geometry-and-trigonometry

[dapper blade]

Chat 🙏🙏

[opal grove]

yall should I expect large numbers when answering for total surface area?

I kinda forgot

[ornate linden]

pretty sure you should expect decimal numbers more

for total surface area

[loud geyser]

Divide the given solid into 2 quadrilateral pyramids

[obsidian harness]

yes, it's 1/3 bh also

from the diagram you can immediately figure out their heights

so all it remains to do is to find their base areas

[obsidian harness]

actually, one quadrilateral pyramid and one right triangular pyramid

[loud geyser]

Oh

Oh yeah

[obsidian harness]

(also, what kind of quadrilateral is it?)

(for Alice)

[loud geyser]

Wait, there're 2 quadrilateral pyramids in my approach , maybe your is different one

[hoary totem]

for the triangle at the top u have the base and height
for the trapezoid at the bottom u have the two bases and the height
they give u the height of the whole structure in the question

plug it all in the known area and volume formulae

[stray skiff]

anyone know how to do this?

[loud geyser]

That's insufficient information

i think

[obsidian harness]

100% insufficient information

really, all it shows is that the legs can't be longer than 17

but it could be any other right triangle

[stray skiff]

thank god i'm not crazy

[kind prism]

hey i think there is a method to do it with some relations in geometry

but i forgot what the relation is exactly

[restive kelp]

uh ( hii ), could anyone explain to me how the linear function works??
i was taught it around august but i never really had a grasp on the topic and now i kinda need to write about it tmrw...

all ik is there's { y = mx + c }
i assume y is the y-intercept, m is the gradient?? x is the x-intercept, completely forgot about the c variable

there's a table method and dual intercept method
2nd method was confusing, and i forgot the table method ;-;
-# im unsure if this is the right channel, mb if its not the right one

[loud geyser]

base on academic level, linear function can be understood in variety of ways.

Through vector is one well-known way

[restive kelp]

hmm

ive heard about vectors before, although in graphics programming
otherwise i dont really know what they are

wait, as in ( x, y )?

[loud geyser]

vector in math you can visualize as an arrow, it has magnitude and direction

Imagine a line, each line unique because of its direction and a point it passing through, so through vector [which contain information of direction] and a point we can determine a line

[restive kelp]

ooo

i tried doing some searching and thinking
im not too sure i understand :/

[loud geyser]

This's probably what you need, you'll encounter vector later in your class, maybe in few more years or so

[loud geyser]

Should try to make sense of this first

[restive kelp]

yea

am i on the right track rn?

[cedar stratus]

im not sure whats going on in your photo

but c is the y intecept of the function

[dapper blade]

Its a prismatoid

I still need the area of the midpoint base

[foggy swallow]

can someone clear my doubt

[grim iris]

Maybe
What is the doubt

[foggy swallow]

if i have a line a-d which is trisected by some points

in ratio 1:1:1

i can use the distance or sector formula to find out the points if i am given the value of a and d

so lets say

i find in a---b--c---d the value of c by using ratio has 2:1

now that i have the value of a and c

can i use mid point formula?

[grim iris]

Sure

[foggy swallow]

as i used it and got wrong answer

why was my answer wrong

[grim iris]

Must be some calculation error because the method is sound

[foggy swallow]

imma send the question

make sure ur taking the first ratio as 2:1

and then using mp formula to find b

imm retry in the meanwhile

[grim iris]

C is (-5/3,2) so b is (-1/3,0)

[foggy swallow]

yes C is correct

but when i try for b

i end up at -2/3 , 0

[grim iris]

Midpoint formula is (x1+x2)/2, (y1+y2)/2

[foggy swallow]

ohh noooooooo

i wrote the formula wrong

THANKS SO MUHHH

T-T

TY BRO!!!!

[grim iris]

Np

[severe ore]

It's trisection so you have to do this

Your just gonna ignore second point while solving first
So that 1:1:1 becomes 1:2

For solving second point
You will ignore 1st point
So that 1:1:1 becomes 2:1

[grave pond]

Rather than speaking about ratios of the parts, isn't it easier to just go 1/3 and 2/3 of the way from a to d?

[red wolf]

can anyone help me with my geogetbra work

i lowk dont even know how it works yet i have to make stuff

[grim iris]

Send the question

[red wolf]

im supposed to use a circle to construct a kite, isoceles trapezoid, and rhombus

i wasnt at the class so idk what im supposed to do

[grim iris]

Isoceles trapezoid is very easy

[red wolf]

alr i got rhombus easily

[grim iris]

Make 2 parallel chords of the circle

[red wolf]

How many circles

[red wolf]

alr

But what conjectures could i even use

[grim iris]

All cyclic trapezoids are isoceles

[red wolf]

i gotta list and justify the conjectures

[grim iris]

This is the only needed conjecture and can be proved be simple angle chasing

[red wolf]

Alr

what about kite

[grim iris]

Make 2 mutually perpendicular chords such that one bisects other (other bisects the first is not necessary) and join the 4 points on the circle

[red wolf]

do you have a drawing by any chance

im more of a visual learner

[grim iris]

SAS congruency

[red wolf]

oh alr

[red wolf]

how many circles

jst one?

[grim iris]

Img is not sending for some reason

[red wolf]

lowk this is what i got

but if i connect its a square

you wanna do in dms

[grim iris]

Take only AC = AB and not AD = AE then connect

[red wolf]

so i remove ac=ab

[shut thorn]

use the property of co-interior angles

oh wait

its solved?

[grim iris]

Ya

[shut thorn]

Oh.

