geometry-and-trigonometry

[dark sparrow]

but what i'm about to show is that this isn't needed, and no mismatch occurs

[fleet rivet]

ok

[dark sparrow]

so i'm going to draw a line and give some points names

[fleet rivet]

mhmm

[dark sparrow]

brb

[fleet rivet]

ok

Ping me when you are bck pls

[dark sparrow]

@fleet rivet i'm back

so

QA = 1, since it's a radius of our circle

is that clear?

@fleet rivet

[fleet rivet]

hai

I am back too!

[dark sparrow]

great

so

QA = 1

is that clear?

[fleet rivet]

yep

[dark sparrow]

thus, by the old definitions, we have cos(θ) = QB/QA = QB and sin(θ) = AB/QA = AB

[fleet rivet]

Wait what, QB/QA = QB?

[dark sparrow]

we just said QA = 1

so yes

[fleet rivet]

Oh yeaaah

I get it

[dark sparrow]

yeah ok

[fleet rivet]

What about tan?

[dark sparrow]

tan(x) is defined as sin(x)/cos(x)

😛

[fleet rivet]

Ahhh ok!

[dark sparrow]

there is a geometric representation of tan though!

[fleet rivet]

The graph is very fun!

Goes to infinity IIRC

[dark sparrow]

yup sure does

[fleet rivet]

Thanks for clearing this up for me!

😉

[dark sparrow]

if you make this blue line (the tangent axis, as my highschool math teacher called it) a number line, with its 0 aligned with that point where it meets the circle and its 1 the same size as the radius of the circle, then the point where your angle's side and this line intersect is precisely tan(θ)

[fleet rivet]

Thanks!

[steady lake]

how many sides does a sphere have

[surreal bolt]

...

google it 😛

[steady lake]

what shape is a human

[surreal bolt]

depends on if it has spherical chicken pet.

[steady lake]

ok

[dark sparrow]

how many sides does a sphere have
define side?

[upper karma]

A human can be said to be a composite shape.

made up of complexed shapes, and the human is formed from DNA, which we can mathematically analyze and look at how the human being will develope into (assuming no outside factors inhibit growth) and even still

We can use parametric equations and even zero-product property to make a sketch of a human being @i am cheese#5604

[visual jacinth]

or we could assume our human is spherical and frictionless , less forces to compute

[celest quartz]

can someone help me for an exercise please

[keen aspen]

sure

[celest quartz]

thanks I'm sending you the photo

[keen aspen]

wut

I don't speak nor understand French lol

[celest quartz]

in English it must be why the points "B,E,O and D are aligned"?

*"why the points B,E,O and D are aligned ?"

you understand?

[keen aspen]

Not really

Why are B E O D aligned?

[pseudo turtle]

why is it a straight line if you connect the 4 points I guess

[celest quartz]

yeah exactly

[keen aspen]

It wouldn't be a straight line

[celest quartz]

the exercise asks why would it be a straight line if you connect these 4 points

[pseudo turtle]

why wouldn't it though

[celest quartz]

you gotta prove why it does that

[keen aspen]

Because if you made a diagonal out of B O D it would contain all points except for E

[pseudo turtle]

do you say that from what you're seeing?

[celest quartz]

yeah found for B O D but but don't know for E

[pseudo turtle]

if we are assuming that the 4 points would make a straight line if connected

[keen aspen]

You are trying to prove that they ARE ?

[celest quartz]

yes

the question is why are they

[keen aspen]

But they aren't..

[copper valve]

but they are

[pseudo turtle]

^

[celest quartz]

they are bro

[keen aspen]

Ok I don't see the straight line

[pseudo turtle]

the page is bent

[keen aspen]

Yes I know that doesn't include E

[pseudo turtle]

it does?

[keen aspen]

That's what I said earlier, if you made a diagonal it would include BOD

not E

[copper valve]

E is between the circled points

[pseudo turtle]

E is on there mate 😄

[celest quartz]

circled points ??

[keen aspen]

Is E the circle ?

[copper valve]

no

its between them

[keen aspen]

Oh shit lmao

[pseudo turtle]

no E is the small line

[keen aspen]

I thought it was the circle lmao

My bad

[celest quartz]

no e is just a point

[keen aspen]

Yeah they need to clarify that

because as a reader I saw it at the circle point

[celest quartz]

yeah ok no it's not the circle sorry not being clear 😂

[copper valve]

BI is half the length of AD, EI is half the length of AE

BEI is similar to AED

something something geometry

😛

[celest quartz]

didn't understand :///

[copper valve]

sorry im not good at this stuff so im even worse at explaining :c

[celest quartz]

thank you anyways

if someone can explain me

[copper valve]

u know the 2 dash lines

on BI, IC

to show they are the same length

[celest quartz]

yeah know that

[copper valve]

and its a parallelogram

so |BC| = |AD|

[celest quartz]

oh yeah i understood all that

but

why does it prove that E is aligned with B O And D

[copper valve]

good question

i will think about that xd

[celest quartz]

ok if you find please say it to me

[copper valve]

ok

[celest quartz]

so nobody found?

