geometry-and-trigonometry

[brisk fog]

Tysmm!! I’ll try that out rn

[minor heron]

glgl!

[wanton hawk]

Why did bro gay react 😭

[tiny acorn]

@languid cedar Explain the 🏳️‍🌈 .

This seems totally unrelated

[languid cedar]

Oh

Oops

Lol

I must have double tapped it while looking through channels

[tiny acorn]

Please stop

[umbral raven]

what the fuck is this bro

[mild prism]

a triangle, a „Trapez“ (german), a thing and a sextagon I think

[proper otter]

well let's see, a triangle (3 sides) has no diagonal, a quadrilateral (4 sides) has 1 diagonal, a pentagon (5 sides) has 2 diagonals, and a hexagon (6 sides) has 3 diagonals

based on this pattern, how many diagonals do you think a heptagon (7 sides) has?

what about 8-gon, 100-gons, n-gons?

[umbral raven]

4

[proper otter]

yeah

[proper otter]

what about these?

[umbral raven]

sides - 4

just not sure this

i quit

[silent plank]

make a structured table with the info mentioned above
sides diagonals
3 ?
4 ?
etc

should make it easier to see the pattern

[loud moat]

I understand how to use trig functions like sine and stuff

But like what js that doing to the number

Like when I do sine of a degree angle what is happening to that number

[tiny acorn]

this

[slim plinth]

Yay finally

I got 102 on my bearing quest

[slim plinth]

I’m finally learning how to graph sine and cosine

[languid cedar]

You did it

You're officially the best

[slim plinth]

We’re u the one who needs help on that

[languid cedar]

What

No I'm way past that

[slim plinth]

I think of wrong person

[pure reef]

bro i am so cooked

i have a math exam and the questions are only gonna be about geometry

i SUCK at geometry💔💔

[shrewd quiver]

5 + 6 = 11

[winged oyster]

area of a square is x²

[slim plinth]

What what tan x looks like

[slim plinth]

Is it take sin x / cos x

[burnt hill]

note when u do this

what can the denominator not be equal to

[slim plinth]

0

[slim plinth]

Would that be VA

[burnt hill]

yes vertical asymptotes when cosx = 0

[burnt hill]

yea basically

and u can transform this ofc however u want

[subtle glacier]

It goes vertically.

[slim plinth]

I wonder how can i graph quarter period

[slim plinth]

I think the pi/2 is the asymptote

[minor heron]

yes, every pi away from pi/2

[slim plinth]

When I checked with desmos

[minor heron]

as such

[slim plinth]

I don’t get the “k”

[minor heron]

k is an element of the integers

the asymptotes are periodic

every pi

basically k is just a letter, can be n or others too

the middle symbol is notation for "is an element of"

and the z looking letter represents the set of integers (eg: -1, 9, 0, 5, 13, and such)

[slim plinth]

Okay

[slim plinth]

What happens if i get sin(x-pi)

[minor heron]

i dont understand what this means

[slim plinth]

I learned their general form of y=a*sin/cos x

[minor heron]

u mean for like tangent?

tangent is sin/cosx i mean i guess u could include a though that would make it not the parent function

[slim plinth]

anyway can u explain what’s this mean

My teacher said “first multiply then add”

[minor heron]

ur shifting the parent function

like

ssay you have at pi/2

2sin(pi/2)+3

sin(pi/2)=1

2(1)+3

you apply the vertical dilation before the verticcal shift

idk we never did it step by step in my class but i assume thats what this means

i mean i jus think the midline is at 3 and it goes 2 up and 2 below that number

and it should follow the same wave pattern as parent sine function because no period changes

[gloomy sierra]

How do people even calculate sin by hand that sounds super cool

[queen juniper]

usually it's memorization for specific angles or taylor approximations

[hasty stump]

memorising

[zinc jungle]

There’s like a unit circle

Just go memorize it

It gives all trig functions and their inverses

[slim plinth]

Coordinate
(Cos x, sin x)

[zinc jungle]

ye and uhh it applies for every fu nction if you know the correlation between them

wait thats a weird way to word it

mb

[minor heron]

also addition, subtraction, and double angle formulas for the non calculus ways

[zinc jungle]

interesting, I forgot about the double angle formulas

[minor heron]

ye... i barely remember them but i gotta study them cs i got a final tmrw

[zinc jungle]

ohh

gl!

[minor heron]

ty

it shoulddd be light

mcq and then two frq's tues

then two frq on wednesday (short period), then more mcq on friday

[slim plinth]

Anyway where would frequency appear on sine function and cosine function

[west narwhal]

If you have an equation like $y=Asin(Bx-C)+D,$ then the period is $\frac{2\pi}{|B|}.$

[west narwhal]

It's the same for cosine as well

[slim plinth]

I did is y=a*sin bx

Is it then 2pi/B

[somber coyote]

OGMath_789

[west narwhal]

yes

[slim plinth]

Then I saw the pattern 0,1,0,-1,0

Is that correct

[west narwhal]

so what's the function

[slim plinth]

y= sin x

Then I found a function y=sin x -4

[west narwhal]

can you clarify what you mean by finding patterns? do you mean ordered points?

[west narwhal]

ok, so the period in this case would still be $2\pi.$

[somber coyote]

OGMath_789

[slim plinth]

It’s for the quadrantal angles

0, pi/2, pi, 3pi/2, and 2pi

Like this

Then I found this

[slim plinth]

Btw I forgot “n” in pattern

[west narwhal]

yep the table of values for cos x is right

[slim plinth]

Thanks

[slim plinth]

Anyways

[slim plinth]

Their midline is -4

[west narwhal]

Also for this one, you can simply draw the graph of y=sin(x) and shift it 4 units down

[slim plinth]

Okay

I think this unit is easy

Not gonna lie

[west narwhal]

yea trig is not that hard

[slim plinth]

Btw last unit on bearings I got 102

I was shocked

[west narwhal]

ohh

what was it out of

[minor heron]

nice

[slim plinth]

60

[minor heron]

ye graphing trig is pretty straightfoward, find characteristics and such

[slim plinth]

Don’t laugh at my artwork

[slim plinth]

They also have bonus 2 points

[west narwhal]

it's okay, don't worry, good luck on your next tests!

