha is 4arcsin(1/4)

[dark sparrow]

and what is alpha

[upper karma]

Provide more context

[dark sparrow]

@dry glen ?

[dry glen]

alpha is the ange

angle

here's the question

not a

b is the question

that I need to prove

[dark sparrow]

ok so $α = \angle CAD$ and you're asked to prove $\alpha = 4 \arcsin(1/4)$?

[somber coyote]

Ann:

[dark sparrow]

@dry glen

[dry glen]

yea

sorry my brother was bothering me

@dark sparrow

[dark sparrow]

yeah ok so like

aight

consider triangle ABD

[dry glen]

mhm

[dark sparrow]

$\angle BAD = \alpha/2$ and you know all of its side lengths

[somber coyote]

Ann:

[dry glen]

right triangle

[dark sparrow]

no

it's not a right triangle.

[dry glen]

it is

[dark sparrow]

no.

its sides are 2r, 2r and r.

[dry glen]

it's tangential to the circle

oh do you mean ABD?

[dark sparrow]

consider triangle ABD

bruh

[dry glen]

it's not a right angled triangle

xD sry

[dark sparrow]

i never said it was

[dry glen]

SORRYYYY

it's 2r 2r r

[dark sparrow]

but that still doesnt contradict the fact that you know all of its side lengths

hence you can obtain cos(α/2)

[dry glen]

how

oh nvm

[dark sparrow]

how do you think you can obtain the COSINE of an angle in a triangle if you know all of its side lengths

[dry glen]

FINE

I GET IT

[dark sparrow]

dont overthink it

[dry glen]

and then

oh

cos^2 + sin^2 = 1

then I can get sin(2/a)

then what

[dark sparrow]

excuse me where the fuck are you getting sin(2/α)

did you mean sin(α/2)

[dry glen]

yea

my bad calm tf down

jesus

[dark sparrow]

you can express $\sin(\alpha/4)$ in terms of $\cos(\alpha/2)$

[somber coyote]

Ann:

[dry glen]

huh?

[dark sparrow]

α/4 = (α/2)/2

[dry glen]

are you in the state of being drunk

[upper karma]

sorry my brother was bothering me
Do you mean that your brother was brothering you?

[dark sparrow]

half angle identity

no i'm not drunk

[dry glen]

oh

xxDDDD

[dark sparrow]

α/4 = (α/2)/2

[dry glen]

mhm

[dark sparrow]

and if you do it right, you should end up at sin(α/4) being 1/4.

[supple onyx]

Wait before contradicting Ann XD

[dry glen]

but I want alpha not alpha over 4

Wait before contradicting Ann XD
@supple onyx a valuable lesson learnt

but I still don't know how to solve it

[obsidian ravine]

Ann knows what she's talking about lol

[dark sparrow]

once you know that $\sin(\alpha/4) = \frac{1}{4}$

[obsidian ravine]

which you obvs don't

[somber coyote]

Ann:

[dry glen]

how do I get sin (a) from sin (a/2)

[dark sparrow]

you don't need to, +c

[dry glen]

which you obvs don't
@obsidian ravine shut up

[obsidian ravine]

lol

[dry glen]

she was making me seem dumb

[dark sparrow]

once you know that $\sin(\alpha/4) = \frac{1}{4}$, it's literally just two steps to $\alpha = 4 \arcsin(1/4)$

[somber coyote]

Ann:

[dry glen]

oh

[obsidian ravine]

making you seem dumb?

[dark sparrow]

i'm not making you seem like anything, i'm trying to show you how to solve the problem without just solving it for you

even though i held your hand throughout almost the entire thing

[dry glen]

okay I see

[obsidian ravine]

she's not the one making you seem dumb lol

[dry glen]

okay chill out

[obsidian ravine]

i'm afraid that's you

[dry glen]

so fucking antagonizing

tf did I do

[obsidian ravine]

you were rude

[dry glen]

put it in nicer words damn

oh my bad

[obsidian ravine]

lol

ironic

[dry glen]

I admit my mistake

sorry about that

[supple onyx]

Everybody chill out just solve your problem @dry glen and let's be done with it

[obsidian ravine]

so fucking antagonizing
@dry glen "put it in nicer words"

[dry glen]

I was rude

sorry

[obsidian ravine]

im sorry too

[dry glen]

Everybody chill out just solve your problem @dry glen and let's be done with it
@supple onyx alright

[obsidian ravine]

we good?

[dry glen]

@dry glen "put it in nicer words"
@obsidian ravine I get it bro...