[keen aspen]

Haha i'm afraid not

it's a difficult question

The only thing I can think of is that if you made a triangle out of ABC, the centroid would be E, because A goes to I (The midpoint of BC) and B goes to O (In this case is the midpoint of AC)

So with that, the intersection of those lines form the centroid, at E meaning why E is on that same line

[tropic stirrup]

Uh

Triangle ADE and IBE are similar
With length ratio 2:1

Proven

[celest quartz]

@keen aspen what is centroid

[keen aspen]

The center of the medians

[celest quartz]

oh ok

[keen aspen]

medians of a triangle is the line from one point to the opposite side, half way

Bisecting the line

[celest quartz]

yeah i know but I'm french so not the same words

[keen aspen]

haha ok

[celest quartz]

ok i understand what you want to say

thank you

[keen aspen]

No problem

[celest quartz]

i had a second exercise if you can help me that would be very kind but if you don't want to no problem

[keen aspen]

Sure just submit it

if I can't answer someone else surely can

[celest quartz]

the question is are (CM) and (MR) perpendicular

[keen aspen]

Whats's M

Does M intersect line EL perpendicularly?

So it doesn't bisect it at all

[celest quartz]

M is a point from the segment [EL]

of

M is just a point

[keen aspen]

Ok

Can you tell me all of the special relationships

[celest quartz]

(MH)//(RE)

and there's LR which is i don't know how to say it English but the line from R which is perpendicular to (EC)

[keen aspen]

ok

[celest quartz]

and the triangle REC rectangle in R

[keen aspen]

?

[celest quartz]

ehmm it means REC is a triangle and the angle ERC is 90°

and that's all there is no more informations

[keen aspen]

Ok so

It asks if MR and CM are perpendicular to each other

[celest quartz]

MR and CH

[keen aspen]

Ahhh ok

[celest quartz]

so you have an idea?

?

[keen aspen]

A bit

It's difficult

What grade are you in?

Yeah I don't see it for this one, it's a bit too hard for me and I was never good with proving stuff 😦

[celest quartz]

I'm in France soo I don't exactly know for England but I'm 15

[keen aspen]

Wow that's pretty difficult

but yeah I don't see how you can prove that sadly, someone else might, i'm by no means the most intelligent lol

[celest quartz]

no that's very kind for your help thank you very much

it's 1 am i gotta sleep right now so good night

[keen aspen]

gn

[tropic stirrup]

That's the same as proving the existence of an orthocenter

Let P be the foot of perpendicular from M to BC, and let Q be the intersection of RM and CH
Then since C, P, H, L are concyclic LCH = LPH
And since R, M, L, P are concyclic LCM = LRM
This proves that LCQ = LRQ, proving that L, C, R, Q are concyclic
This is sufficient to determine that CQR = CLR = 90°.

[copper valve]

concyclic!?

[tropic stirrup]

Ye, concyclic owo

[surreal bolt]

Eh bored:

Theorem: The distance between (a, b) and y = x is |a - b|/(root(2)).

Likely pointlessly long but imho cool proof: (a, b) is the same distance away from y = x as (a + d, b + d) ... we are sliding along a line parallel to y = x.

Lemma: When y = -x, the coordinate (x, y) becomes (x, -x) and
the distance between (x, -x) and line y = x is the same as the distance between (x, -x) and (0, 0) or |x|(root(2)).

Let d = -(b + a)/2. (a + d, b + d) becomes ((a - b)/2,(b - a)/2). Distance = |x|(root(2) = |a - b|/(root(2))

Reason: Reddit.

https://www.reddit.com/r/calculus/comments/7jbuoq/help_attempting_to_find_the_volume_of_a_solid_of/

[brisk root]

I have this two part question on a maths assignment that I need to get done by Monday else I will really badly affect my final grade for the course I’m on.

The functions for x1 and x2 are from the prior question, I wrote them in the space below to avoid needing to take more photos. If my writing is bad I can post better versions of said functions.

[upper karma]

sin(a+b) = sina cosb + cosa sinb

that one?

[dark sparrow]

but yes

[upper karma]

no

[dark sparrow]

👀🔨

[brisk root]

I’ll upload the digital version of the functions for you. I’m sorry I couldn’t photograph the question any larger

Oh dear

That should be better

[upper karma]

just expand that

according to the formula

[brisk root]

Oh

I was thinking I’d need to rearrange stuff

[upper karma]

um no

[brisk root]

The ways to find R and alpha for the second part I have on a formula sheet so I should be ok for the second part

[upper karma]

oh

so which part are u stuck

[brisk root]

Only the first part if anything, and with formatting working out.

[upper karma]

for the first part just expand it out

[fierce tide]

what is the second answer

[thorn talon]

You need to answer the other three questions

Which all have the same answer

[upper karma]

every pentagons sum of interior angles is the same which is 54

[copper valve]

do u mean 540

@upper karma

[upper karma]

just woke up

[copper valve]

ok

[waxen gorge]

Ik this is dumb but how to find the slope of the tangent line formed by a point on a circles circumference

[dark sparrow]

it's perpendicular to the corresponding radius

[gritty flare]

does perpendicular mean it is the same?

or it is opposite

[dark sparrow]

"it"?

perpendicular = at a 90° angle

[gritty flare]

😐

[upper karma]

the slope of the tangent line is opposite to the slope of the radius in the sense that it's -1/m if the slope of the radius is m

[dark sparrow]

that's called perpendicular

[upper karma]

lol

[waxen gorge]

But like

That's not what I'm asking

Cuz if the point is 1/8 up the circle the slope is -x

But if it's 1/6 up it's not

[dark sparrow]

define "1/8 up the circle"?

do you have a picture?

[waxen gorge]

No but I mean like 45°

[dark sparrow]

of the problem, preferably?