[slim plinth]

I got 0.5 off out of 60

[slim plinth]

It’s out of 60 btw

[minor heron]

sine should start at the midline

[slim plinth]

Yea

[minor heron]

oh wait i read it wrong nvm

looks right

[slim plinth]

Like this

amplitude is 1, period is 2pi, and quarter point is pi/2

[minor heron]

*amplitude is 1

[slim plinth]

Is that correct

[minor heron]

amplitude cannot be 0

[slim plinth]

Or that’s a straight line

[minor heron]

my teacher never made us find "quarter points" but period is right i assume quarter point is too

[slim plinth]

It’s something over 4

The period/4

[minor heron]

ye i figured

its just a weird characteristic to find if ur alr getting period

[slim plinth]

Yea

How does a quarter point help me with graphing

[minor heron]

i assume its meant to help u space out the points where sine hits midline, max, min

[slim plinth]

Amp is just getting wider or narrower

Is that right

[minor heron]

ummm

wdym by wider or narrower

[slim plinth]

Like getting spaced outside or closed together

[minor heron]

do you mean horizontally or vertically

[slim plinth]

Oh it’s a dilation

[slim plinth]

Yes

[minor heron]

im asking a this or that question

[slim plinth]

Vertically

[minor heron]

is it a horizontal or vertical dilation

[minor heron]

right

[slim plinth]

It’s vertical dilation

Will the space and spaced out or will it spaced in

Now i see this

a=2

[minor heron]

mmhm

[slim plinth]

Goes up 3 units

[minor heron]

right

[slim plinth]

Midline is y=3

[minor heron]

no

thats the function

[slim plinth]

I mean y=3

[minor heron]

right

[slim plinth]

There u go

[minor heron]

mhm

[slim plinth]

My teacher said cosine graph is like a cup

[minor heron]

uhh kinda igs

[slim plinth]

What’s igs

[minor heron]

i guess

i mean its kinda like a u

[slim plinth]

Okay

If i get this in one day

I would be good for the whole unit

Is that correct

It would be piece of cake

[minor heron]

idk

depends whats in the unit

[slim plinth]

It’s all graphing sine and cosine

I wonder if there is a sine cosine word problem

[minor heron]

we learned trig modeling

its not that bad

[slim plinth]

Is it SOHCAHTOA

[minor heron]

no

[slim plinth]

But in a graph

[minor heron]

no

[slim plinth]

What’s that about

[minor heron]

u can search up

frq 3 ap precalc for examples

eg: a ferris wheel goes up and down

and moves closer and away rom a fixed point

or somethin

[slim plinth]

Omg that’s familiar

What I’m doing

Is it take the info that’s given and graph them

[minor heron]

we did this one on a worksheet

[slim plinth]

Using sin and cos

Yea

That’s familiar

But in my case the equation is given and i just need to graph it

[minor heron]

Question 1 of the FRQ is worth 2 points, provide the x and y values of F G H J K which make up one cycle of the graph

Question 2 of the FRQ is worth 2 points, provide the values of a b c and d in the form asin(b(x+c))+d or the same thing with cosine

Question 3 and 4 are one point each, where you analyze an interval between two of the points say G and H (positive/neg, inc/dec make four options) then analyze the same interval's rate of change (inc/dec using concavity)

So that's the trig modeling we learned

[slim plinth]

Ok

I showed u what’s it about right

U can use my notes

If u want

[minor heron]

nah i should be fine

we're done with our curicullum

[slim plinth]

Okay

[minor heron]

have been for a week

[slim plinth]

Okay

[minor heron]

just got finals and ap exam left

[slim plinth]

Have u done bearings

[minor heron]

no

we did not learn those

[slim plinth]

Okay

Trig modeling in my works is

Take a Ferris wheel and make them into waves and explain them

[minor heron]

mm

[slim plinth]

Like this

[slim plinth]

What do u think what would this look like

[minor heron]

period pi

midline 4

up to 7, down to 1

[slim plinth]

7?

[minor heron]

unsure what they mean by graph in seconds because the period is not a integer

[slim plinth]

How would the b in y=a*sin(bx)

[slim plinth]

Okay

[minor heron]

2pi/b

2pi/2=pi

[slim plinth]

Does it shrink

[minor heron]

ye

[slim plinth]

Like b

In y=3sin(2x)

[minor heron]

rough sketch

[minor heron]

ye 2 is 'B"

[slim plinth]

Oh it gets wider

[minor heron]

no

the period is pi

it gets compressed

[slim plinth]

Okay

My idea was set the inside equals to the y value on the unit circle

Like i had the pattern 0,1,0,-1,0

Then is it
0, 1/2, 0, -1/2, 0

[minor heron]

no

its on the INSIDE

affects the x values

not the y

[slim plinth]

Do we just leave it alone

[minor heron]

where you had (pi/2, 1) before, you now have (pi/4,1)

because when u plug in sin(pi/4*2) u get sin(pi/2)

[slim plinth]

Okay

[slim plinth]

Like i have 0, pi/2, pi, 3pi/2, and 2pi

Would it be 0, pi/4, 2pi, 3pi, and 4pi?

[minor heron]

im not sure how you got the last values

[slim plinth]

Oh divide by 2

[minor heron]

pi/4, pi/2, 3pi/4, pi are the x values

[slim plinth]

Ohhh

I have 4, 7, 4, 1, 4

4 is the midline

[minor heron]

ye

[slim plinth]

Yay

Is it get x/2 then it’s the opposite of shrinking

[slim plinth]

I wonder what will happen if we get y= sin(-2x)

Would we move the - out making it y=-sin(2x)

[minor heron]

reflect across y axis

[minor heron]

absolutely not-

DONT overcomplicate trig functions

[slim plinth]

Ok

[minor heron]

this would be exactly the same as y=f(-x)

[slim plinth]

Ohh

[minor heron]

the effect on the x valeus of f(2x) is the same as sin(2x)

etc

[slim plinth]

Ik y=sin(x-pi) means plot it on (pi,0)

Then start there

[minor heron]

mmhm

thats what we call a period shift

[exotic chasm]

the elegant (but useless) formula of a radiant sector (area and perimeter)

https://media.discordapp.net/attachments/1397581939501961357/1501101142258749450/588143980747685889.png?ex=69fad8e1&is=69f98761&hm=be9780af47cc486eb27e4befee58d5cd7cbccd7199adf48adfe602de4858db5b&

[manic shoal]

Guys i need help for this question, tysm

[somber coyote]

tsuitachi (tuitati)

[exotic chasm]

1. mark G at BC so DG perpendicular with BC, or use the above formula
2. find angle DCG such that ang. DCG=BCD=CBF
3. find angle CBF from BCF triangle
4. find angle EBF (that is just 90deg-CBF)
5. find EF via cosine law (with length BE and length BF)

[slim plinth]

Hey for cosine graph where would the period be

Would it be the inside of y=a*cos(bx)

[exotic yarrow]

The period of $\cos(x)$ is $2\pi$, so the period of $\cos(bx)$ is $\frac{2\pi}{\left \lvert b \right \rvert}$. $a$ does not contribute to the period since it only dictates the vertical stretch/compression factor.

[somber coyote]

Civil Service Pigeon

[slim plinth]

If I get period pi/2

Would it be 2pi/4

Then b=4

[exotic yarrow]

or -4. Though it doesn't really matter since the cosine function is even.