[long geyser]

Why does a circle have connected points around a center? Are there points between the real numbers 4 and -4 that are vertical that are square roots of 16? This isn’t very intuitive for me

[stark spear]

the sqrt of x²+y² isnt x+y, its √(x²+y²)

what the equation of the circle says is basically that the perimeter can be described as a set of points that all lie a certain distance (4 in this case) from a given center (0,0)

it would probably help your intuition to grab a ruler and draw this irl, make a center dot and draw a bunch of dots in different directions from that dot but at a set distance and you will see it forms a circle

[long geyser]

But you can rewrite it as sqrt of parentheses sum of x and y raised to the second power cant you?

[long geyser]

Can you put in X and y coordinates each point on the graph?

[stark spear]

do u mean like (x²+y²)=(x+y)²? if so, no

[long geyser]

Right because the parentheses has to be added first?

But either way you can square root both sides right?

[long geyser]

Yea that makes sense, and logically you can do that infinitely many times for all real numbers around the center

I don’t understand how this can be put into a table though

[stark spear]

u can take the square root but that would give u the expression √(x²+y²)=±4

[long geyser]

So I assume that’s not what you’re supposed to do?

I’m new to this stuff so pardon me

[stark spear]

u wouldnt want to yea

no worries!

for what purposes do u want to put it into a table? you could do that for each pair x,y that satisfies the equation

[long geyser]

To get an intuitive grasp, is there not a formula to find any point?

[stark spear]

u should keep in mind that the x and y in the expression both correspond to a single point in the plame

[long geyser]

So there are infinitely many points?

[stark spear]

ie its a coordinate describing one point that lies on the circles perimeter

[stark spear]

precisely

[long geyser]

Yea

[long geyser]

Can you get a semi circle from a function

[stark spear]

if u substitute either x or y for a value you can find the other corresponding value and find that point, if it lies on the circle

[long geyser]

Interesting! Thanks

[stark spear]

you could if you impose boundaries on what value some x- or y-value can take

[long geyser]

Like greater than and less than etc?

[stark spear]

so if u have x²+y²=4² u could say y≥0 which would give u a half circle with a radius 4 centered around the origin

[stark spear]

yea

[long geyser]

That makes sense, thank u so much!

[long geyser]

Oooo

[stark spear]

no problem!

and different configurations with x or y and ≤ or ≥ would give u different semicircles

[gilded chasm]

Hi can someone help me out here
I always get confused when plotting on the x-axis

[obsidian harness]

right, so a period is max to min back to max again

you should know that cos(0) = 1

alright, then keep moving forward a quarter of a period, which is 2pi/5 * 1/4 = pi/10 units on the x-axis

you get 1, 0, -1, 0 in this repeating pattern

so the 5 points have y-coordinates 1, 0, -1, 0, 1

[gilded chasm]

So like this?

[obsidian harness]

yep! nicely done

[gilded chasm]

Thank you so much

[upper karma]

I would suggest drawing it out on paper

here are the steps for sine and cos: asin[b(x-c)]+d or asin(bx-c)+d

(keep parent function in mind: y = sinx and y = cosx)

1. check if reflected or not (is ‘a’ negative?)
2. check for vertical shift if there is one (d)
3. find amplitude |a|
4. solve for x: 0 <= (bx - c) <= 2pi (shortcut method) you get the starting and end points of one full cycle
5. find other mid points, so half then half of that (you only need 5 points in total to graph) you can use midpoint formula if you’d like.
6. plot points and draw the wave

do like 3 of sine and 3 of cosine, and you’ll breeze through them

once you know how to do that, you pretty much can graph the reciprocal functions as well since you’ll know how to graph sine and cosine.

Also, do you notice that the graph is the point moving around the unit circle? ⭕️

once you see the connection, the graphs are simply that

[plush sorrel]

im stuck

[hollow wraith]

to set it up, do the following:
a = 31
sin(A) = sin(42deg)
sin(B) = sin(85deg)

then isolate b and take the arcsine

[hollow wraith]

you can let the known angle and side be c as well doesn't matter

[tidal niche]

omg hp laptop

[cloud garnet]

Damn bro how do yall do this algebra 1 is hard enough

[cloud garnet]

I feel you bro

[plush sorrel]

how do i isolate b

[warm tendon]

a/sinA = b/sinB
31/sin42 = b/sin85
(31/sin42)*sin85 = b

[plush sorrel]

im at
31 = b

---

sin42 = sin85

the dots are the little horizontal bar

[warm tendon]

so 31/sin42 = b/sin85 ?

[plush sorrel]

yes \

[warm tendon]

then you would multiply both sides by sin 85 to cancel out sin85 on the right side so you get
(31/sin42)*sin85 = b

and you evaluate that to get b

[plush sorrel]

okay so b would be left by itself but wouldnt you need to multiply sin 85 to other side

[warm tendon]

yea i did that

[plush sorrel]

im sorry im dumb

[warm tendon]

its ok

[plush sorrel]

would i do 85 x 42 under 31

[warm tendon]

you would do 31 divided by sin42 then multiply that by sin 85

you could rewrite as (31*sin85)/sin42

[plush sorrel]

i got 62.7

[warm tendon]

i got 46.15

what are you putting into the calculator first

[plush sorrel]

i did 31 multiplied by 85 then i divided that by 42

[warm tendon]

so you gotta do the sin of that

so sin85 and sin42

sin85 is like 0.996

then times 31 which gives you 30.882

[broken geode]

He does not know what he is doing

He got an 80 last quiz

[warm tendon]

bro be quiet

[broken geode]

Then bombed this one

[warm tendon]

i do

[broken geode]

Not reliable

At all

[warm tendon]

https://tenor.com/view/ishowspeed-try-not-to-laugh-gif-7682731162751353849

[broken geode]