[waxen gorge]

it's not a problem I was just wondering cuz in a competition thing I didn't know what to do

Nvm

[dark sparrow]

okay but do you have a picture of the setup you're trying to describe?

[waxen gorge]

No it's fine

So do I use trig to get the slope of the radius?

NVM u get the coordinates of the point

[gritty flare]

Slope is rise over run right?

[waxen gorge]

Ye my brain is ded rn

[gritty flare]

but in a circle from Center point wouldnt that be one

just a question

[waxen gorge]

But u would know where the center is

So u just move accordingly

[gritty flare]

What is Circumference of the circle

C = PiD

How do you find the slope of a tangent line?

1. Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

[dark sparrow]

tangent line to the graph of a function

[paper yew]

x/sqrt(d-x^2) V -x/sqrt(d-x^2) ?

d being the diameter

[dark sparrow]

fuck i'm not in a good state of mind right now

i've got two lines in R^3, L1 and L2, and i have their direction vectors

u and v respectively

u is for L1, v is for L2

[copper valve]

me neither xd

[dark sparrow]

i want to find the eq of the plane that passes through L1 and is perpendicular to L2

i've got n = u x v calculated from previous parts of this assignment

[copper valve]

u mean L1 is on the plane? completely

[umbral snow]

That's only possible if L1 and L2 are orthogonal

Wait no

Nvm!

[copper valve]

they always are

[dark sparrow]

they
aren't

[copper valve]

o wait

xd

[umbral snow]

No wait, maybe I was right

[upper karma]

nx+uy for scalars x,y is every pt in the plane

[dark sparrow]

hhh

okay wait

i think i figured it out

the vectors n and u have to be in the plane

yup

[upper karma]

that spans the 2D space

[dark sparrow]

so i can just compute n x u

and use that as my normal, and that point i had on L1

thanks y'all

i think i just needed a place to talk this out

[brisk crystal]

Could anybody help me with a problem?

https://imgur.com/a/6UpUn

[upper karma]

find h in terms of x?

[brisk crystal]

I had to convert it from English so if you need any other/better explaining I'm here

[upper karma]

whats asked by the question

[brisk crystal]

I need to find the diagonals

[upper karma]

which one

[brisk crystal]

I gave info in the imgur album

of the trapezoid

[upper karma]

i mean what is the question asking

[brisk crystal]

I need to figure out the length of the diagonals

[upper karma]

both AC and BD?

[brisk crystal]

yeah, in an actual number

[copper valve]

well |BE|×|EC|=|AE|×|ED|

[brisk crystal]

the problem is I can't seem to produce any isolated equations

[upper karma]

area of ABD is 0.5(4x)(h) = 156; hx = 78

no thats useless

[brisk crystal]

I can give the diagonals 4y+9y and 4k+9k values

but I have messed around with it and couldn't get anything from it

[upper karma]

AE^2 + BE^2 = 16x^2

wait

[waxen gorge]

Cheeze ur disappointing me :/

[upper karma]

sryyy, what am i doing

[waxen gorge]

:(

Lemme try

[brisk crystal]

I've messed around trying to do similar things for quite a while

and couldn't find anything useful

[waxen gorge]

Look at shared sides

[brisk crystal]

wanted to help my little sister with homework

and got stumped 😄

[waxen gorge]

Ec(Be) = 216 and ec(de) = 486 so we found a relationship for one diagonal

Alsoo

That is not rly useful

And I'm dumb

And I need to use my brain

243 triangle is 279 and 108 is 274

[upper karma]

ikrrr

[waxen gorge]

Times

Be is 4

Ed is 9

Bd is 13

Ec is 27

Wait lemme retry

Wait

That's wronf

[upper karma]

0.5(AC)(BE) + 0.5(AC)(DE) = 507
AC(BD) = 1014

that seems useless

[waxen gorge]

It's not

Find another relationship with ac or bd

Wait

[upper karma]

BC^2 = 97x^2 - h2

[waxen gorge]

Look at ratio of bases

48:243

They're similar

[upper karma]

thats like (4x:9x)^2

nothing useful lol

[waxen gorge]

How bout

[upper karma]

BE:ED = 4:9

AE:EC = 4:9

[waxen gorge]

Ok so top triangle is 2^5(3)
Bottom is 3^5(2)
Left and right are 3^3(2^3)

Right and bottom share one side.

Bottom and left do too

[upper karma]

man this is like unsolvable

[waxen gorge]

Pretty sure there's a way to do in like 10 seconds

[upper karma]

ahahaha

[brisk crystal]

its so bizarre

[waxen gorge]

Like all problems smh

[brisk crystal]

I spend over an hour on it

trying different things

[upper karma]

can u like

[brisk crystal]

I don't really remember math

[upper karma]

translate the entire question

[brisk crystal]

but it seemed easy

[upper karma]

there must be something that we missed

[waxen gorge]

Wait I'ma write it on a piece of paper so I can think

[brisk crystal]

sure 1 sec

In a trapezoid ABCD the diagonals AC and BD meet at point E (see picture).

1. It is given that the bases of the trapezoid are ratio'd 4:9 and the surface of BEC is 108. What is the surface of the trapezoid?