[dark sparrow]

yall

[dry glen]

man I'm apologizing and this guy is runnning the tractor over my big head

xDDD

[obsidian ravine]

sorry

[dark sparrow]

for real
this entire discussion couldve been avoided

[dry glen]

yea bro we good

[dark sparrow]

like

[dry glen]

yea my fault

[obsidian ravine]

good

[dark sparrow]

was that addressed to me or lj gibson

[dry glen]

huh?

yea bro we good
@dry glen this one?

LJ gibson

[obsidian ravine]

lol this is too convoluted

[dry glen]

and sorry for being rude

my bad

[obsidian ravine]

np, dw

[dry glen]

was a bit excited

won't happen again

[obsidian ravine]

we good

[dry glen]

thanks

[obsidian ravine]

🙂

[dry glen]

@dark sparrow Thank you for helping me. I got through the question

I understood everything you said

[dark sparrow]

next time please take the time to read what i say carefulyl

carefully*

bc usually if i say something i say it with a reason

[dry glen]

Yea, I'll do that

sorry, I just didn't understand and felt dumb

It was my lack of self confidence that lead me to act that way

[upper karma]

I leave for a half hour and it’s a nuclear bomb going off

[pastel anvil]

💥

boom

[little osprey]

I blame the IB

[pastel anvil]

what is IB

[upper karma]

;---------------------;

[pulsar fiber]

Im gonna be in alg 2 w/ trig next year. What could i do to prepare?

[upper karma]

read books, talk to people about it, watch some videos etc

if you need a boost i can probs help you up

[pulsar fiber]

Are there any specific topics i should probably look into to make it easier?

Or simpler

[upper karma]

Build and prepare strongly your base first

Like check if you feel confident with your knowledge on the maths you have taken till now

[upper karma]

i agree

maybe do some exams on khan academy to see how much you've retained

but also beware that most classes begin with a week or so of review

[silent plank]

basic manipulation of equations, order of operations

translating word problems to mathematic equations
basic geometry concepts

[upper karma]

yes i agree ^^^

[pastel anvil]

@tidal river why the slope tho

how can u find the length from the solpe

[final aspen]

u need to check if u can use the pythagorean theorem

i mean actually u know the hypotenuse is the bigger side of the triangle

so if u just see their distances u can know which one is the hypotenuse and the his length

correct me if im wrong

[tidal river]

Could someone help me with this problem

[dark sparrow]

what is giving you trouble here?

@tidal river

also this isn't geometry just ssyin'

[versed river]

well you can cross out the first answer pretty quick

[dark sparrow]

you can but quantum here has chosen to ghost me

[rich wolf]

52 cards in a standard deck

36 of which have numbers

[tidal river]

@dark sparrow it is geometry because it is in my geometry course and the thing thats giving me is if 36 out of 52 cards are numbers and we need to pick two the probability should be 2 in 52

but thats not one of the options

[rich wolf]

Why would it be 2 in 52

There's 36 number cards

[tidal river]

because 2 face cards need to be chosen out of 52 toal cards

ohhh

[dark sparrow]

no

[tidal river]

wait

is it 1/52 times 1/51

[dark sparrow]

no

[tidal river]

then what do I do

[dark sparrow]

the total number of ways to pick two cards w/o restriction is 52C2

the total number of ways to pick two NUMBER cards is 36C2

[livid moss]

Is there a 1/52 chance of drawing one number card?

[dark sparrow]

put two and two together...

[tidal river]

is the chance 36/52 times 35/51

[earnest echo]

Maybe they don't understand, combinatorics

[dark sparrow]

if you insist on doing it that way, sure @tidal river

also do we know quantum goes by he/him

[earnest echo]

Okay I'll make it they

[dark sparrow]

cause i am not making that assumption

[tidal river]

yes im a he

[earnest echo]

Doesn't matter now

[dark sparrow]

oh you are. ok

[tidal river]

ok so what's the other way to do it

[dark sparrow]

the total number of ways to pick two cards w/o restriction is 52C2
the total number of ways to pick two NUMBER cards is 36C2

hence the probability of having the two cards you draw (w/o replacemenet) both be number cards is (36C2)/(52C2)

[tidal river]

so the answer must be 105/221

because of the things you said above

correct me if im wrong

[rich wolf]

,calc (105)*1/(221)

[somber coyote]

Result:

0.47511312217195

[tidal river]

what

how did you do that

,calc 2*1

[somber coyote]

Result:

2

[tidal river]

oh

nvm

I figured it out

[rich wolf]

Lmao!