What did you get last quiz again

I forgot

[plush sorrel]

https://tenor.com/view/f-gif-16992623890208731454

[warm tendon]

then divide by sin 42 which is 0.669

[plush sorrel]

the problem is that when i view a learning video i cant rewatch it so im cooked

[broken geode]

False

[warm tendon]

then ur final answer is around 46.15

[warm tendon]

you can find more learning vidoes online

[broken geode]

You r going to be more cooked if you listen to this guy trust

[warm tendon]

just search it up

[broken geode]

He got such a bad math mark last year

Like a 67

[warm tendon]

https://tenor.com/view/ishowspeed-try-not-to-laugh-gif-7682731162751353849

[plush sorrel]

should i watch a trigonometry video or something more specific from what you can tell

[broken geode]

Video

Don’t listen to this guy

[warm tendon]

if you dont fully understand sine law you should watch a video on that

[warm tendon]

stop

[plush sorrel]

alright i will

should i start on youtube . com

[warm tendon]

yea sure

[broken geode]

You can’t do sin laws

R u cooked

[gilded chasm]

Thank you

[warm tendon]

bro stop being mean

[broken geode]

Like is everything ok at home

[warm tendon]

stop it

ur gonna get banned

[plush sorrel]

im retarted sorry

my moms kinda homeless

[broken geode]

Honestly don’t listen to this coolayu fellow

He didn’t do so well on his first g10 test

His coding isn’t the best either

Can’t code python to save his life

[warm tendon]

never say that again

[broken geode]

He’s the type of guy to do coding bat at home

[warm tendon]

stop describing yourself

[rugged sluice]

guys

am i cooked

im doing proofs

[grave pond]

Your entire history in this server appears to have been dedicated to harassing that person. Take a day off to think about whether that is really the path you want to go down.

@warm tendon, please ping mods or DM ModMail if they keep it up after coming back.

[warm tendon]

Alright thank you

[dapper blade]

any help at #help-2 🙏🙏

[plush sorrel]

im at
42/22=23/a

do i distribute the a

should i do 22/42=a/23 instead

ping me if someone responds

[trail tendon]

this and solve for a, but also
don't forget to plug the angles into the sine function
it would actually be 22/sin(42 deg) = a/sin(23 deg)
then you'd solve for a

[warm tendon]

@plush sorrel

[plush sorrel]

okay thanks, i dont have a calculator to calulcate the sins or whatever. is there one online

[warm tendon]

yea just find calculator website or app or use google and put in sin(whatever number)

[plush sorrel]

i tried it on my phone i did:

22/sin(42) multiplied by sin(23)

and it rounded is 12.8

[warm tendon]

yea i got that too

[trail tendon]

oh my bad i thought responding would ping 💀

[plush sorrel]

thank you thank you

[warm tendon]

How would you quickly figure out the first vertical asymptote and the domain of any transformed tan function is there a formula for the asymptote

[pearl vigil]

12.8458

[obsidian harness]

for example, tan(3(x - pi/6)) has a period of pi/3 and a vertical shift of pi/6 to the right

given you know that tan(x) has a vertical asymptote at pi/2

pi/2 + pi/6 = 2pi/3 : keep adding pi/3 to see that the other vertical asymptotes are pi, 4pi/3, 5pi/3, 2pi ..

and similarly subtracting pi/3 each time, you also have 2pi/3, pi/3, 0, -pi/3...

[keen hedge]

reframing what south said - you can also solve where tan(3(x - pi/6)) is undefined - the asymptotes of tan(x) occur at π/2 + πk where k ∈ ℤ.

hence, we can solve 3(x - pi/6) = π/2 + πk for x which yields the same answer

[ornate linden]

ik this isnt rlly a math related question but whats the answer for this

[obsidian harness]

it's B

[ornate linden]

oohk thanks

[obsidian harness]

as to how carbon monoxide even gets into our atmosphere, it's a product of incomplete combustion

[ornate linden]

yeah

[obsidian harness]

when you try to burn carbon, but there's not enough oxygen, like in a coal plant, you get CO

[ornate linden]

yeahh

thankss

[whole flame]

B

But why in maths

[warm tendon]

Wait so is the first positive VA always period/2

Cause the first VA of tanx is pi/2 and tan (0.5x) is pi

[keen hedge]

yes - but not because of the reason you stated

if you rewrite tan(ax) as sin(ax)/cos(ax), it's essentially where cos(ax) = 0 in which the first positive solution gives you x = π/2a

[warm tendon]

Oh ok

Thank you

[keen hedge]

no worries

[warm tendon]

Could you show me the first positive solution for tan(a(x-b)) —> this is is just what’s in a transformed tan function with horizontal compression and phase shift right ?

[keen hedge]

tan(x) = 0 means x = πk, k ∈ ℤ
so tan(a(x-b)) = 0 means a(x-b) = πk and solve for x from there

and yeah you can think about it as applying a dilation of 1/a from the y-axis and a translation b units left, to the roots of tan(x)

[warm tendon]

So is it (pi *k )/a +. b

[keen hedge]

yes, where k is an integer

[warm tendon]

And when k is one is that the first positive va?

[keen hedge]

Uh not necessarily, that will depend on a and b

[warm tendon]

Oh ok

[warm tendon]

Wait this is for solving when y=0 right

[upper karma]

if i remember, it’s setting up the proportions then solving for that value you want

pretty quick to do

if you are not sure, watch a video on what ratios and proportions are

[long ember]

May I ask for a lil guidance here?