[slim plinth]

I made this equation
y=3 cos (4x) -1

amplitude = 3
period = pi/2
midline: y=-1

Would that pass (0,2)

[exotic yarrow]

yes

,w y=3cos(4x)-1, x=0

[somber coyote]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[exotic yarrow]

also the midline is a line, so saying "-1" in isolation does not make sense

[slim plinth]

Thanks

Okay

[slim plinth]

So if the inside is 4

With the radians everything multiplies by 1/4

With whole it’s by 4

[delicate grotto]

hi guys
im having some trouble with geometry
i have 4 shapes rectangle square rhombus and parallelogram
there are some theorems regarding provingthat diagonalys bisect each other, bisect each other at right angles
proving opposite sides and angles are equal/parallel
and im kinda having trouble understanding them
chatgpt doesnt rlly help
i js want some guidance 🙏

[minor heron]

well 15x+30=120

15x=90

x=6

pretty ez like 3 lines of work

[slim plinth]

Is the triangle equals to 180

So 180-120=60

Inside is 60 degrees

[minor heron]

well also

120 is the

exterior angle

so 5x+10+10+20=120

[slim plinth]

5x+10+10x+20+60=180

[minor heron]

without neeing to do all of that

[slim plinth]

10?

[minor heron]

*10x

5x+10+10x+20=120, 15x+30=120 first line of working

[slim plinth]

Oh right

What theorem is that

Exterior angle theorem

[minor heron]

mmhm

[slim plinth]

So it’s

120=(10x+20)+(5x+10)

Combined liked terms

120=15x+30
120=15(x+2)
8=x+2
6=x

[minor heron]

yes

you dont need to factor

u can do 15x=90 x=6

same result

[slim plinth]

I missed doing geometry

[slim plinth]

The last one i did used traversal rule

[minor heron]

is really most of the work

[slim plinth]

With bearing

True

I remembered supplements shaped like “c”

[slim plinth]

What was the one that looks like “F”

[minor heron]

i have no idea

what a supplement is

[slim plinth]

Like this ignore the watermark

[minor heron]

um

[slim plinth]

Look upside down

It’s a “F” shape

But I forgot what’s the theorem called

[minor heron]

oh

that was a terrible way to descript it

[slim plinth]

What should i say next time

[minor heron]

idk its not really a shape

[slim plinth]

Like transversal looks like a “z”

[minor heron]

it is this theorem

[slim plinth]

Yea yea yea

[minor heron]

might not be able to see if its dark mode

[slim plinth]

So it’s angle 1 = angle 2

[minor heron]

corresponding angles theorem

1=3=5=7

in the other image

[slim plinth]

6x+10=5x+20
x=10

Easy

10 degrees

That’s an acute i think

Or obtuse angle

Ik it’s something less than 90 degrees, 90 degrees, and more than 90 degrees

[minor heron]

accute less than 90

90 is right

moer than 90 is obtuse

[slim plinth]

Okay

[slim plinth]

So that’s an acute angle

[minor heron]

ye

[slim plinth]

Bc it’s 70 degrees

According that that theorem

I can plug x value to angle one or two

It will be the same

[minor heron]

ye

[slim plinth]

I never did this for two years

Since when i was a sophomore

[minor heron]

oh

ic

[gloomy sierra]

Theory would it be possible to find every INTEGER sin value using only sin(1) , sin(89) , the double angle sin rule and this expansion

Oh that didn’t

[white fossil]

Hi everyone

Is there anyone who can solve that

[exotic chasm]

use (1/2)xy=84
a. plug in the x and y as what you got asked for (remember sec=1/cos) and see if final result is 84. point a is independent from point b and c bcos it's just "what if".
b. substitute y as 31-x so you get smth like quadratic roots thing
c. find the 2 quantities in terms of x or y, ig?

[normal saffron]

can someone help 🥹 i can't distinguish the difference between the letters for sin cos tan regardless any triangless

im stuck

[wanton hawk]

Were you taught SOH CAH TOA?

[normal saffron]

yea i got taught that

[normal saffron]

but like im not sure like whats the differnece between those letters and for SIN COS TAN

😭

R or T

[wanton hawk]

Oh!

So R and T are your angles. O means opposite, a means adjacent, h means hypotenuse (side across from the right angle)

Adjacent means the side that’s touching the angle that is NOT the hypotenuse, opposite is the only side that isn’t touching the angle

So for angle R, side length 15 is opposite

For angle T, however, opposite is side 36

Does allat make sense?

[normal saffron]

so based on the position ur standing on the angle it's different right?

liike LOL i can do for R but T wth

[normal saffron]

kind of

[wanton hawk]

Yeah

So for T, the hypotenuse stays the same

What side is touching angle T that isn’t the hypotenuse?

[normal saffron]

HELP WHAT

im trying to roate the paper hella

[wanton hawk]

No need man

Adjacent just means “next to”

[normal saffron]

is it even 15 or 36 im CRINE

[wanton hawk]

Welllll it’s not 39

[wanton hawk]

Two sides are next to T. One is the hypotenuse, the other is your “adjacent”

[normal saffron]

is it 15

help

cus it's next to "T"

💔

[wanton hawk]

Yea it’s 15

That means your opposite is 36

[normal saffron]

wait so like i have to imagine myself standing at that specific angle and mirror the adjacent/opposite/hyp based on the position

😭

[wanton hawk]

If you wanna imagine yourself yea

Hyp is always the same

[normal saffron]

OHHH I GOT IT

okokok

thanks alot gosh

[wanton hawk]

Hyp js means the longest side

[normal saffron]

noted

[wanton hawk]

Yw bro

It’s time for sleep

https://tenor.com/view/kung-fu-panda-kung-fu-kungfupanda-timetogo-imustleaveyou-gif-4308363678620630598

[normal saffron]

me too bro

im so done with trig

nighty

https://cdn.discordapp.com/attachments/1421525270665629890/1449569681940811940/IMG_7987.gif

[left mist]

Uhh can someone help me see if this proof is valid

[exotic yarrow]

This image as a whole is very hard to read, but this quadrilateral is definitely not a parallelogram.

I stopped reading here

[left mist]

Uh I can type it if you want

[left mist]

Uh yeah I meant to say a quadrilateral, a shape with 4 Sid's basically

[left mist]

Let angle ABC be x.
Let angle ADC be y.

Let a line be constructed from point d to b, forming a DB and creating 2 triangles from the quadrilateral.

In triangle ADB, DA isn't equal to AB, AD > AB, so angle ABD > ADB

In triangle CBD, DC isn't equal to BC, DC > BC so angle CBD > CDB

So, both CBD and ABD that make up angle x are greater than in measure angle CDB and ADB which make up y.

x > y #

[exotic yarrow]

looks good to me

[finite nexus]

low cortisol hand writing 😭

[formal bane]

Guys how do you to solve this?

<@&286206848099549185>

Ping me if someone responds

[wanton hawk]

First that isn’t geometry, second read the rules, third read the rules

[formal bane]

Mb I’ll put it in alg, may I ask what I did wrong other than send a question in the wrong topic?

[wanton hawk]

Yeah you’re not supposed to ping helpers unless you have a help channel open

[formal bane]

Oh I’m sorry about that thank you for letting me know

[wraith pilot]

Can someone help me with 14a?