[upper karma]

surface?

what do u mean by surface

[brisk crystal]

I'm not sure what the correct term is in English

you know

the "area"

[upper karma]

oh the area

[brisk crystal]

X*H/2

for a triangle

😄

2. It is given that the tapezoid is a right trapezoid (90 degrees) and the diagonals are perpendicular. What are the diagonals length?

and the given drawing is http://prntscr.com/hod6cp

[upper karma]

AE^2 + BE^2 = 16x^2
DE^2 + CE^2 = 81x^2
AE^2 + BE^2 + CE^2 + DE^2 = 97x^2

AE^2 + DE^2 = h^2
BE^2 + CE^2 = 97x^2 - h^2
BC^2 = 97x^2 - h^2

BC^2 = (DC - AB)^2 + AD^2
BC^2 = 25x^2 + h^2

97x^2 - h^2 = 25x^2 + h^2
72x^2 = 2h^2
h = 6x
area of ABD = 0.5(4x)(h) = 0.5(4x)(6x) = 12x^2 = 156
x = sqrt(13)

i finally solved it

[waxen gorge]

GOT IT

One diagonal is 26

The other is 39

@brisk crystal

[upper karma]

is that guess and check?

[waxen gorge]

No

Prime factorized areas

[upper karma]

oh

[waxen gorge]

Found shared stuff

[upper karma]

thats a simpler way i guess

[waxen gorge]

Did thingies

There must be a fast way

[upper karma]

whats a prime factorised area

u mean something like 48 = 2^4 * 3

[waxen gorge]

Yes

I'm gonna ask someone ik (a highschool pleb)

[brisk crystal]

damn nice

but that is insane

It has nothing to do with the given new information

Maybe there is something wrong with this question

anyhow thanks a lot guys @b l e h.#5296 @upper karma

@b l e h.#5296

@waxen gorge

[upper karma]

theres nothing wrong with the question

[brisk crystal]

Wait cheeze

sqrt(13) doesn't really work

you then have BD^2=4sqrt(13)+6^2sqrt(13)^2

[waxen gorge]

Lol

[brisk crystal]

what did you do @waxen gorge?

[upper karma]

what doesnt work there

[waxen gorge]

I found the prime factorizations of the areas

And then linked them

To ones that share sides in the triangles

It's pretty slow and there must be a faster way to do it in like a minute

[upper karma]

it gives BD^2 = 16x^2 + 36x^2 = 52x^2
BD = sqrt(52)x = 26

what do u mean sqrt(13) doesnt work?

[waxen gorge]

@upper karma :GWwlaHug: ?

Wut

:GWowoKannaBear: ?

Wait what's happeninggg

[upper karma]

idk how to mention u cos its difficult to mention but what

[tropic stirrup]

Here we go, the right channel x'D

[waxen gorge]

So

Bad is similar to bac

Lemme think

[copper valve]

oooooooooooooooooooooooooo

[harsh idol]

youre probably gonna need to prove that angle bfe is congruent to angle bef

[copper valve]

i see it

ya

thats what i saw

😛

[waxen gorge]

Notice it's a bisector

[copper valve]

angle AFD = 90 - o = angle BFE
angle AEB = 90 - o = angle BEF
so angle BEF = angle BFE

so triangle BFE is isosceles

and BF = BE

seems legit enough to me

[waxen gorge]

Ya

[tropic stirrup]

👍🏼

[copper valve]

woohoo

i did 1 geometry question 😛

[waxen gorge]

Lol

[tropic stirrup]

Another one if you wanna give it a try :p

[harsh idol]

looks like we're gonna use isosceles triangles again

gotta prove that angle dah = angel dha

[tropic stirrup]

mmhm

[upper karma]

i extended BM until it cut AD extended at P and got BCM congruent to PDM

[tropic stirrup]

mhmm!

[upper karma]

no idea how to continue

[tropic stirrup]

You're almost there though x'D

[upper karma]

let angle DAH = x, angle DPM = CBM = 90 - x

if i assume DA = DH id be able to do it lol

[tropic stirrup]

So close qwq

[upper karma]

yeah u know what i mean

lol

how do u do it help

Where did u get P

i extended BM until it cut AD extended at P and got BCM congruent to PDM

Ah

[tropic stirrup]

Lemme visualize it for you
you're just one step away from proving it

[upper karma]

yeah that

[surreal bolt]

analytic geom will always get this kind of stuff right 😃

[tropic stirrup]

D is the midpoint of AP

"And therefore D is the circumcenter of APH, proving that DA = DH"

[upper karma]

OH MY GOD

[tropic stirrup]

that's all you needed xd

[upper karma]

AAAAAAAAAAAA

[tropic stirrup]

ikr x'D

[copper valve]

a

[upper karma]

im super close

my god i knew it it has sth to do with a circle

man these geom problems are always fun

[copper valve]

really?

[surreal bolt]

nah >)

[upper karma]

theyre challenging

good warm ups for my half awake brain

[copper valve]

if only i knew enough geometry to make decent problems on them xd

[surreal bolt]

Like Erdos says problems are fun only if you know how to do them or if the Devil isn't asking you for the answer 😃

[upper karma]

[tropic stirrup]

Here, a famous problem

find the red angle without using trigonometric ratios and pythagorean theorem

[lofty stratus]

Define trigometric ratio

[surreal bolt]

oof. Couldn't find the Erdos quote.

[harsh idol]

sin, cos, tan, and their inverses?