[keen hedge]

cos⁻¹(7/2) is undefined in ℝ. intuitively if you look at your diagram it should raise alarm bells that the adjacent side length is longer than the hypotenuse

[long ember]

Ohhh ok ! I thought I was going crazy

So this answer will be undefined as it doesn’t really work?

[keen hedge]

depends if you're in ℂ or not

but yeah. in a high school trigonometry context dealing with real-valued functions, it would be undefined

[long ember]

Ok !!! Ty

[tidal niche]

geometry dash

guys i just beat clubstep

[stark spear]

#chill

[civic rock]

noob

[harsh meadow]

Can you round out the ° from 75 to 60 or 90 cause 75 is the root of 2 +the root of 6 all divided by 4

I don't know if this channel is for help or should I go to the help channels

But i remember getting told to not go here for trigonometry

[grave pond]

First and foremost you need to describe a lot more context for what you're doing.

[harsh meadow]

Im given a,beta,gama

I need to find b,c,alfa

I found alfa by
Alfa+beta+gama=180

[grave pond]

You need to explain what the problem is, instead of just reciting the names of some quantities in it.

[harsh meadow]

I mean he didn't really give anything else

[grave pond]

(By painful experience, the best way to do that is post a picture of everything you were given as part of the problem).

[harsh meadow]

He did say that we needed to find the rest of the elements

[harsh meadow]

I mean this is it

[grave pond]

That's not a question.

If you don't have any other explanation of how all of those letters are supposed to relate to each other, there's nothing you can do.

[harsh meadow]

Wee did use this

Like we did this question before

But its always been sin30,60,90 even numbers that I can easily find the numeric value of

But now its 75

[harsh meadow]

We just replaced what wee got in this formula

[strange pond]

!xy

[lime crown]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[harsh meadow]

I have

Find b,c,and alfa

Found alfa

Now i have to find b,c

I have the formula

I just need to know if I can round up 75° to 90°

[silent plank]

no

75 is 75

and not 90

[harsh meadow]

Or if I can do sin75°differently

[dark sparrow]

you can if you're fine with getting completely wrong answers that make no sense

[jaunty quail]

Do you have access to a calculator?

[harsh meadow]

Ok then how else do i do it

[harsh meadow]

Yes but the answer is too long it dosent seem right

[harsh meadow]

Well...
No

[jaunty quail]

It's okay, you're probably not expected to have really high of an accuracy

[dark sparrow]

the value of sin(75°) has some roots in it

that's unavoidable

[jaunty quail]

You can work with maybe 4 decimals and then truncate at the end

[dark sparrow]

esp. given you don't have any route here except sine law

[harsh meadow]

Yeah that's the thing

[silent plank]

you had the exact value of sin(75°) being (sqrt(2) + sqrt(6))/4

[jaunty quail]

Oh if you're working with the closed form then it's kind of unavoidable

[silent plank]

don't arbitrarily change values to something nicer just because

[harsh meadow]

Ok then if use that what's gana happened if I replace it here?

[silent plank]

you get an equation with radicals

for which there isn't any real issue

it's just a number, don't get intimidated

[harsh meadow]

Is there a way i can turn 75 in something else with minutes (as in ' not time)

[silent plank]

you could multiply by 60 to get the total amount of minutes but why do you want to do that?

[harsh meadow]

No intimidated
Just 99% that that's not the answer I'm looking for

[silent plank]

what answer are you looking for exactly

[harsh meadow]

The other problems that I have solved that are very similar to this have 26.18 and one with ° minutes and seconds

[silent plank]

if you want to change the 75° to something not equivalent to 75°, you'll get a different result. you could convert the angle to just minutes or anything else but that doesn't help you

you mentioned

you had the exact value of sin(75°) being (sqrt(2) + sqrt(6))/4

simply use that value

[silent plank]

it seems that in that question, the goal was to find an angle

[harsh meadow]

Yes?

[silent plank]

in this question you have the exact value of the angle

and you also the exact value of the sine of it

simply use that value
don't overthink

[harsh meadow]

Ok i see they turned 85.56° into 85°33'36"

[harsh meadow]

Well ok then

I'll just use that

Thanks

[silent plank]

like you weren't think about rounding those ugly angles to some else like 90° right?

[opaque ember]

Can someone help me

[strange pond]

what have you tired?

[opaque ember]

Setting x=23/2-3y/2

for x

and that didnt work\

[strange pond]

and why do you do that?

[opaque ember]

I have no clue\

[strange pond]

do you know what BD being the bisector of AC tells you? In particular with how it relates the lengths AB and BC?

[opaque ember]

It means 18 = 7x-2y

[strange pond]

and what can you say about triangles ABD and BCD?

[opaque ember]

iDK

They are equal

[strange pond]

they're congruent.

[opaque ember]

What does that mean

[strange pond]

do you know the congruence tests for triangles?

[opaque ember]

No

Like 3'4'5?

[strange pond]

Two triangles are congruent if they have equal corresponding side lengths and equal corresponding angles

[opaque ember]

Yeah

[strange pond]

there are a few tests for if two triangles are congruent; the one that is most relevant here is the SAS test, which states that two triangles are congruent if two pairs of corresponding sides are equal and one pair of angles between those two corresponding sides are equal.

[opaque ember]

idk bro

[strange pond]

were you really not taught this?

[opaque ember]

i forget

[strange pond]

well okay

i'll find another simpler solution then

@opaque ember you know the pythagorean theorem right?

[opaque ember]

yes

[strange pond]

notice that since AB = BC, AB^2 + BD^2 = 23 is the same as BC^2 + BD^2 = 2x + 3y

[opaque ember]

yeah

[strange pond]

so... what can you say about AD and DC?