[minor heron]

1/sqrt2 = sqrt2/2... so its asking, what angle outputs a sine value of sqrt2/2?

[wraith pilot]

Pi/4

Is there a way I can do it without using the unit circle

[shy cloud]

it really comes down to just memorization and if u can associate the angle outputs with its respective part

[minor heron]

welll

you could ah

draw a triangle

sine is opposite / hypotenuse

so 1 would be a leg

sqrt2 would be hypotenuse

thru pythag theorem, the other leg is also1

then u could recognize its a 45-45-90 triangle, so theta must be 45deg = pi/4 radians

[winged oyster]

its basically js solving sin(x) = 1/sqrt(2)

thats what an inverse function is

[glad sleet]

I really don't know how many times do I have to repeat this in EVERY channel, but do NOT ping helpers here.

It may be allowed but its not good practise.

[iron violet]

ots just inverse functions, for example if sin 30 equals 1/2 then inverse sin of 1/2 is 30 degrees

[wraith pilot]

Thank u guys

[iron violet]

👍

[grand gate]

well i wanna review geometry once again

[left mist]

is it really that bad😭 cause thats like one of my proofs with hte best handwriting how does my teacher read it😭

[finite nexus]

i mean itd not THAT bad compared to some of the ones ive seen but still, i dont get how teachers read those 😔

[iron violet]

You are doing good. Just improve a bit more so the teacher does not reduce your marks like mine did

[left mist]

frrr

[left mist]

they reduce marks for handwriting??

[iron violet]

mine did idk about yours

[left mist]

I mean, if you do give me time I can write very beutifully

[left mist]

thats crazy

[iron violet]

But you really need to improve your handwriting

[left mist]

well i could try

[tepid charm]

Handwriting is fine tho. imo

(I have seen worse 💀)

[iron violet]

doctor's handwriting?

[tepid charm]

No.
4 AM mathematician handwriting

[left mist]

Genuine flow state

[drifting hedge]

How did my teacher get 4•4•4 can someone explain and where did the root go

[subtle apex]

whats the original problem

[drifting hedge]

The height of a four sided pyramid is 3cm the sharp edges are 5cm find its area

I think I translated it right

[subtle apex]

send the problem in its original form

i dont exactly get what 'sharp edges' mean

[drifting hedge]

I drew it

Here

[rancid flint]

If the interior angles of a triangle ABC satisfy the equality,
sin^2 A + sin^2 B + sin^2 C = 2(cos^2 A + cos^2 B + cos^2 C),
prove that the triangle must have a right angle.

[rancid flint]

Help pls

[wanton hawk]

https://tenor.com/view/brisk-eminem-that-is-pretty-good-gif-3062792511368974134

[exotic yarrow]

Reposted here: #help-12 message

[stuck creek]

Any tips on how to do this?

[exotic yarrow]

In the future, please show what you've done so far when asking for help along with any other relevant context — it gives us more to work with and saves time from explaining things unnecessarily. \
\begin{parts}
\part Note that $|z|$ represents the distance from a point to the origin in the complex plane. So, $1 \leq |z| \leq 2$ represents all points whose distance from the origin is between $1$ and $2$ (both inclusive). This means you should be shading two solid concentric circles (why?), I'll let you fill in the rest yourself.
\part I'd convert this to Cartesian first. Letting $z=x+iy$ (for $x$, $y \in \mathbb{R}$) yields
$$\sqrt{x^2+y^2}=2\sqrt{(x-3)^2+y^2}.$$
Some algebra bashing should again yield the equation of a circle.
\end{parts}

texit?

[somber coyote]

Civil Service Pigeon

[exotic yarrow]

welp a bit delayed but we got there eventually

[left wren]

in terms of math and trig in general does anyone have comprehensive tips or strategies to study math because the approach is different than how you would study for other classes. if so please help me because i’m struggling learning trig identities and also not reaching the mastery i want in my current trig class. thank you!

[hasty stump]

understand the concept

if in doubt, ask

do you have any worksheets with you at the moment?

[left wren]

I do yes

[exotic chasm]

are geometry formulæ, especially for compound shapes, bound to look not so simple?

[left wren]

For the trig identities now, I memorized all the formulas and know I need more practice problem repping to build the pattern recognition. But in general trig like cos sin tan graphing, unit circle stuff, i want complete mastery but I’m still getting B+ on tests after studying 7 days before a test and it’s frustrating

[exotic chasm]

like, look at circle sector's perimeter\
$P=(\theta+2)r$

[somber coyote]

tsuitachi (tuitati)

[exotic yarrow]

Reposted here: #help-7｜zen1thxyz message

[solid pivot]

guys please help

im stuck on math rn

for some reason i cant figure out how to find the area of a pentagon

by making the small triangles

[solid pivot]

nvm

[solid pivot]

guys wish me luck

i give up on circles

ill figure it out tmr pre test

or cheat somehow

idk

i dont like to cheat but id rather cheat than get a bad grade

gn guys

im going to bed

[muted mango]

@rancid flint , this is what i did

and obviously there are multiple ways to solve this

proof by contradiction can also be thought of here ig

[acoustic stirrup]

Snke game

[rancid flint]

Ok, thanks for helping

[visual snow]

Lmaooo

[exotic chasm]

are numbers eligible in "classical" geometry just π, positive and negative sqrt(Q), and combination of these under +,-,×,÷?

[exotic yarrow]

In compass-and-straightedge compass geometry, the valid lengths are called constructible numbers. It can be shown that these are the numbers formed strting from integers using addition/subtraction/multiplication/division/extraction of nested square roots. So numbers like sqrt(3+sqrt(5)) are constructible. Also, pi is not constructible (note this relates to why squaring the circle is considered impossible).

[exotic chasm]

oh arcs don't count huh

as in, arc length, or in an extent, circumference

[grave pond]

I think it's a bit more subtle than that, because even if we cannot construct a length of pi, geometry is still supposed to work if we're given such a length by an oracle. So it's not really a strict dichotomy between "valid" and "invaid" numbers.

In particular, if we're given a length of 2pi, it ought to be geometrically true that the sum of sides in any incribed polygon in the circle is smaller than that, and the total length of any curcumscribed polygon is longer. So in that sense the property "this line segment has length 2pi" has geometric content -- even if the axioms don't allow us to prove that something with the property exists, it still might.

[willow kiln]

sin^2 is the derivative

[twin idol]

phobos

[muted mango]

there are no derivatives here

[slim plinth]

What about sin = cos

[regal kraken]

I hate to ask this but does anyone have a study guide or a website that has all the terms and stuff for high school geometry? I want to study for finals but I kind of goofed off for the first half of the year and my book is useless without a teacher in the room, anything is appreciated

[slim plinth]

Khan acedemy

[marsh marlin]

What grade are you

[regal kraken]

10th

[marsh marlin]

You can chuck all your lessons into notebook LM

It will generate notes

[regal kraken]

will do

[regal kraken]

interesting

[orchid cobalt]

I've been somewhat nerd-sniped by the following seemingly basic problem recently and I can't tell whether I'm just bad at geometry or if it's much harder than it looks:

Suppose you've got three interior-disjoint unit squares on the plane (not necessarily axis aligned). What is the minimum perimeter of the triangle formed by their enters?