[austere dragon]

are coincide lines parallel?

[paper vale]

in euclidean geometry, no

[austere dragon]

thank

whats euclidean geometry?

[paper vale]

if u dont know what it is, it means that is what u are doing

[austere dragon]

okay...

[next jackal]

@austere dragon Google it, there are good definitions :)

Or duckduckgo it

[austere dragon]

weird stuff

[rich wolf]

@paper vale actually it depends on context

Some authors do define a line to be parallel to a coincident line

[paper vale]

yea obviously those lines are parallel, i though he meant concurrent lines

lines that coincide

[dusky yacht]

If u is a vector from R3. What does span(u) generates?

A line in R3?

[weary drift]

yes if u!=0

[dusky yacht]

Right, and what set does that set generates?

[weary drift]

you said it

[formal tartan]

can xy=8 be an inverse variation?

[brisk palm]

Yes, because it implies that y = 8/x which is an inverse variation

[formal tartan]

also, y = 2/x cannot be an inverse variation right

because it just wont work

[brisk palm]

It just won't work? It appears that y and x vary inversely, so it should be fine

[formal tartan]

wait so i have super basic question but kinda rusty rn, its all the following are examples of inverse variations except, y=3x, y=2/x, and xy=8

[brisk palm]

Only y=3x isn't inverse variation because it's direct variation

Aka linear

[formal tartan]

Ohhhh, so thats what it meant

[brisk palm]

Yeah a relation varies inversely if it can be written like $y = \frac{k}{x}$

[somber coyote]

Jack Papel:

[formal tartan]

ah okay

school starts in like 3 days lololol

[brisk palm]

Well it's a good thing you're getting ready

[formal tartan]

going to HS

[brisk palm]

First year?

[formal tartan]

yea

just prepping for honors pre calc

[brisk palm]

As a freshman? Impressive

[formal tartan]

nah its eh at my school i mean theres only like 10-20 kids overall in the entire district that do it but yea

at my school 8th grade was geometry but i skipped bec my other friends did it as well

my friend is big brainer tho

think he got state in mathcounts

california too

big place

[brisk palm]

Oh actually I do know some people like that where I live as well

I'm one year behind you then. I took honors Precalc in sophomore year

[formal tartan]

i wouldve done that but im a sweaty

i aint gonna skip anymore bec i dont see a point

ima focus on other stuff

[brisk palm]

Alright

[formal tartan]

ima try to change my schedule tho for 9th grade

Spanish I -> Spanish II and Freshman English -> Honors English

[tidal river]

Could someone help me with this question.

[formal tartan]

is this BYU

[tidal river]

I think the answer is 250

but Im not 100 percent sure

and yes it is byu

[formal tartan]

I see

[tidal river]

not gonna lie that website is preety bad

[formal tartan]

yep

[tidal river]

it laggs to much

tuff doesnt load in

[formal tartan]

language version is way better for me at least

[tidal river]

it stuck in its code faze

[formal tartan]

i sweated so hard in BYU pre calc and finished it in 5 days

[brisk palm]

If I'm not mistaken, you can just multiply the amount of gondolas by that arclength you have

[tidal river]

I'm taking geometry

[formal tartan]

my friends are also taking geo

on BYU

[brisk palm]

,w 21.94 * 36

[somber coyote]

Results provided by WolframAlpha

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

Requested by Jack Papel#8773

[tidal river]

becuase my teacher decided to be annoying and put me in math 8 instead of algebra 1 even after I got all A 's

[formal tartan]

yo ur one of those kids

i started in 6th grade

went to 7/8 but the highest was alg 1

[tidal river]

sweat

[formal tartan]

then went to geo for 8th

[brisk palm]

I think it's 790 if I'm not missing something

[formal tartan]

and skipping to pre calc for 9th

[tidal river]

I originally wanted to do the same but

I transfered school

[formal tartan]

holy crap, my geo teacher was hard

giving AMC10-12 questions for warmups

[tidal river]

and they didnt trust my other school or something

[formal tartan]

thats what happened to me

but i sweated it

[tidal river]

Im gonna take algerbra 2 honors next year

anway

help me with da problem

[formal tartan]

he did

[brisk palm]

I think it's 790 if I'm not missing something
@brisk palm

[tidal river]

how did you get it

jack

[formal tartan]

21.94x36

[tidal river]

could you explain becuase I also have to show my work

Its one of those questions

[brisk palm]

Multiplied the arclength between each gondola times the number of gondolas

[tidal river]

Not gonna lie I googled the quesition becuase it was a real world object

And it said 250

[brisk palm]

Oh

[tidal river]

How ever to make sure

I looked up the ditance between the gondolas as well aand it was the exact sanme number as the quesstion so it has to be legit right.