[opaque ember]

they are equal

[strange pond]

right so you have a system of two equations
$$\begin{cases}18 = 7x - 2y\23 = 2x + 3y\end{cases}$$
which should be easy to solve.

[opaque ember]

23=2x+3y? @strange pond

[strange pond]

yes

[opaque ember]

Yes so how does one solve that

[strange pond]

this?

[opaque ember]

Yes

So now what do we do

[strange pond]

just curious, what grade of math is this?

[opaque ember]

freshmen

[strange pond]

Express x in terms of y (or vice versa) using one equation, substitute that into the other equation and solve for y (or x). Then, go back to your first equation and solve for x (or y).

[strange pond]

Do you really not know how to solve simultaneous equations -_-

[little cradle]

What is an interval and how do I do it

[spice knoll]

Can someone help me pls

I genuinely don’t get this at all

[flat fox]

is this just ASA?

[spice knoll]

Wdym

It’s SAS

I’ve figured it out with another helper

[flat fox]

im not good at those

[spice knoll]

Twins

😭

[flat fox]

ye

[spice knoll]

You take geometry?

Taking*

[flat fox]

ye

i am

[spice knoll]

Dangg

What unit r u in

[flat fox]

im in unit 7

[spice knoll]

What r u learning in unit 7?

[flat fox]

i dont remember but i can send a pic

[spice knoll]

Shure

[flat fox]

got it simalarity

[spice knoll]

Boi idk what the hell is that🫩✌️

https://tenor.com/view/ishowspeed-meme-trying-not-to-laugh-laugh-homeless-gif-9458928528704746136

[flat fox]

dilations

[spice knoll]

Ooh

It’s the shape changing in size but the measurements it’s self

Youre learning about rotations too right it that unit

[flat fox]

no

[spice knoll]

Reflection

Oh

[flat fox]

Similarity

Proving Triangles Similar (SSS, SAS, AA)

Similarity in Right Triangles

[spice knoll]

Ooh ok

[flat fox]

Proportions in Triangles

[spice knoll]

Not the forbidden ASS🫩

[flat fox]

ye

[spice knoll]

Btw

R u taking a test called the “Regents”?

[flat fox]

no...

[spice knoll]

Ooh

What type test you taking

For us a regents is like an end exam

[flat fox]

online the worst kind

[spice knoll]

Google forms or smth else?

[flat fox]

something else

lockdown browser

[spice knoll]

Never heard of it lol

Sounds bad

[flat fox]

yes

[spice knoll]

Which state do you take that in?

[flat fox]

minnesota

[spice knoll]

Sigma

https://tenor.com/view/sigma-sigma-letter-sigma2-sigma-math-gif-13598321048744509210

I take mines in NYC

[flat fox]

it forces you to close everything websites games etc. just for a 5 minuite test then you have to reopen all of our tabs again

[spice knoll]

Gang what da hell

[flat fox]

ye

[spice knoll]

Sounds rigged asf

[flat fox]

it is

[spice knoll]

I’m bouta head to sleep Gn alpha beta

[flat fox]

night

[spice knoll]

Gn gng

[zealous pike]

The figure is a square. i need to find the coordinates of U.

I tried to find the size of the sides, which I got 2sqrt(5), but I'm totally stuck here

[spiral lodge]

You can use the fact that sides are perpendicular

So that you can get the coordinate of U by combining two things together:

• UV is perpendicular to VS
• length of UV = length of VS

[zealous pike]

Yeah, and I found that US = 2sqrt(10)

[obsidian harness]

verify that $(x, y)$ has the same length as $(-y, x)$ and is also perpendicular to it

[somber coyote]

south

[grave pond]

You're getting yourself sidetracked by focusing on length as a separate property of a vector here, I think.
Instead think of (x,y) -> (-y,x) as turning an entire vector by 90° degrees counterclockwise.
You can use that to calculate VU (in coordinate form) from SV.
No lengths ever need to appear in your work here.

[keen hedge]

A cool way to do it with complex numbers is $\left(8+6i\right)+i\left(\left(8+6i\right)-\left(6+2i\right)\right)$ which is the position vector of V plus the vector SV rotated 90 degrees

[somber coyote]

Roy

[keen hedge]

which is basically what Troposphere is doing without complex numbers

[zealous pike]

Am still stuck

I found the functions for the lines, but I can't find the coordinates for U

[wise zodiac]

well do you know vectors?

[zealous pike]

No

Dont think so

Im aware of the concept

[grave pond]

Well, if you draw the situation out on graph paper, you can count your way up to U, grid point for grid point.

[zealous pike]

6, 10?

[grave pond]

How does that look on your graph paper?

[zealous pike]

It doesnt intercept the line

Hey

Hmm

[zealous pike]

Time to study some linear algebra ig

[trail perch]

How do i prove that a point is the center of a homothecy

[zealous pike]

I counted 4 up and 2 back, but I got it wrong

[grave pond]

This is what it looks like on graph paper for me.

[zealous pike]

What if I don't have a graph paper at my disposition? 😭

[grave pond]

Draw a bunch of parallel(ish) lines, and then another bunch of parallelish lines perpendicular to them. Now you have.

(Also which kind of mathematician are you that doesn't keep a pad of graph paper within arm's reach at all times?)

[zealous pike]

They don't let us bring anything besides a pen to exams

Entrance exams

[zealous pike]

Btw

How do u know how much you have to go "up" and "left"?

[grave pond]

The line from S to V is made of two 1×2 pieces -- so the line from V to U has to be made of two such pieces too, just turned by a right angle.