[surreal bolt]

It is in N is a Number though

[harsh idol]

kinda reminds me of this problem: https://www.youtube.com/watch?v=m5evLoL0xwg

[surreal bolt]

It is a documentary from 1993 and I think I got the video and the clip on youtube. Ramsey numbers.

https://youtu.be/uPsFjRvNQG4?t=24m7s

[upper karma]

@tropic stirrup is it 45

[tropic stirrup]

Ye

[upper karma]

let the squares (from left to right) be ABCD BEHC and EFGH
i extend the line FH until it meets point J when FJ = 2√2
the red angle is angle CDF + angle HAF = arctan(1/2) + arctan(1/3)
from triangle DFJ: DJ = √2 and FJ = 2√2, so angle DFJ = arctan(1/2)
from triangle DFJ, angle JDH + angle HDF + angle DFJ + angle FJD = 180°
45° + arctan(1/3) + arctan(1/2) + 90°
arctan(1/3) + arctan(1/2) = 45°

[tropic stirrup]

Fokkin hell

[main sluice]

what the fork

[upper karma]

i was drawing lines after lines and kinda found a way to do it

i guess gurls geom problems always need auxiliary segments to solve

[tropic stirrup]

come on

It can be solved much simpler than that qwq

[upper karma]

sorryy

OHH WAITTT

nvm

[tropic stirrup]

Here

[upper karma]

WHAT

okay

[mossy vine]

how do you show that's 45 without pythagoras?

[tropic stirrup]

You see the right angle on the top

isoceles

[upper karma]

its isosceles

[mossy vine]

I can see it's isosceles

why is it right angled?

[tropic stirrup]

....

Basic congruence application, dude

[mossy vine]

congruent to what?

[tropic stirrup]

Gah

[mossy vine]

I'm tired ok :^)

I don't see what it's congruent to

[tropic stirrup]

Tiredness doesn't justify your oblivion of basic congruence

those two blue triangles are congruent

(SAS congruence, if you ask)

[mossy vine]

o ok

[tropic stirrup]

uwu

[mossy vine]

I thought you were saying the 45-90-45 triangle was congruent to something

[tropic stirrup]

lol

[mossy vine]

so I was very confused :^)

[tropic stirrup]

Shush you got the point across

[mossy vine]

I'm not trying to make a point, pls

I'm just very bad at seeing what people mean tbh

[tropic stirrup]

Just
shhhhush

[waxen gorge]

Lol

[fierce tide]

@nocturne tinsel

@noble heath

someone

[rare talon]

Do you know what is the sum of the interior angle of a triangle?

[fierce tide]

180?

[rare talon]

Ok

[fierce tide]

wait wait

[rare talon]

Now divide that polygon to 2 triangles

I hope you know how to divide it (there's 2 ways, either way is fine)

[fierce tide]

k

thx

got it

[rare talon]

👌

[waxen gorge]

@fierce tide the sum of the interior angles of a polygon with n sides is (n-2)(180)

[fierce tide]

@here

[copper valve]

x+all those =360

x = 360-all those

[upper karma]

why is that true?

[fierce tide]

got it

[copper valve]

exercise

[waxen gorge]

Because

(n-2)(180) is the sum of the interior angles

Where n is the number of sides

[fierce tide]

@copper valve

[copper valve]

by above formula given by bleh

angles of a 6 sided figure will add up to (6-2)(180) = 4*180 = 720

we have two right angles, so thats 90+90=180 degrees

180 + 4x = 720

4x = 720-180 = 540

x = 135

[fierce tide]

k

thx

[fierce tide]

@copper valve

[copper valve]

6 sides

x + 3x + 45 + 45 + 135 + 135 = 720

4x + (45 + 135) + (45 + 135) = 720

4x + 180 + 180 = 720

4x = 720 - 360

4x = 360

you can do the rest 😛

[fierce tide]

k

@copper valve

than whats 3x

[copper valve]

x times 3

[upper karma]

that looks like some

nonagon

sum of interior angles = 180(n-2)
since nonagon is 9 sided, 180(9-2) = 1260
1260/9 = 140

[fierce tide]

@upper karma

[upper karma]

okay i have to ask u

how many sides does that polygon have

[fierce tide]

3+

@upper karma

[upper karma]

what 3+?

[fierce tide]

3 or more

[upper karma]

how many sides does that polygon have

dude u gotta count

[fierce tide]

like 12

i think

[upper karma]

yeah 12

what is the sum of the interior angles?

[fierce tide]

2160?

[upper karma]

no

180(n-2)

[fierce tide]

ok

[upper karma]

try again

whats the sum of the interior angles of a 12 sided polygon

[fierce tide]

wait wait

what's the n-2 part

that got me confused

[upper karma]

oh

sum of the interior angles of an n-sided polygon is 180(n-2)

[fierce tide]

so 12-2*180?

[upper karma]

(12-2)*180 yes

[fierce tide]

1800

got it

[upper karma]

that is the sum of the interior angles of a 12 sided polygon

[fierce tide]

1800/12

150

[upper karma]

so whats the measure of each interior angle?

[fierce tide]

150

[upper karma]

yep

[fierce tide]

thx

[upper karma]

no problem

[west dune]

Hey there!
I got the next problem

ABCD is a Trepeze
A + C = 180
I need to prove that the Trepeze's DA = CB```

[dark sparrow]

A + C as in

alpha + delta?

[west dune]

Yea

[dark sparrow]

well

you know α + γ = 180°

and β + δ = 180°

[west dune]

I don't know that D + B = 180

[dark sparrow]

i said beta + delta = 180°

[west dune]

uh

Ok keep going please 😅

[dark sparrow]

it follows trivially that α = β and γ = δ

[west dune]

I need to prove it tho

[dark sparrow]

alpha + gamma = 180

alpha + delta = 180

alpha + gamma = alpha + delta

gamma = delta

[west dune]

How do you know that alpha + delta = 180?