If the squares are axis aligned (or just all share the same rotation) the answer is trivially 1 + sqrt(5). (Achieved by putting two squares touching eachother and stacking the third symmetrically between them on top).

The configuration where two squares have one corner touching and the the other is shoved in between them with a corner poking between is always strictly worse than this.

But I can't seem to figure out a good argument that the general case should always be >= 1 + sqrt(5). I assume there's some neat argument about how you can always replace a configuration with a better one if it doesn't look like this, but I'm not seeing it.

[swift sleet]

https://www.desmos.com/calculator/qvlt7xzjw7 what's up! I made geometric sin(sin(a)) in desmos.

I basically just took sin(a) from the unit circle then put that length as an arc on the circle so that I can turn it into an angle using radians because sin expects an angle.

It's a very simple idea but I can't find anything on it

[torn gulch]

find the parametrization of y=sin(sinx) frfr

wow sin(sinx) looks really close to sinx

also kinda the reason we do sintheta~=theta in calculations for the period

of a simpel pendulum

[tall pasture]

Can someone tell me what does sin= what does tan= and what does cos=

[silent plank]

sin,cos,tan are functions

[fluid arrow]

You mean sin equal perp over hyp?

[fluid arrow]

Oh so these r jst different terms

The way i learnt what these equals is by memorizing" some people have curly brown hair that play basket ball"

Take the first letter of those words from this sentence

Sin equals Perp /hyp
Cos equals Base/Hyp
Tan equals perp /Base

Btw perpendicular(opp) and base (adj)

[silent plank]

most places use
soh cah toa

[fluid arrow]

Ye that works too

[marsh marlin]

yup

soh cah toa most easy

[fluid arrow]

Ig most countries have their own ways

I heard sm indian guy had another acronym as well

I forgot that

[marsh marlin]

acronyms are pure memorization

[tall pasture]

Thx

[modest violet]

hey

is 4 weeks enough to learn trigo foundation

4 hours per day

[silent plank]

yes

[fluid arrow]

Yes

[silent plank]

More than enough

[swift sleet]

I haven't really looked into pendulums, I have done very little physics so far. I'm going to do physics for my leaving cert though.

Leaving cert is like the 10th-12th grade equivalent to other countries in Ireland

[grim pewter]

in australia we use SOH CAH TOA
where
sin = opp/hyp
cos = adj/hyp
tan = opp/adj

which makes sense cuz tan = sin/cos

[swift sleet]

https://www.desmos.com/calculator/mvzq9yzdmw you can repeat it too

I just had a thought, what would sin(sin(sin(sin...(1))) approach? Does it approach 0???

[upper echo]

yep, it approaches 0 as sqrt(3/n), where n is a number of iterations

[swift sleet]

?

They don't match up

How did you get that?

Or did I misunderstand something

[grave pond]

They look like they might converge asymptotically, though.
I don't know whether it's actually true, but plotting just the five first points won't be able to show that is isn't.

[swift sleet]

Oh I guess I misunderstood something.

I thought he meant f(x)=sin(f(x-1)) f(x)=√(3/x)

[upper echo]

It's asymptotics, namely, if a(n+1)=sin(a(n)), then a(n)/sqrt(3/n) -> 1

[swift sleet]

But I guess that doesn't make sense because that would mean you could express sin using simple operations

[upper echo]

you can find proof here https://math.stackexchange.com/questions/4129806/limit-of-infinite-composition-of-sinx

[grave pond]

I tried it out numerically (up to 20,000 iterations) and it does seem to approach sqrt(3/n) asymptotically ... no matter where between 0 and pi I start the iteration.

[upper echo]

you probably did something wrong.

[swift sleet]

What is asymptotically? Is it like they never cross as it goes down the asymptote?

[upper echo]

it's this #geometry-and-trigonometry message

[gilded ridge]

it approaches 0 regardless of input
because fixed points

[swift sleet]

Where did you get √(3/n) ?

[grave pond]

Um, why? Starting the iteration at a different place would just shift the iterated sequence a constant amount to the left or right, so it's not unreasonable that this would not change the asymptotics, especially since the logarithmic derivative of sqrt(3/x) goes to 0.

[upper echo]

I've given the link to the proof

[gilded ridge]

say
the equation is
sin(sin(sin....()))))))...)))
now
as
sin(sin(sin....()))))))...)))=sin(sin(sin....()))))))...)))
and since we repeat it infinitely let y=sin(sin(sin....()))))))...)))
so
we see
sin(y)=y
solving this we get y=0
so th einfinite sines go to 0

oh is it solved

im stupid

[upper echo]

no, this doesn't prrove that it is exactly zero

[gilded ridge]

true yeas

[swift sleet]

I'm not really educated enough to even really follow the proof

[grave pond]

(I see the same asymptotics numerically by iterating x-x³/6 instead of sine, so it's not really a trigonometric property).

[swift sleet]

So I guess I'll have to leave this be

[grave pond]

Experimentally it looks like iterating x-ax³+o(x³) always ends up going like sqrt(1/(2an)) -- for starting points that end up converging to 0 from above at all.

[marsh marlin]

Troposphere

Are you an imo participant

[grave pond]

This is a correct argument that if the iteration converges to anything, the limit must be 0. It doesn't in and of itself show that it does converge.

[gilded ridge]

yes , my apologies

im js leaning ts stuff

[grave pond]

Not something you need to apologize for.

[grave pond]

No.

[marsh marlin]

Ever close to being one?

[grave pond]

No, didn't do competitive math when I was of HS age.

[swift sleet]

Why is this?

[gilded ridge]

because

[gilded ridge]

this

id say

[swift sleet]

Oohh

[gilded ridge]

because the substitution assumes the limit convergess to somme y

what if its infinity thats the problem

[swift sleet]

I've seen those cool substitutions like the x=√(2√(2√...)) x=√(2x) but didn't know there was a catch

[swift sleet]

That makes sense

[gilded ridge]

yep theres always a catch

[grave pond]

Depending on which function you're iterating, it's also possible that it neither converges nor escapes to infinity. A famous example is iterating 4x(1-x) from a point between 0 and 1. Most starting points in that interval lead to a sequence that keeps jumping around chaotically in the unit interval.

[gilded ridge]

oh yeah true
but say x=0

right

most
not al

[swift sleet]

Wait what??? Could you expand on that expression a bit

[grave pond]

There are infinitely many starting points where the sequence ends up at either 0 or 3/4 exactly (and then stays there for ever), but there are even more infinitely many starting points that don't.