[zealous pike]

Ohhh

Gotcha

Hi

[zealous pike]

Banana

[opaque dock]

The first one is really confusing me

[still token]

js find the length of sv and make a parallel line to sv that is that far away and then find the perpendiculars which intersect u

[regal kraken]

find the slope of SV and lenth SV, with that find the slope and TS and UV which will be the same and after that, you can use parametric coordinates to find the coordinates of T and U

[night marten]

how abt finding distance bw s and v and using that to find the coordinates of u

[zealous pike]

I did that

But got nowhere

How do you relate length to the coordinates?

[night marten]

distance formula

d= sq root of (x2-x1)

wait

[zealous pike]

With the distance between two points you'd be left with two unknows (the coordinates for U) Ig

[night marten]

oh yeah

sorry i dint realise

[stark spear]

you can get only one unknown and solve because you use the fact that the y can be expressed in terms of x if you got the equation for the line

[night marten]

how do you get the equation for the line with only coordinates

[obsidian harness]

@night marten

[night marten]

i havent learnt about vectors yet but that probably helps solve this

[obsidian harness]

exactly, you really can't do much with coordinates without vectors

vectors are how you can add and subtract two coordinates

say I am at 3 units east and 2 units north
and I want to go 5 units east and 4 units north

in coordinates, I start from (3, 2)
now, you can think about the direction as another coordinate, (5, 4)
then you just add the two to find where I end up
(3, 2) + (5, 4) = (8, 6)

[night marten]

oh that makes sense but what if you want to go in another direction

[obsidian harness]

you also add the vectors

so if you want to go -1 units east and -2 units north
(that's 1 unit west and 2 units south)

you'd do (3, 2) + (-1, -2) = (2, 0)

[night marten]

thats pretty cool, i havent learnt it in school yet

idk much abt coordinate geometry only the basics

[grave pond]

It would be decently smart not to crosspost the same ad in four different channels.

[hazy sleet]

Hm

Nah

[broken geode]

Ts was tuff

[drowsy knoll]

yo guys! i didn't get this, so like we can express a line in vector form but based on resultant of vectors shouldn't r vector be a vector from the origin, instea dof the result being smth scaled along the blue vector in the pic?

[obsidian harness]

not all lines pass through the origin

[knotty quiver]

the result is a line. Each point in that line is a vector from the origin to that point

so the line is a whole set of resultant vectors

[obsidian harness]

ah I see, so that diagram explains how you get to the coordinates of r from the origin (vector addition)

you need a reminder that when there's a coordinate, the vector from the origin to that point is implied

before I didn't understand where you were confused, cheers

[drowsy knoll]

ohh alr

thanks guys

[knotty quiver]

so yea, the blue vector is the tv being added to r0

[ripe flame]

Is anyone available to help in my help forum? If so I will ping you to the forum

[sick shell]

hey guys. just want to ask, what grade are you guys in/ what grade are you learning geometry or trigonometry in? (ping)

[lime drum]

Freshman in college

Actually highschool as a senior but i guess the credit didnt transfer

[obsidian harness]

here's a non-US perspective:
geometry is one of the core areas of maths, so of course we were learning about different kinds of polygons and 3D solids (for example, pentagons, spheres, cylinders, cuboids) in primary school

we were introduced to coordinates and simple equations of lines in the second half of grade 6; bearings and similar shapes in grade 7
I took accelerated classes (by 1 year) after that, so we studied circle theorems and trig (no trig graphs) in grade 9
grade 10 was when we did trig graphs and function transformations

for context I went to an international school following the British curriculum

[lime drum]

Man i wish i had your curriculums

I think i was still learning some algebras 2nd year of highschool

[delicate ocean]

Hello

[muted prawn]

hi

[thorny dirge]

area of a triangle

[dark sparrow]

where is the actual question

[wanton yacht]

1/2 base times height, no?

[dark sparrow]

sure but OP forgot to ask where his actual confusion is or what he was trying to do

[queen venture]

need a crisp solution 🤤

[wanton yacht]

Oh that's a fun one

Probably first start by finding the intersection point

Then you can figure out what the slope needs to be to divide that cirucumference by that ratio

[warm shuttle]

Finding lines that pass through a common intersection feels easy.
The other part feels like a chore to me.

[wanton yacht]

I think the second part of this problem is definitely harder than the first

[severe ore]

Yo is it conic sections

🔥🔥

[warm shuttle]

I tried to solve it, but that's clearly not how you solve it

[wanton yacht]

Do you want some help?

[warm shuttle]

Yes, actually

Like a hint or something

[wanton yacht]

I'm honestly ready to sit and do this problem, it looks fun lol

Let me think about it

So we know that the intersection point is (7,1), right? And we need a line y = m(x - 7) + 1 that divides the circumference into 2:1. I notice that if we define m such that it goes through the center of the circle (0,0), we divide the circle into two equal parts. That's interesting...

We're looking to define m so that the circle is divided into 2:1 though

[warm shuttle]

Yeah

Maybe consider line passing through 0 and perpendicular to the line connecting (7, 1) and 0?

[wanton yacht]

Hm, no

I was thinking maybe a line that passes through 0 and is parallel to our variable line

Then we can maybe derive an angle between the origin and a point that intersects the circle and the variable line, then we can use that to calculate how much of the circumference is being divided

Then we need to figure out the right angle, and we can use that to calculate the right slope

Or something like that

[warm shuttle]

Consider instead a unit circle

and a vertical line

At what x do we need to place it to get 2:1?

+- 1/2

right?