[brisk palm]

Hmm

Look up the number of gondolas

[tidal river]

21.94

[formal tartan]

btw jsut wondering bec rusty with probality tables, [0, 1, 2, 3, 4] = [0.2, 0.1, 0.5, 0.1, 0.1] Find P(X=2 or 3) = 0.6 righ

[brisk palm]

That's the diameter

240m to feet is 790

[tidal river]

oh

I guess ur right

i small brain

Jk

[brisk palm]

Lol we all make silly mistakes sometimes

[formal tartan]

do u go to california

[tidal river]

stop stalking me how u know

orange county

[formal tartan]

i see

im from bay area

[tidal river]

I dont know exactly orange county or LA

[formal tartan]

i can get this server to 15 boosts if someone becomes my butler for math

[tidal river]

what does boosting a server do

[formal tartan]

cool things

[tidal river]

dang so PAcific

get it

[brisk palm]

I mean if you ask all your questions here we're pretty much your butlers for math help

[tidal river]

Alright jack Im donna send you a video of all the question i have left and you do them

ok

cool

[formal tartan]

im also heavily assuming that ur asian too quantum

is that true or no

[tidal river]

you dont have a choice

kinda

I was born here but

my parents are Indian

so yeah

[formal tartan]

indian is asian

[tidal river]

yeah I know

you lowkey acting sus tho

[formal tartan]

btw jsut wondering bec rusty with probality tables, [0, 1, 2, 3, 4] = [0.2, 0.1, 0.5, 0.1, 0.1] Find P(X=2 or 3) = 0.6 righ

no

[tidal river]

we live in the same area

[formal tartan]

im just relating bec of my school

[tidal river]

alright

Im not telling you my school

[formal tartan]

of course

[tidal river]

but I think I know which one you go to

[formal tartan]

no way

what

also just to make sure, j1/k2=j2/k1 = inverse righg

[tidal river]

@brisk palm could you help me with two more question

"personal butler"

[brisk palm]

Lol sure

[tidal river]

thx

and this

also could you do some minor explanation

on how you got the answer

[formal tartan]

ur so lucky

[brisk palm]

For the second one, the lines FC and BE intersect the circle to form 4 points

[formal tartan]

my

[brisk palm]

These 4 points make up a rectangle

[formal tartan]

school geo

was intense

legit scary

first semester got a 92.2% A was a 92.0+ and second 95.1%

[brisk palm]

Which means the length of CE is equal to that of BF

Which means the arc length is the same

[formal tartan]

j1/k2=j2/k1 = inverse righ

[brisk palm]

Do you understand?

[tidal river]

so the answer is

......

[brisk palm]

I just told you

CE

[tidal river]

oh

wrong question

my bad

[brisk palm]

Or CDE as it says

Do you understand the reasoning I used?

[tidal river]

Yeah you use a triangle

[brisk palm]

Oh well I actually used a rectangle but I'm sure it'd work similarly

[tidal river]

rectangle

thats what I meant

Im brain ded today

[brisk palm]

Lol

[tidal river]

Ok

nice

and what about the first one

[brisk palm]

Ok give me a sec for that one

[tidal river]

take ur time

[formal tartan]

should i move to alaska

easy 90% stanford acceptance rate

[tidal river]

cap

stnaford

is mine

get ur hand offf

[formal tartan]

no bueno

[tidal river]

me no comprara

[formal tartan]

if y varies inversely with x, and y = 18 when x = -3, find y when x = 4

y = -13.5 correcto?

wdym me no comprar

[brisk palm]

IFN is 74 degrees

which means ITN is 37 degrees

Which means ITE is 180 -37 = 143 degrees

Since GFT is 18 degrees, GIT is 9 degrees

Since the angles of a triangle add up to 180, EIT + ITE +IET = 180

IET =GET

GIT = EIT

[tidal river]

74 isnt an option

[brisk palm]

I wasn't saying that was the answer

[tidal river]

oh

my bad

[brisk palm]

9 + 143 + mGET = 180

mGET = 180-143-9

mGET = 28

Do you have any questions?

[tidal river]

no

looks right

[formal tartan]

@tidal river are u on part 1 or part 2

[tidal river]

im done

[formal tartan]

wdym done have u done the final?