[gilded ridge]

also there are unstable fixed points right like x=1
for x^2?

[swift sleet]

What is an unstable fixed point?

[fluid arrow]

Ye same thing tho

[fluid arrow]

I use these terms when necessary otherwise we jst use perp base hyp

[gilded ridge]

start from x=0.999
we repeatedly apply x^2 to it we get
that 0.999^k
which decays to 0
if we say x=1.001
we get 1.001^n
which goes to infinity
so anything not like +1 of -1 blows up to infinity or goes to 0

thats unstable

ig

mr trop might have a real explanation

[swift sleet]

Wouldn't that just mean it's a fixed point?

[gilded ridge]

its fixed but like anything even close to it goes away

[grave pond]

It's one of the standard examples in chaos theory. The function 4x(1-x) itself is a parabola with x-intercepts at (0,0) and (1,0) and vertex at (½,1), so it maps [0,1] surjectively to itself.

[upper socket]

@hollow hound

[swift sleet]

Wouldn't this be true for most fixed points?

(sorry if its a stupid question)

[gilded ridge]

well i never said anything about number of fixed points that do this and no of em that do that

[gilded ridge]

also i dont think so

[grave pond]

For smooth functions is depends on the absolute value of the derivative at the fixed point. If it's less than 1 it is stable; if it's more than 1 it is unstable.

(And if the derivative is ±1 a more careful analysis is needed. It might be stable but the convergence will be slow, as in the case of the sine).

[gilded ridge]

dont we check the modulus of the derivative

also im sorry but arent f'=1 like neutral points?

[grave pond]

For example for sin(x) like we started with, the fixed point has f'(x)=1 -- it still attacts, but slowly.

[gilded ridge]

oh

[grave pond]

On the other hand tan(x) has the same fixed point with the same derivative, but it is unstable.

[gilded ridge]

i see

[exotic chasm]

2d shape nomenclature discussions go here also?

[exotic chasm]

or is it actually a kinda useless topic for #geometry-and-trigonometry

[exotic chasm]

and 3d also btw

[upper echo]

I meant that you first have to prove that the limit exist. But in this case it is easy. Since iterated sines make a decreasing sequence sin(a)<a and the sequence is bounded by 0 from below (in case you start from some a0, for which sin(a0)>=0), then it has a limit. And for that limit a, you should have sin(a)=a, which means a=0.

[upper echo]

I think this code in Python shows fairly well that iterated sines are asymptotically equivalent to sqrt(3/n), as it gives 0.999233170242103
from math import sqrt, sin x = 3 N = 100_000 for n in range(1,N+1): x = sin(x) print(x/sqrt(3/N))

[grave pond]

So we're in agreement?

[upper echo]

oh, yes. I first read your message as '...it doesn't seem to approach' :)) Sorry.

[exotic yarrow]

<@&268886789983436800>

[swift sleet]

<@&268886789983436800>

[swift sleet]

I was playing around with kth iteration of f(x) and changing around the values when I found this interesting thing that converges pretty quick to some value https://www.desmos.com/calculator/p7qk0udoqf

Another number pops up if you reverse the order of cos and sin

Can these numbers be expressed using some constants like pi I wonder

[grave pond]

I think that's unlikely.

Though for real fast convergence, try iterating x -> x + cos(x)

[long geyser]

I'm trying to find trig identities on my own, can someone help me understand if these are correct? I was looking at a unit circle that I made to try and see the relations between these two basic trigonometric functions.

[grave pond]

Next to last seems to be a typo; the others check out as far as I can se.
Congrats on developing some intuition instead of just taking the identities on faith!

Whops also the cos(t) = -cos(-t) must be a typo. No, that was just Discord cropping it badly.

[long geyser]

Thank you

[long geyser]

sin(45)=sin(135) though, no?

And sin(-45)=sin(-135)

[grave pond]

Yeah, but that's a pretty special case.
You don't have sin(0°) = sin(90°), for example.

[long geyser]

Ohhhh, thanks!

Yeah my mistake, any one counterexample means that it's not an identity

I guess I got lucky for the other ones then because I was only using 45 for reference?

Tysm

[long geyser]

These relations are so beautiful to me

[grave pond]

yeah, 45° is an unlucky choice of main example because sin(45°)=cos(45°).

[long geyser]

Yep

[long geyser]

Are there plenty more btw if you don't mind me asking

I tried to look at the pinned images for identities similar to the ones I've been finding but there are only a few in the image that look similar to this and some of the ones I found aren't in the images

Also I think that the ones I found can also be true for different multiplicities of for example pi right?

like cos(theta)=-cos(theta+pi*n)?

[long geyser]

That was indeed the goal of the instructor on Khan Academy that led me to attempting this to begin with! I'm really glad I learned a lot and that I didn't rush moving onto the next lessons without having the intuition that I have now.

[grave pond]

That is only true when n is odd.

[long geyser]

Right!!

I didn't realize that

so maybe 3n?

or a sidenote saying only when n is odd when writing the equation?

[grave pond]

What what one usually does is write an arbitrary odd number as something like "2n+1", so we can say
$$\cos(\theta) = -\cos(\theta+(2n+1)\pi)$$

[somber coyote]

Troposphere

[long geyser]

Oh, ok! that makes sense

[grave pond]

Typically one wouldn't bother with writing down all of those variants, since they can be derived as needed by combining one of your base identities with cos(x) = cos(x+k·2pi) and/or sin(x) = sin(x+k·2pi).
But it's definitely good for learning to have thought of them explicitly.

[long geyser]

Thanks!

[grave pond]

One can also be super-fancy and write $$\cos(\theta+n\pi) = (-1)^n \cos(\theta).$$
(But that's more of a party trick, though one can probably think up some cases where it would be useful).

[somber coyote]

Troposphere

[long geyser]

Ooo interesting!

[long geyser]

So the reason I don't see some of the ones I discovered in the pinned images in this channel is because you can derive them when needed and the main ones are more important?

like this

ah in the image it says "relatively small list of trigonometric identities," I don't assume that a student would be looking for the ones I discovered as opposed to these ones which are in normal curriculum

[grave pond]

Yeah, there's an almost infinite supply of variants, and it only makes sense to remember so many of them.
That doesn't mean your time coming up with the variants is lost; that's exactly the kind of practice that will enable you to think them up again later.

[long geyser]

Omg there are so many here, and I think I saw some of the ones that I found https://en.wikipedia.org/wiki/List_of_trigonometric_identities

[long geyser]

Tysm! I see

that's wonderful

[atomic crypt]

hi

[minor heron]

hi

[fallow elk]

What is sin and cos

Math vocabulary hurts my brain sometimes

And right now this is one of those times

[grave pond]

If it hurts your brain to see people talking about concepts you haven't yet been introduced to, math might not be an ideal hobby for you.