[wanton yacht]

yes

I was thinking that exactly, but instead of on the x I was thinking on the y

Well

Kinda, yea

[warm shuttle]

Oh I think I know how to solve it now

[wanton yacht]

yep

I think I see it too

[warm shuttle]

Yep, consider the smaller circle x^2 + y^2 = 5^2, an arbitrary line through (7,1) and solve for descriminant = 0?

gtg will be back

[wanton yacht]

Uh

Alright

[wanton yacht]

Ahh, yep

I figured it out

lmao

The distance between these two lines just needs to be R/2

For the angles to line up right, and that line is just perpendicular to both and intersects (7,1)

But the algebra gets a little complicated from here

$\left|\left(7,1\right)-\left(\frac{m+7}{m^{2}+1},m\frac{m+7}{m^{2}+1}\right)\right|=\frac{R}{2}$

[somber coyote]

pebble

[reef stump]

can someone explain to me why the derivative of tan(x) = 1/cos^2(x)? maybe a simple proof or visual example of that?

or should i put that in #calculus

and also unrelated question are we allowed to use latex in these channels?

[wanton yacht]

Yes

And yes

That's a calculus question

And I'll answer it in the calculus section

[warm shuttle]

Is this correct?

I know the typesetting is sloppy, but I don't particularly care if it's readable

My live preview wasn't working for whatever reason

[wanton yacht]

Why don't you just use pointslope form?

y=m(x-7)+1

Then solve for m

I mean

ax+by+1=0 seems way too convoluted. You're dealing with unnecessary terms. y = mx + b, where b is the y intercept is what I learned, so you want m to vary, y and x to map to (7,1),

1 = 7m + b, now define b such that this line intersects (7,1), the equation you get is y = m(x - 7) + 1

[warm shuttle]

Well, y = mx + b can't represent vertical lines

[wanton yacht]

You're right

But do you need it to?

[warm shuttle]

No

[wanton yacht]

Alright

Well anyway

[wanton yacht]

This might be right, but I did it simpler than that

Hmm, actually

[wanton yacht]

What's the purpose here in introducing a smaller circle?

[warm shuttle]

Well, I'm introducing it so that I can solve for my line to be tangent to it

[wanton yacht]

Why?

[warm shuttle]

Because that means the line from intersection of the line and the small circle and origin is perpendicular

because it's a radius of the smaller circle

And it's also 1/2 of the radius of the big circle

Which makes the whole construction similar to the imaginary unit circle and vertical line scenario

"similar" as in the geometry term

[wanton yacht]

Are you talking about like this?

[warm shuttle]

Yes

[wanton yacht]

Okay, so what does that do for you

[warm shuttle]

Wait, no

The other way around

[wanton yacht]

Hm?

[warm shuttle]

Like this

[wanton yacht]

I see

What does that do for you?

[warm shuttle]

Those are the solutions

[wanton yacht]

Ahh

[warm shuttle]

Because the distance from the points where it touches the smaller circle to the center is exactly 1/2 (of the radius of the big circle)

Which is the win condition we decided

[wanton yacht]

Makes sense

I didn't think about doing it that way

Did you find an expression to calculate the slopes though?

[warm shuttle]

Oh yeah, I found the line equations, so you can calculate the slopes quite easily from it by just dividing the coefficients

4/3 and -3/4

[wanton yacht]

Nice

[warm shuttle]

Which is curious. I wonder why they are exactly perpendicular?

[wanton yacht]

I think that would depend on the pivot point

(7,1) is just a very special point

[warm shuttle]

it's distance sqrt(50) away is the condition for that clearly

[wanton yacht]

yep

R sqrt(1/2)

[warm shuttle]

sqrt(1/2) = sqrt(1)/sqrt(2) = sqrt(2)/2 = sin(60 deg 45)

Is my guess

[wanton yacht]

sin45

[warm shuttle]

oh yeah

This is why it's 45 degrees

[wanton yacht]

Ahh, yup

makes sense

[jade plank]

figured out a way to connect two pentagons at a corner while tiling them and i hate it so much

[warm shuttle]

Are you trying to flatten a dodecahedron?

[jade plank]

trying to tile pentagons

it can be done periodically with gaps btw

[warm shuttle]

Idk. I just drew the red "star", and then at each end of it I drew another star of the same size, etc. 6 levels deep. But Idk how this helps tile pentagons

I did round prematurely though, so maybe It wouldn't quite align where it should?

[onyx owl]

how can i get away with not learning trig

[warm shuttle]

e^(ix) = cos(x) + i sin(x)

Pretty much every trig identity is readily derivable using exponent rules from that

[wanton yacht]

Trig is very important if you want to do math as a career

Do you want to do math as a career?

[dark sparrow]

you kinda can't

[sonic lantern]

jesus

[sonic lantern]

what is this

[long geyser]

i just finished all of Algebra 1, I won't have geometry until some time in my school, are there any recommendations where I could pre-learn it in the meantime like on YouTube etc? i'd really appreciate that 🙏

[thin acorn]

Same situation w aurora, but with algebra 2, im planning on finishing up geometry early with the approval of my district

[long geyser]

Oo good luck!! ❤️

i have some ideas like maybe Khan Academy and the organic chemistry tutor, but I'd love to hear if anyone else has done something different and recommends that instead

[thin acorn]

Okk thxxx

[long geyser]

Yww!! ❤️

[wanton yacht]

My recommendation is to pay attention in class so you don't have to teach it to yourself now, lol.

[long geyser]

im in online classes

[wanton yacht]

What do you mean until some time?

[long geyser]

unfortunately

[wanton yacht]

Ohh

[long geyser]

because i have a different structure in my school

different from normal

[wanton yacht]

Well then you're basically going to have to teach it to yourself anyway then, hm?

[long geyser]

Ye

i mean it has notes and everything in the lessons, but i have to read it

instead of just sitting in class and listening

do you recommend desmos to teach myself? messing around with stuff and proving things?