[brisk palm]

if y varies inversely with x, and y = 18 when x = -3, find y when x = 4
@formal tartan correct 👍

[formal tartan]

also

odds in favor of getting all tails on nine coin tosses is 1/512 right

or is it 1/511

[brisk palm]

1/512 yes

I'm curious what your reasoning for 511 was

[formal tartan]

bec

ratios?

or something like that

also picking an ace or jack from standard deck of cards id 2/13 right

[versed river]

yes 2/13

but the reasoning for that is that there's 4 jacks and 4 aces, out of a deck of 52 cards, so thats (4+4)/52=8/52=2/13

[formal tartan]

yes just making sure

must get 100% correcto maximus

[earnest echo]

What's terminal side?

😅

[formal tartan]

easy to display, not easy to explain

[earnest echo]

Then display

[formal tartan]

also which one

[earnest echo]

As far as I understand, It means that the sine is in the 2nd quadrant

Which trig function relates base and hypotenuse?

[formal tartan]

A and c

which one

bec i could use sin

[earnest echo]

If we have got angle A

[formal tartan]

we got A and c

[earnest echo]

It means x is perpendicular and c is hypotenuse

Which trig function relate perpendicular and hypotenuse?

[formal tartan]

cosine?

[earnest echo]

No, think again

[formal tartan]

sine?

[earnest echo]

Yeah

[formal tartan]

oh yea

brainfart

[earnest echo]

$sin(A)=\frac{x}{c}$

[somber coyote]

The Godfather:

[formal tartan]

also plz

help with this, i have solved these things before

but i dont want to solve again

gives mental aids

[earnest echo]

If you don't want to solve, then what you wanna do

[formal tartan]

bribe

[earnest echo]

Wanna get banned?

[formal tartan]

no

i own china

[dire sand]

They understand this concept now.

[brisk palm]

You don't have to do anything special for this one

Since both sine and cosine are both something / hypotenuse, the denominators will be the same. And what's the sign of sine in the 4th quadrant?

[main lintel]

Hi guys. I'm slightly retarded today. I want to calculate the equation for the line in 3D, but I'm missing something.

Now the line's equations should be:
f(x,y) = ax + by + c right?

I have line's 2 points which is sufficient to define the line. One is (0,0,0) and the other is (x1, y1, z1).
From the first point I know that c=0 cause 0 = 0 + 0 + c

And from the second point I know that b=(z1-a*x1)/y1

[earnest echo]

Now the line's equations should be:
f(x,y) = ax + by + c right?
@main lintel
That's 2D, isn't it

[main lintel]

No, it's 3D

f(x,y) is the third dimension

[earnest echo]

No wait, it's 3D

[main lintel]

Introducing this in the initial equation I get:
f(x,y) = a*x + (z1 - a*x1)/y1 * y
Which still leaves me one coefficient.

[earnest echo]

Use the other form

[main lintel]

I guess this above gives me a plane or something.

[dark sparrow]

Now the line's equations should be:
f(x,y) = ax + by + c right?
that'll give you a plane

yea

[main lintel]

OK. So the line has only one independent variable.

[earnest echo]

$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$

[somber coyote]

The Godfather:

[main lintel]

Yes, makes sense.

[earnest echo]

That's the equation of line I know of

l,m,n are direction cosines which can be determined by the given points

[main lintel]

So f(x,y) = a*x + (z1 - a*x1)/y1 * y gives me the family of planes which contain the line defined by (0,0,0) and (x1,y1,z1) I guess.

[snow quest]

why is the answer D

[livid moss]

There are only two y values for y = sin(x) that have only one x value in that interval which map to it, those are the max and min values of 1 and -1

[keen wing]

The amplitude is 2 and then the midline is 1

[livid moss]

So you need (b-1)/2 to be one of those

[keen wing]

And the question is asking for the positive real number

So

[upper karma]

Either 3 or -1

[keen wing]

Ye

[snow quest]

i see

thanks

[surreal vector]

I'm trying to solve cosx(2sinx-4)=0

and I get that arc cosx = 90

so following this formula, shouldnt the answer be x=±90+360k?

[upper karma]

solve cosx=0

[surreal vector]

thats 90

[upper karma]

Only 90?

Aight

so following this formula, shouldnt the answer be x=±90+360k?
Correct

[surreal vector]

according to symbolab the answer is

I don't know where -90 went and where 270 came from

ohhhh -90 degrees

is 270

fml im dumb xD

[upper karma]

Yes

[upper karma]

What have you got so far?