[dark sparrow]

you're given that, no?

[west dune]

I said A + C is 180, that's it

[dark sparrow]

yes

and on your picture, you marked A and C with the letters alpha and delta respectively

[west dune]

ohhh I got you now ok

alpha + gamma = 180 (cause trepeze)
alpha + delta = 180 (given)
alpha + gamma = alpha + delta / alpha goes away cause algebra and
gamma = delta

Thanks!

[real remnant]

does anyone know how to do proofs

[waxen gorge]

Ya

[upper karma]

@shy shale ideally in #help-1 , #help-2 or #help-3

[dark sparrow]

just post your problem

[restive void]

hey anyone here, if anyone can help me dm me please?

[copper valve]

or u can get help

in this channel =p

by posting ur question

[restive void]

oh

well

see

i have a lot of questions

[copper valve]

we cant help you on a test though =p

[restive void]

as part one of my finals is tomorrow

and

i need help with my review packet

as i dont know half the shit im doing

[thorn talon]

Post it here

[restive void]

well

i dont know where to start

okay heres one - point q is the interior of <ROS. S is in the interior of <QOP. P is in the interior of < SOT. m<ROT = 127, m<SOT = 71, and m<ROQ = m<QOS = m<POT

and i have to find ROS and QOT

[topaz valley]

did you get a diagram with this?

[restive void]

nope, i can draw one

[topaz valley]

yes that might be useful

[restive void]

except this is confusing in words

wait nvm im stupid

wait is anyone here

[topaz valley]

they come and they go

why do you ask?

[restive void]

cuz im still confused on this same question, i got m<ros, im stuck on how to get qot

[topaz valley]

ping @help and if someone can help you, they will

[restive void]

oh okay <@&286206848099549185>

there we go

[vale kraken]

Oh

THere's a room for this

how about that

[past mantle]

I hope I did good on my geometry exam

[copper valve]

i hope so too!

[waxen gorge]

Lol

[past mantle]

the only thing i was confused on was when i use CPCTC

[past mantle]

Anyone able to help me find a way to use CPCTC

[tropic stirrup]

@drifting wigeon

Ehhhh

......wait a min

Well if ya don't want the answer, fine shrugs

[past mantle]

I just want to know when to use CPCTC in a proof @tropic stirrup

[tropic stirrup]

The hell even is a cpctc

[copper valve]

i think it is short for "Congruent Parts of Congruent Triangles are Congruent" @tropic stirrup

[tropic stirrup]

:disgust:

[past mantle]

Basically, you use it after you prove the required, then you get the rest

[dark sparrow]

"congruent things are congruent"

what kind of tautological formalized statement is that

.-.

[past mantle]

Idk, we learned it during congruent triangle proofs

It's not used alot, that's the problem

[dark sparrow]

let me guess

you are being forced into the rigid 2 col proof format

[past mantle]

Yea

It's easy, we didn't learn the other 2

[dark sparrow]

the other 2 what

[past mantle]

Types of proofs

We are writing proofs about quadrilaterals being a parallelogram

[haughty prawn]

if you don't do a resolution proof with constructive tarskian geometry can it be called real geometry 🤔

[royal oyster]

Someone please help me

[upper karma]

ok

[royal oyster]

Okay

So I rotated a triangle clockwise 90 degrees

Do I need to add more marks to it?

Compass marks or something?

[upper karma]

I don't know what you're trying to do

if you have grid paper then you don't need to use a compass to rotate 90 degrees

if you used the compass to do the rotation by 90 degrees, then you'd just end up with some compass marks

you don't just add them in after the fact or something

that's why your question is nonsense

[royal oyster]

Thanks a lot.

[upper karma]

lol you're very welcome

[royal oyster]

Here's another way of saying it

Is there anything I'm missing from this?

Or is it correct with all of its markings and whatnot

[crude kraken]

There're proof other than paragraphs and 2-column?

[dark sparrow]

2 col needs to die

[final prairie]

agreeee

i never do it i just do claim (reason)

[copper valve]

same lol

when i really dont feel like deriving something, I'll just be like
i claim this:
here's the proof that it works:

[crude kraken]

gg

Come to think of it, how is 2 col surviving anyways?

Like, aside from school, is there any use for it?

"A particular way of organising a proof using two parallel columns is often used in elementary geometry classes in the United States." Welp

[mossy vine]

there's not really any use to it

although I suppose it could be useful for those who don't know how to read paragraphs

[copper valve]

wow you have green title!!

green name

thing

[final prairie]

yeah contest winner

thing

;P

[copper valve]

cool!

what a good idea

[haughty prawn]

I recently saw a 2 column proof for solving some topology thing, was funny.

[past mantle]

Shoe me

[haughty prawn]

https://topospaces.subwiki.org/wiki/Compact_Hausdorff_implies_normal

[slender gyro]

Is this style bad? It has advantages but it seems rowned upon

[past mantle]

What does the big U mean?

[waxen gorge]

Union

Basically it means the combination of two sets

[past mantle]

So like...?

[dark sparrow]

"combination" is a bad way of putting it

but basically the union of two sets A and B is the set of all things that are either in A or in B (or perhaps both)

[haughty prawn]

Aye, many combinations out there. Hard to tell which would be the right one based on just that knowledge.