[fallow elk]

Oh maybe ur right

Bye

[fallow elk]

(its a joke)

[minor heron]

so sine and cosine are just functions

specifically, periodic ones, which means their values repeat

this can be used, most typically in triangles, to look at ratios

[grave pond]

(as opposed to capricious and arbitrary functions)

[minor heron]

w-what are those e.e

[grave pond]

the ones that aren't just.

[minor heron]

all ik are transcedental functions, algebraic functions, and periodic..

[minor heron]

so, say you have a triangle. specifically, a right triangle.

[fallow elk]

Alr

[minor heron]

with sides of length a and b (legs), c (hypotenuse), and angles D and E

[fallow elk]

I know about hypotenuse

[minor heron]

now, say you have the measurement of angle D

the side a is "adjacent" to it, side b is "opposite" to it, and the hypotenuse is just... the hypotenuse

so, the sine ratio tells us that sine(D) will be the opposite side over the hypotenuse side

or, essentially, b/c

and lets say we know the hypotenuse is 2

so sin(D)=b/2

now, we can rearrange this to 2sin(D)=b

we could then plug this in to a calculator to find the side length b

for cosine, you have the similar ratio adjacent/hypotenuse

[fallow elk]

By 2sin you mean as 2 x sin correct?

[minor heron]

2 times sin(D)

[fallow elk]

Ok

Just making sure

[minor heron]

so, sine and cosine basically allow us to work with ratios of sides and angles of right triangles (and non right, but i don't think its appropriate to explain the unit circle to you at your level of geometry that i've gleaned)

[fallow elk]

Ok

Thanks

[fallow elk]

Oh I think I get it now.
If a triangle has 3 sides, 4cm 3cm and 5cm. Like in your example, let’s say there is also an angle D and E.
Let’s say this:
3cm is the opposite
4cm is the adjacent
5cm is the hypotenuse

Sin is going to be 0.6 correct?

[minor heron]

right!

[fallow elk]

Cos is 0.8 as well im pretty sure

[minor heron]

yup

[fallow elk]

https://tenor.com/view/i-understand-it-now-ok-i-understand-it-now-i-understand-it-gurm-bear-gif-4859748791707698675

[minor heron]

Do keep in mind that with a different angle, the sides would switch relationships (with angle E, the opposite side becomes adjacent and vice versa)

[fallow elk]

Yeah I now that

Lowk never been this invested in math

I’ve always been more a history person

But no need for Americas got talent sad backstorys

[minor heron]

mm ic... not for everyone

[abstract rain]

I discovered something while drawing a sphere.

You can represent a sinusoidal wave as the x-axis. Cosinusoidal wave as the y-axis and Tangential wave as the z-axis.

This can be used to split the EM wave into two waves and show the EM wave as an x-axis wave and a y-axis wave.

E(t) becomes a y-axis wave. M(t) becomes an x-axis wave.

[exotic chasm]

would steradian number stuffs also a topic here?

[spiral lodge]

I guess so, yeah

[timid thistle]

fellas do you have any practice problems for trig equations? and like geometry proofs in 2d and 3d

[exotic yarrow]

🎁

[somber coyote]

Civil Service Pigeon

[timid thistle]

aight gimme like 2 hours

[exotic chasm]

||wait, CD is not a diameter...||

[exotic chasm]

also idk if this counts but there's this "heptagon miracle" that says

for a regular heptagon ABCDEFG, 1/s = 1/t + 1/u (or so the saying goes), i forgot which line segments corresponds to s, t, and u (iirc these are AB, AC, and AD)
perhaps if this isn't familiar to you yet, you might be interested to prove or disprove this thing

[timid thistle]

you're thinking too high

please

[winged oyster]

cancel out C on each side fr

and D

[winged oyster]

anyways i think uh

first draw a line parallel to af on e labeled g

below e

so ae = fg and eg = af

oh wait cd is a chord not a diameter

[upper echo]

it follows from the similarity of ADF and CAF and from the fact that the ratio of areas of ACB and ABD (which are right triangles) equals EC/ED.

[winter slate]

Hey does anyone remember the construction for the geometric mean of two segments?

[upper echo]

you can use this

[winter slate]

Well I mean only using a compass and a ruler, construct a segment equal to the geometric mean of two segments

[upper echo]

that's exactly this . Just draw a circle with the diameter a+b. Then draw a hight till it intersect the circle

[winter slate]

I thought the height had to be the P.bs of the two segments tho

[upper echo]

As you can see from the diagram, the hight should be perpendicular at the point where two segments meet.

[winter slate]

Ohh yeah I think i was confused bc you have to get perpendicular bisector so you can find the center of the circle

[upper echo]

yes, to find the center you need Pbs

[exotic chasm]

i overlooked the fact that ABD is a right triangle, damn

🤦‍♂️

via "double angle theorem" and the fact that AB line segment is a secret angle AOB that is 180°

[charred karma]

Hii I need help

[lime crown]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[charred karma]

b) find coordinates of B
c) coordinates of D
d) area of the quadrilateral

[left mist]

Well you can measure the distance between two points you can search for the formula online

That way you got triangle CAB

[slim plinth]

Can someone make a graph that has A to B, B to C, and C to A also to the primes

[marsh marlin]

i dont think my math english is good enough to comprehend what your asking for

[slim plinth]

I mean to say I want 3 equations

Like what’s the equation from (1,-1) and (3,2)

[marsh marlin]

Linear equation?

Are you doing coordinate geometry?

[slim plinth]

Yea

[slim plinth]

No I’m just want to know

[marsh marlin]

So you dont know how to find that linear equation that represents the line connecting the two points?

[slim plinth]

Ik it but I wonder if u can

[marsh marlin]

Yeah I know how

[slim plinth]

Sure

[marsh marlin]

I already learned analytic geometry

[slim plinth]

I get A to B; y=3/2 x - 5/2,B to C; y=6x+20, and A to C; y=-x

[marsh marlin]

Im too lazy to find it

[slim plinth]

Understandable

[slim plinth]

Good news is from C’ to C is y=x

[lone yew]

what would the transformation rule be for reflecting over a line like y=(1/3)x - 4

[marsh marlin]

The slope would be the same

Hmm

All points are same distance to the line of reflection

[lone yew]

for example im trying to prove triangles congruent with transformation

points are:
T(-2, 6)
S(-1, 2)
R(2, 3)

L(7, -5)
M(6, -2)
N(9, -1)

so im trying to get TSR to LMN so i first did a translation <7, -4>

and im pretty sure reflecting over y = 1/3x - 4 gets T'(5, 1) to L(7, -5) but i dont know how to check

S' and R' already ended up in the spots I wanted them to

[exotic yarrow]

If you want to reflect $P$ over $\ell$ to obtain $P’$, then draw the perpendicular to $\ell$ through $P$. Suppose this line meets $\ell$ at $Q$. Then, $Q$ is the midpoint of $\overline{PP’}$.