@keen wing

[keen wing]

I just got it

I was thinking, really dumb

I like this problem

[upper karma]

It's not easy

Similar triangles right?

[keen wing]

Yeah

Very nice

[sudden locust]

https://youtu.be/C9tMc4Ndcmg What do you think about this proof? What is you guys favorite Pythagorean Theorem proof?

[paper vale]

ptolemy's theorem in a rectangle

[upper karma]

Not my favourite

[silent mortar]

Hello, could somebody assist me with these questions? Our teacher didn't have the chance to go over them because of corona and I have no idea where to start. Thanks.

[silent plank]

how much trig have you learned?

[silent mortar]

up to about the point where my teacher started introducing the unit circle

i haven't done math in a while, so i'm a little rusty.

[silent plank]

do you know about related acute angles?
signs of trig functions in each quadrant
special angles/ratios
reciprocal trig functions

[silent mortar]

i know signs of trig functions in each quadrant, special angles/ratios, and reciprocal trig functions.

related acute angles, i'm not too sure.

[silent plank]

the related acute angle is the acute angle between the terminal arm and the x-axis

in the case of something like 225°, that would be 45°, sin is also neg in quadrant 3,
hence sin(225°) = -sin(45°)

[silent mortar]

okay, im following.

[silent plank]

and try applying that general idea

[silent mortar]

i don't understand, do i use the unit circle?

[silent plank]

the above is applying properties of the unit circle

you could look and identify values values from the unit circle directly

[silent mortar]

we never really learned much about the unit circle, sorry, do i just match the angle?

[silent plank]

yeh

there's one pinned in this channel

[silent mortar]

it doesn't matter what trig function either?

[silent plank]

sin(theta) gives the y coordinate
cos(theta) gives the x-coordinate

[silent mortar]

okay, so you can't use the tan function then correct?

only sin and cos are valid?

wait i might just be dum

[silent plank]

for tan you could divide sin by cos

[silent mortar]

yeah

lol

okay thanks

[jovial hedge]

Hi, can anyone help me solve this question? thx

[earnest echo]

Do you know trig identities?

[upper karma]

@jovial hedge ^ what did you tried too

[paper vale]

that expression is equal to 1/2(cos(a+b) + cos(a-b))

[upper karma]

How am I able to solve this? It says it was the trigonometric Identity... Hmmm... I just don't have any idea.. is this solve for theta?

Look at confunction part

@upper karma

Ah Thanks :)

[weary drift]

give credit c:

[upper karma]

True

[somber coyote]

Al𝟛dium:

[upper karma]

Next time i will appropiately

[weary drift]

$\bR\sigma\k\alpha\bold b\ep^{\Gamma\bold M}$

[somber coyote]

RokettoJanpu:

[surreal vector]

a small question - is x * sin(a) the same thing as sin(x*a)?

[earnest echo]

No

[upper karma]

$\sin(2x)=2\sin(x)$?

[somber coyote]

HoboSas:

[surreal vector]

yeah

[paper vale]

bruh

[upper karma]

Try plugging x=pi/2

[paper vale]

or actually think about what sine is

[umbral snow]

sin(2x) means to double x, then take the sine of that.

2sin(x) means to take the sine of x, then double that.

The difference in order is important - these two are not the same thing

[surreal vector]

well put, thanks.

[sudden locust]

@upper karma What's your favorite way?

[upper karma]

I feel like that one is not very rigorous

I like the one that uses Euclid theorem

[oak badger]

I need some assistance with a formula. I'm trying to find the best way to fill the largest possible area of a cone, with either a single circle or a single rectangle. The rectangle can not be rotated either. The cone can be any size length, facing any direction, and can be up to 180 degrees wide. Does anyone know of a formula to find this?
or, the best fit of a conic shape using a circle or a rectangle
Example:

[upper karma]

You need some cases

[oak badger]

As in?

[upper karma]

Hold on

[oak badger]

the variables i have access to are the center line, the length, and left and right lines.

[upper karma]

Huh?

If $2\pi r>a\pi$

[somber coyote]

HoboSas:

[upper karma]

Where a is the length of the apothem

The radius of the inscribed circle is a/2

You can easily see it drawing it

So if 2r>a the "area" is bigger than the semicircle with radius a

[oak badger]

so i want to find the distance between these points following the arc?