Like. How would you define union categorically 😈

[green marsh]

halp

I don't know anything about geometry

but the last topics of a platform i use to learn math are about geometry

is there any resource you can recommend to learn about geometry?

[tight totem]

https://www.khanacademy.org/math/geometry
https://www.ck12.org/c/geometry/#/
try those

[waxen gorge]

@green marsh Art Of Problem Solving - Introduction to Geometry

[copper valve]

mitch is doing that already :P

[waxen gorge]

Then why did he ask .-.

NVM yesterday at 10

[copper valve]

for secondary resource

i think

[mossy vine]

has anyone here used the book "plane euclidean geometry" by gardner and bradley?

[rugged moat]

If tanA + secA = e^x

what is the value of cosA

[dark sparrow]

(sec(a) - tan(a))(sec(a) + tan(a)) = 1, so sec(a) - tan(a) = e^{-x}

thus 2sec(a) = e^x + e^{-x}

=tex \cos(a) = \frac{2}{e^x + e^{-x}}

[dark sparrow]

@rugged moat

[rugged moat]

Ohh

Thx

If sin(x+y)/sin(x-y) = (a+b)/(a-b)

what is tanX/tanY

[dark sparrow]

try expanding out sin(x+y) and sin(x-y), then dividing the numerator and denominator by cos(x)cos(y)

[rugged moat]

We haven't learned expanding the ratios yet

[dark sparrow]

ahem?

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)? you can't not have learned that

you... kind of need it here lol

[rugged moat]

Is there any other method?

[dark sparrow]

don't think so

[upper karma]

would it be sin(x)cos(-y)+cos(x)sin(-y) for sin(x-y)?

[dark sparrow]

sure, or you could rewrite that as sin(x)cos(y) - cos(x)sin(y) 😛

since cos is even and sin is odd

[rugged moat]

I will ask my teacher, he probably gave it ny mistake

spacebar crash

[upper karma]

also u wrote ny

doesn't matter

though

[rugged moat]

Last question: sin^6(A) - cos^6(A)/ sin^2(A) - cos^2(A)

[dark sparrow]

=tex \frac{\sin^6(a) - \cos^6(a)}{\sin^2(a) - \cos^2(a)}

[dark sparrow]

this?

[rugged moat]

yup

[dark sparrow]

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

[rugged moat]

I tried that

Wait

Ohhhhhhhhhh

I spotted my mistake

Thx

[upper karma]

that is an easy one

Lemme try that

$$sin^3(x)+sin^2(x)cos^2(x)+cos^3(x)$$?

[dark sparrow]

^4, not ^3

also, \sin and \cos exist

[upper karma]

but that would result in sin^8 no?

[dark sparrow]

no

i was correcting your ^3 exponents

they should have been ^4

[upper karma]

yeah ok soz mb

I get it now

also what's the point of writing \sin if the difference is pretty much nothing?

[dark sparrow]

it looks better

[upper karma]

$$\sin=sin$$

[dark sparrow]

=tex a\sin(x) \text{ vs. } a sin(x)

[upper karma]

typing sin for me is just faster since negative slash is all the way to the right

[dark sparrow]

negative slash

kek

[upper karma]

I thought it would make sense like

[dark sparrow]

it's usually called a backslash 😛

[upper karma]

If the slash is a linear function having a negative slope

I'll call it backslash then

[dark sparrow]

the other slash is accordingly called forward slash when it needs to be distinguished

[upper karma]

not just slash?

[dark sparrow]

"slash" is fine but when you need to clarify you can say forward slash

[upper karma]

ah

I think i start to realize my mom is waking up soon and I haven't slept that drinking coffee at 20:00 wasn't the greatest idea

and that my grammar is bad

[upper karma]

"negative slash" is so genuine

[ornate orchid]

Help plox im stuxk

Stuck*

ABCD has equal sides

We need to calculate AE CE

Pls pls hel0

[waxen gorge]

Ok

Is CD 15

[upper karma]

how can ABCD have equal sides

[waxen gorge]

Wait wut

[upper karma]

trapezoid with equal sides= square

[untold tinsel]

at 53 a they want me to explain why the area of the ring net is s/h bigger than the area of the net of the cilinder with h as hight

the two templates are right next the question

<@&286206848099549185>

[upper karma]

hello

for the first one

the area of the ring net is like finding the area of rectangle

the width is s

the length is curved but the length is given which is 2 * pi * a

so the area of that net is width * length = 2 * pi * a * s

the area of the cylinder net is simply width * height which is 2 * pi * a * h

the ratio of those areas is simply s/h

[untold tinsel]

alright thanks

[upper karma]

no problem uwu

[untold tinsel]

is the area of a sphere with radius r the same as the area of a cylinder with radius r and hight 2r?

<@&286206848099549185>

[upper karma]

ah do u know how to find the area of a sphere?

[untold tinsel]

with 4* pi *r^2right?

[upper karma]

yes

and what would be the area of a cylinder then

[untold tinsel]

2 * pi * r * 2r

[upper karma]

are they the same?

[untold tinsel]

yes

[upper karma]

yay u did it

[untold tinsel]

it felt like a cylinder in this case would have a bigger area than the sphere

[upper karma]

thats just ur perception

but mathematically their areas are equal

[untold tinsel]

true

[untold tinsel]

@upper karma Their asking to prove that the area of a cylinder is equel to the area of the sphere at 58 haha

I guess I now know the answer

[proper sequoia]

halp

[proper sequoia]

nvm

[upper karma]

i just learned about hyperbolic trig functions, which is just x^2-y^2=1 , is it possible to get trig function values as they are in hyperbolic functions but for any function?