[somber coyote]

Civil Service Pigeon

[exotic yarrow]

,w reflect (5,1) over y=(1/3)x-4

[somber coyote]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[exotic yarrow]

[lone yew]

yo what

[exotic yarrow]

,w ((4x+3(y+4))/5, (3x-4(y+9))/5), x=5, y=1

[somber coyote]

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Requested by civil_service_pigeon

[exotic yarrow]

Checks out

[lone yew]

bet thanks

[exotic yarrow]

[limber dagger]

how do I solve these two?

ok i was able to solve the pyramid one but not the other one

[silent plank]

what have you tried

[subtle glacier]

Note that all the sides are all rectangles.

[rigid crescent]

hello can i have some help with trigonometry like i understand sin cos and tan but idk where to use for example sin-() idk

oh i meant like the two sin i dont know where to use them

but i do understand the basic of it

[lapis matrix]

Yk what sin an angle means so

So sin unknown angle = 6/7

To find the angle

Sin -1 6/7 = unknown angle

[rigid crescent]

tyy

[upper echo]

use the fact that the angles A and C are equal

[slim plinth]

Ik segment AE Is 6 according to 6-8-10 triples

[upper echo]

you don't need that

[slim plinth]

Meant to do 25-6=19

[upper echo]

or you can use similarity of triangles.

8/10=x/25

[slim plinth]

Segment AB is also 25

[slim plinth]

Oh yea

The geometric mean

sqrt(ab)

[upper echo]

nope

it's just sin(A)=sin(C)

[slim plinth]

x=20

[slim plinth]

Can we make segment BC 10

Since we can bring down that triangle and forms a rectangle

[upper echo]

it's a parallelogramm. So, its opposite sides are always equal

[slim plinth]

Thanks

So x=20

[fluid arrow]

This can also be solved using the concept of vector product

[vestal basin]

how can i determine if the vector/point thing is going in a cw/ccw direction relative to the red center

i think its really simple but i'm not getting it

[exotic yarrow]

cross product

though if you treat the red dot as the centre of a clock, then the purple is pointing in the direction that the hands would move

meaning that it's going clockwise

@vestal basin

[vestal basin]

sweeping?

[exotic yarrow]

edited (kind of, the meaning is the same)

[vestal basin]

6

Let A denote the swipe vector, and B the vector from the start of the swipe to the center of the screen. You can then calculate the determinant of the components of A and B:

| A.x A.y |
| B.x B.y |

= A.x * B.y - B.x * A.y
The sign of the determinant will tell you whether B points to the right side or to the left side of A.
i saw this on stack overflow but i dont quite get why it works (?) or what it means

[exotic yarrow]

yeah this is basically what I said earlier about the cross product

take the 2D screen as a flat plane in 3D space by setting z=0

[vestal basin]

why does cross product work 😭

[exotic yarrow]

then taking the cross product of the purple vector and the vector to the centre creates a theoretical 3D vector that points either into or out of the screen (along the z-axis)

this is just the magnitude of that vector

[vestal basin]

uh huh

oh

[exotic yarrow]

and you can use the sign of that z value to determine whether the motion is clockwise or counterclockwise around the centre point

because of the right hand rule

[vestal basin]

i cccc thanks

[exotic yarrow]

[vestal basin]

ok i lied

theres actually a surface normal that must be taken into account

its like kinda weird because its 3d in a 2d projection

so basically the orange normal is pointing left

when i move the orange face using the white/blue sides, the direction is OPPOSITE to what would be intuitive

but the face opposite to orange works correctly

so i suspect its because the surface normal is the opposite direction

but how would i account for this

its not like i can hard code it

[drifting otter]

Hlo

I have a doubt

[vestal basin]

what is it

[vocal sentinel]

Got a question from my sister, suppose triangle ABC right at A, with AB > AC. Let AH cut BC, such that AH perpendicular to BC. From AC, let I be the midpoint, and let IN perpendicular to BC. We want to show AB^2 = NB^2 - NC^2.

I solved it using Pythagorean, but is there a more efficient way to solve?

Sounds a tad silly, innit?

[exotic yarrow]

I believe that you should be able to multiply the result of your 2D cross-product by the sign of the $z$-component of the face's 3D surface normal in the camera space. The faces on opposite sides of the cube point in opposite directions relative to the camera, so the $z$-values of their normals will have opposing signs. Multiplying by this sign flips the counterclockwise/counter-clockwise result for those "mirrored" faces:

$$\operatorname{sgn} \left(\begin{vmatrix} A_x & A_y \ B_x & B_y \end{vmatrix} \right) \cdot \operatorname{sgn}(n_z)$$

[somber coyote]

Civil Service Pigeon

[sudden talon]

I never thought about it but how do we know that side a will increase in length as theta approaches 90?

[vestal basin]

just think of it like a ladder on a wall and push the end toward the wall

[sudden talon]

Well yeah I can imagine that but

Thats not math

[vestal basin]

uh yeah it is

write that relation in math

then it becomes math

[sudden talon]

ok how

i cant think of how like trigonometricaly angle theta increasing would make side a increase

like ok tan = opp/hyp

so hyp * tan = opp

[vestal basin]

you are decreasing one side and increasing the other side

[sudden talon]

no we arent

[vestal basin]

just think of it like a ladder on a wall and push the end toward the wall

does the ladder change length

[sudden talon]

ok ok ok hold on i think you misunderstood

imagine that point a going upward indefinitely

that'd make theta approach 90

but then why would theta approaching 90 make the point go upward

like why is the converse true

[vestal basin]

do you not see how that is equivalent to just pushing the ladder toward the wall

it's a similar triangle

[sudden talon]

Yeah yeah but

why'

mathematically why

[vestal basin]

it's a similar triangle

[sudden talon]

is there some relationship or

[sudden talon]

similar to what other triangle?

[vestal basin]

the triangle you described by pulling A up and the triangle i described by pushing theta towards the wall a

[sudden talon]

yeah that latter example was never what i was talking about

[vestal basin]

but its the same thing

[sudden talon]

how?

Oh yeah i can imagine that

but how

sorry if im being too euclidean

Actually ok wait

speaking of triangle stuff

[vestal basin]

ok let's say you pull A up until theta = x
i push theta toward the wall until theta = x
by ASA they are similar triangles

[sudden talon]

the opposite side to the smallest angle in a triangle is always the smallest side

[vestal basin]

ok

[sudden talon]

if I increase theta then the other complimentary acute angle will decrease

Thus the side adjacent to theta will graudally be the smallest in the triangle relative to the other sides

and so the side opposite to theta a increases as theta increases

is that math enough?

[subtle glacier]

Intuitively that theta angle is connected to 2 points, if one point stays unchanged, the other going upward, then the angle theta must approach 90.

[crude inlet]

I wish I cared about maths during my teens

I've been thinking of something related to this and this actually helped me get something down I was thinking about for over a year

[gray raft]

guys i need help what is this

😭

[exotic yarrow]

Reposted here: #help-7｜zen1thxyz message

[boreal bison]

Can anyone teach me some topics? Vectors matrices, construction, circle theorem, got a test tomorrow