[upper karma]

You know the length of the green line (from the radius of the base)

And the black line (apothem)

So you can easily get the angle between the two radii

From which you can easily get the radius of the red circle (drawing the perpendicular radii to the black line)

[oak badger]

that would be my variable dir with angle difference between the black lines would be my ang and the radius of the circle section would be my lng

[tidal river]

Could someone help me with this

[paper vale]

it is just 2x23x22x21x20x19

[tidal river]

is the x stand for times

[paper vale]

yea

[tidal river]

so I just mulpty those and I get the answer

[upper karma]

You need sqrt

[tidal river]

what

why

[paper vale]

it is how the answer is requested for some reason

[upper karma]

^

[paper vale]

wait there are 26 letters

not 24 oops

[tidal river]

bru

[paper vale]

so add 2 to each term except 2

[tidal river]

when ur too deep into math

and forget about english

[paper vale]

i mean it isnt really that deep

[tidal river]

So what would the final answer be

after you correction

[upper karma]

You calculate it

[tidal river]

so i do 2x26x25

[silent plank]

not 26*...

[paper vale]

dont use * as it makes things italic

[silent plank]

use \*

[paper vale]

yea u cant use the W or K from the first position

[tidal river]

Im confusd all of you are talking and I dont know who to listen to

Can one of you just give me the equation

[paper vale]

bruh i already did

[silent plank]

2 choices for the first letter,
left with 25 for the second letter
left with 24 for the third letter
etc

and multiply accordingly

[paper vale]

and try and understand it instead of just getting the answer

[tidal river]

So I can do 2x26x25x24

all the way to 1

[paper vale]

no wtf

[tidal river]

isnt that what you said

[paper vale]

there are only 6 characters

[tidal river]

oh yeah

so its

[paper vale]

also we just said not to include the 26

[tidal river]

2x25x24x23x22x21x20

so its that

right

[paper vale]

no...

[tidal river]

that 6 chracters

[paper vale]

um no it is 7

[tidal river]

the two counts as a chracter

so its 2x25x24x23x22x21

[upper karma]

"the first letter..."

[rose tulip]

Would the opposite side always be equal?

[upper karma]

@rose tulip ok

[rose tulip]

Would it?

[brisk palm]

The opposite side is equal because the lines are straight

You can also think of it like this

Let's say our angle is theta

We want to prove that beta = theta

So first Let's find alpha

Alpha is equal to 180°-theta

And likewise the other alpha is also equal to 180°-theta

We know that all of these four angles must add to 360 degrees

So 360° = β+α+α+θ

360° = β+180°-θ+180°-θ+θ

360° = 360°+β-θ

0°=β-θ

θ=β

Hope this helps

These angles (theta and beta) are called "vertical angles"

@rose tulip

[tidal river]

@brisk palm Can you help me again

Private buttler

[brisk palm]

Sure

[rose tulip]

theta and beta?

And I was talking if it's a transversal angle

@brisk palm

OH wait

There prolly the same thing.

[brisk palm]

Looks like it lol

[tidal river]

petition to make @brisk palm an honorable

he been a huge help

to everyone in geo and trig section

[bitter sequoia]

Can anyone help me out? I’ve been having trouble with probability recently.

[brisk palm]

Well since you have a 65% chance of getting one dollar, and a 35% chance of losing two dollars

Your expected outcome for one game would be
.65*1 - .35*2

Since those are the probablilities of getting those results

Hope this helps!

Also this doesn't really belong in #geometry-and-trigonometry. I'd put probability in #probability-statistics or a question channel

[bitter sequoia]

Thanks a bunch, will do next time!

[covert pine]

Hello! I'm quite new here. This problem gives me a headache, can anyone help me?

[upper karma]

@covert pine what have you tried

[covert pine]

Well

Quite honestly

The only thing I got is the length of the hypotenuse of the triangle with lengths 4 and 2

And that's 2√5

Other than that ...

Don't know where to proceed

@upper karma here, sorry

[upper karma]

If you put that in a Cartesian plane, nice things will happen

Then you divide the quadrilateral in 2 equal triangles

Which are right

Or

[little osprey]

Osas

[upper karma]

You can notice some similar triangles

[little osprey]

Ye

That was my approach

[upper karma]

Nice

[paper vale]

yea i just quickly did it, all u need is similar triangles

[little osprey]

kane flexing his olympiad skills

[paper vale]

[covert pine]

@paper vale How did you guys know that it's similar?

@upper karma Hey, I actually modeled it in a Cartesian Plane. And I discovered that AN and DP are perpendicular lines

Thus the similarities

@upper karma @little osprey @paper vale Thanks, you guys helped me greatly!