[mossy vine]

idk what you mean by that

you mean like hyperbolic versions of any trig function?

[upper karma]

yeah

[mossy vine]

yeah there are

they're all just written with an h at the end

[upper karma]

but instead of hyperbola, what if i replaced it with any other graph

how to determine the trig functions then?

[mossy vine]

hmm

they aren't trig functions so much

trig functions are specific to a circle

[upper karma]

but arent hyperbolic trig functions related to a hyperbola?

[mossy vine]

yeah

the unit hyperbola, x^2 - y^2 = 1 can be parametrised by x = cosh(t), y = sinh(t)

[copper valve]

wow sneaky, asking in more than one channel at once

[upper karma]

lol i am just curious

[copper valve]

u are too good - .-

i cannot multitask well

[upper karma]

multitask isnt really good for the brain i heard

humans do better when their focus is on one thing

[mossy vine]

the same way that the unit circle x^2 + y^2 = 1 can be parametrised by x = cos(t), y = sin(t)

[copper valve]

aye

[upper karma]

so is there something like a unit triangle

[copper valve]

🤔

[upper karma]

or unit hexagon

[mossy vine]

hmm

they technically exist

[copper valve]

ya just take a regular polygon :P

[mossy vine]

but they'd probably have to be defined by a limit or by piecewise functions

[upper karma]

like if there is a line with angle theta shooting out to infiny right

and where the line touches the triangle, is there any possible way to determine the point of intersection of the line and the shape?

[copper valve]

wouldn't that be given from the equation of the shape ;o

same way as the circle and hyperbola

[upper karma]

i made something really quick to demonstrate what i mean https://www.desmos.com/calculator/gwojtynqna

[mossy vine]

the easiest way would just to be to convert the shape to polar coordinates

[copper valve]

Ok!

[dark sparrow]

simplest case, where one of the sides of your angle is the diameter

[copper valve]

Wat

😮

[dark sparrow]

AOB is isosceles

[copper valve]

ya

[dark sparrow]

ye so

[copper valve]

i see the 2 theta but hows that the same shape ;o

[dark sparrow]

well i'm about to show you how to reduce the general case to this one

[upper karma]

^

[copper valve]

OK

[dark sparrow]

the red line here is a diameter

this is what you can do if your 1θ angle contains the center

[copper valve]

are u drawing this now?

[dark sparrow]

basically you split it up into a sum of two different angles

yes i am

[copper valve]

😮 !!

[dark sparrow]

and this is what you can do if your thing doesn't contain the center

BAC = BAD - CAD

BOC = BOD - COD = 2(BAD - CAD) = 2BAC

[upper karma]

makes is sense

[copper valve]

O_O

no im blown away

im trying to follow

[tropic stirrup]

That's called 중심각과 원주각의 관계 here :p

[copper valve]

how is BOC = 2(BAD-CAD)

[tropic stirrup]

BOC = BOD - COD

BOD = BAO + ABO = 2BAD, COD = CAO + ACO = 2CAD

BOC = BOC - COD = 2BAD - 2CAD = 2(BAD - CAD) = 2BAC

[copper valve]

how is BOD = BAO + ABO

O_O

[dark sparrow]

here, i think this might be easier to grasp

[copper valve]

oh right

ABO is isosceles

and angles of triangle add to 2pi

[dark sparrow]

1π

[copper valve]

woops

then

[upper karma]

in rad?

[dark sparrow]

ofc

[copper valve]

AOB=π-2(θ+φ)

[tropic stirrup]

squints

[copper valve]

then BOD = π-(π-2(θ+φ))=2(θ+φ)

then u can do the same thing for just theta

wait then how do we go back

[dark sparrow]

define "go back"?

you've got the 2(φ+θ) and 2θ angles

now it's obvious that BOC = 2φ

which is what we were trying to prove in the first place

[copper valve]

maybe im a little lost on how this picture was drawn in the first place 😮

how does this theorem work

we have the quadrilateral to start?

or do we pick 3 points and the center

[dark sparrow]

what quadrilateral

[copper valve]

OABC

[dark sparrow]

we have the points A, B and C

O is the center

[copper valve]

ya

[dark sparrow]

we know that ABC doesn't contain O

because we already covered the cases when it does

and we want to show BOC = 2BAC

[copper valve]

ohh okay

[tropic stirrup]

Hey woog

[copper valve]

hello!

[upper karma]

hi!

[tropic stirrup]

familiarize yourself with those x'D

[copper valve]

thank you @dark sparrow !!

[dark sparrow]

@tropic stirrup lol those are good names

[tropic stirrup]

x'D

[dark sparrow]

so jeongri is the word for theorem

[tropic stirrup]

mhm

[upper karma]

Triangles in butterfly theorem must be proportional right?

[dark sparrow]

no

[copper valve]

just has to be a butterfly

[upper karma]

so it can be completely different triangle?

[tropic stirrup]

mhm

[copper valve]

hey that makes sense

cause of intersecting line

those missing angles e = f

[upper karma]

Flag one is really ez

anyone knows that

[copper valve]

oy

[tropic stirrup]

stares at woog

ehem

[upper karma]

because it's

180-c

which is

a+b

[copper valve]

im slow ok T.T

[upper karma]

Because a+b+c

[tropic stirrup]

Try and prove the star theorem