[upper karma]

Nice

[paper vale]

you dont need to use cartesian, just angle chase

[upper karma]

We don't do that here mate

[pallid sierra]

Hello! I need help with understanding how I can approach solving this problem. Thank you! 🙂

[gritty sail]

i feel like multiple graphs could be possible unless im dumb

[pallid sierra]

An infinite amount of linear graphs?!

[gritty sail]

is it the first max?

an infinite amount of sinusoidal graphs

[pallid sierra]

WTF

I HAVE NO TIME FOR THIS

[agile siren]

chill dude

the maximum is at y=5 so

y(x)=5sin(something)

[upper karma]

@pallid sierra is it a test?

[pallid sierra]

Of course not!

Just practice 🙂

[gritty sail]

wait is that max point the first max point?? the second max point?

[pallid sierra]

You are making more questions than answers 😦

[agile siren]

what does a midline in a sinusoidal function mean

[pallid sierra]

If you can’t completely help then please don’t try :/

[agile siren]

jesus you got no chill im just not native english ok

[pallid sierra]

It isn’t your English.

[upper karma]

I HAVE NO TIME FOR THIS
Are you sure it's not a test?

[pallid sierra]

With all due respect

No it isn’t a test

[agile siren]

@upper karma its not a test he's just your local karen

[pallid sierra]

And my capitalized sentence was not anger, just joking

Seriously, if you cannot completely help me do not attempt.

[agile siren]

uhhh alright

the function is -5sin(2x)

[pallid sierra]

No

[agile siren]

ok

[upper karma]

Don't give away answers

@pallid sierra are you here?

[pallid sierra]

I just need help

Not asking for answers please

[upper karma]

Okay

[agile siren]

Don't give away answers
oh, okok im sorry

[pallid sierra]

I know that the amplitude is 4

Considering the midline

[upper karma]

Yep

[pallid sierra]

5-1=4

[upper karma]

Tell me what you have tried so far

Anything more?

[pallid sierra]

I don’t know how to transform the function so that f(7π /4)=5

All I know is 4cos(something here)

Hmmmm

[upper karma]

f(0)=1

[pallid sierra]

Oh

4sin(k)+1

[upper karma]

$a\sin(bx+c)+d$

[somber coyote]

HoboSas:

[pallid sierra]

I need a coefficient for k that satisfies f(7pi/4)=5 I think

Am I on the right track or nah

[upper karma]

There's probably another coefficient

c in my formula

[pallid sierra]

C transforms the function to the right or left

[upper karma]

Yes

[pallid sierra]

I just need x rate transformation I think

Ermmm

[upper karma]

Not really

[pallid sierra]

Well I did it

I thought you guys would help me but I helped myself

Thanks anyway

[upper karma]

So it wasn't needed

Good job

[pallid sierra]

Thanks

[agile siren]

so aaa about this

i took an approach like this but it was way too long (talking about dθ/dφ) and

not very satisfying either

im trying to find the maximum amount θ can have

R>r obv

how do i approach this geometrically?

considering the angle φ is known

[upper karma]

I do not understand the question

[agile siren]

so basically imagine two circles with the same center

but one is larger

lets call the radius of the small one r and the greater one R

[upper karma]

Sure

[agile siren]

if the center is O, a point on circle with radius R is "A" and a point on circle with radius r is "B"

whats the maximum value that the angle OAB can have?

like its always a very small angle but whats the maximum?

aka "θ" in this pic https://cdn.discordapp.com/attachments/326138757474680852/742839432800895129/unknown.png

im just showing my not really satisfying approach here

[upper karma]

Angle is maximum when

Big brain

AB is tangent to smol circle

I'd say

[agile siren]

that would make sense but how do you figure that out

[upper karma]

I wouldn't know

You have many constraints

[agile siren]

wdym?

[pallid sierra]

Extremely big brain.

[exotic gate]

Quadrilateral $ABCD$ has side lengths $AB = 20$, $BC = 15$, $CD = 7$, and $AD = 24$, with diagonal length $AC = 25$. If we write $\angle ACB = \alpha$ and $\angle ABD = \beta$, then $\tan (\alpha + \beta)$ can be expressed in the form $-m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

[somber coyote]

Dualist:

[exotic gate]

<ADC is right obv

javen

haven't gotten farther than that

<ABC is also right

bceause 3-4-5 triangle

[tidal river]

Could someone help me with this question

I think its 77 but im not sure

correct me if im wrong

[pastel anvil]

yea it's 77

what is this

[tidal river]

geometry

could you help me with like 3 more questions

[pastel anvil]

sorry I typed an smote and I was asking what the emote was

sure what's the questions