[wanton yacht]

Yes

Absolutely

[long geyser]

ooo

Ty

i've tried the trig thing in desmos where you make lines and circles

idk about any proofs though

i can make lines and stuff but idk what for example the angle notation is because i haven't learned it before

like if you want to write that one angle is the same as another or a line is, etc.

i've learned it a while ago but i forgot all of that

[wanton yacht]

I mean, if you're willing to do stuff like that I reckon you enjoy math and have a genuine interest in it. I was the same way, and this is exactly what I did which helped a lot with my algebra and geometry skills. It didn't really teach me calculus, which is unfortunate since I'm doing lots of that now that I'm in the class now, but it was still very fruitful for me to do that

So yeah, I recommend you do that.

If you're trying to do proofs now, which geometry will definitely require of you, hmm

I mean, it will maybe help with some of that?

[long geyser]

Yesss

[wanton yacht]

How so?

What angle notation are you talking about

ohh wait

I know what you're talking about

[long geyser]

well having logic is essentially what algebra is right? it's a consistent system of language that describes relations between objects, right?

[wanton yacht]

$\congruent$

[somber coyote]

pebble
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wanton yacht]

Partly

[long geyser]

this ∠

[wanton yacht]

Yeah, I figured out what you're referencing

[long geyser]

Mhm

[wanton yacht]

$A\cong B$

[somber coyote]

pebble

[wanton yacht]

Like this

[long geyser]

i wanted to try and learn all of this before but it was hard for me because i didn't know algebra 1 a while ago

[long geyser]

Whats the difference between double ~~ stacked and =~?

[wanton yacht]

I mean, Algebra is just symbolic manipulation of equations. The logic you learn along the way is in applying that math to problems, and knowing what to do with numbers and equations; knowing what they represent, all that. Desmos will help improve both skills

[long geyser]

Yeah but would geometry help with learning the pillars behind algebra maybe?

Because knowing how to manipulate isn't the same as knowing why to manipulate a certain way?

[wanton yacht]

$x\approx y$ means that x is approximately equal to y. For example, $\sqrt{2}\approx 1.414$, whereas if I said like $\triangle ABC \cong\triangle PQR$, then it means those two triangles are congruent, which means they have the same angles and side lengths, and A corresponds to P, B corresponds to Q, C corresponds to R, etc, so A and P have the same angles, B and Q, etc. It's not that hard to get.

[somber coyote]

pebble

[long geyser]

For example, in completing the square it's helpful to know that you want to have a specific length of a square to add to make the square whole, right?

[wanton yacht]

Maybe

Depends on how you define 'geometry,' lol

[long geyser]

i see!

[wanton yacht]

I mean, all of this elementary math that you lear nis all connected though

[long geyser]

well it's just shapes?

[wanton yacht]

Yeah

So do graphs count as geometry?

[long geyser]

Yea

[wanton yacht]

There's shapes in graphs

[long geyser]

Mhm

even a curved line

[wanton yacht]

What about the geometry of imaginary numbers, lol

[long geyser]

a sphere too

[wanton yacht]

Yup

[long geyser]

it's just 4d right?

it's still geometry

and vertices/points

[wanton yacht]

Depends how you define it, but yeah it could be

[long geyser]

interesting

[wanton yacht]

Right. So I could take a curve and put a point on it. That's geometry

[long geyser]

i think that's a less complete definition

[wanton yacht]

Of what a point is?

[long geyser]

Maybe the study of shapes is a better definition?

[wanton yacht]

Oh

Maybe

I mean

[long geyser]

Geometry is super useful in art and architecture right?

For example, designing and building a strong structure

[wanton yacht]

Yes

But most of that comes down to just how forces are dispersed through that geometry, which comes down to angles and things

If you take physics you'll do all that

[long geyser]

physics and math problems have been around since ancient greece right

[wanton yacht]

You'll also need geometry skills for calculating things like moment of inertia, which is a measure of how much an object resists being accelerated rotationally

[long geyser]

with aristotle, euclid

etc

[wanton yacht]

Yes

[long geyser]

and without all of these the Eiffel tower would be weaker right?

any skyscraper

[wanton yacht]

Back then it was all mostly applied math though. Now we see lots of pure math, etc

[long geyser]

Right

[wanton yacht]

Probably, yea

[long geyser]

but you still use imaginary numbers in quantum computers right? and in physics and engineering?

or is there even purer math?

is a circle polar coordinates?

[long geyser]

nvm there totally is, there are so many niche areas of math

[wanton yacht]

I think imaginary numbers come up in quantum mechanics, and probably in quantum computing too. Not so much in physics and engineering. For physics and engineering we just use real numbers and vectors to represent most problems.

[long geyser]

ah

[wanton yacht]

Imaginary numbers come up with 3d graphics though, specifically with camera rotations and quaternions

[wanton yacht]

$(r,\theta)$

[somber coyote]

pebble

[wanton yacht]

There's also spherical coordinates, $(r,\theta,\phi)$

[somber coyote]

pebble

[long geyser]

Really? Does linear algebra use matrices with 4 dimensions to represent a 3d camera?

[long geyser]

super interesting

[queen adder]

arent they a big thing in uhh electricity

[long geyser]

do i learn this in high school geometry?

[wanton yacht]

I haven't learned that yet, lol. That's my next semester, but I don't think so. I think it's used in fluid dynamics actually

[wanton yacht]

No, lol

[long geyser]

Did the guy who invented the light bulb know about imaginary numbers? /genq

[long geyser]

oh XD

[wanton yacht]

spherical coordinates you probably won't learn unless you take Calculus 3 or higher physics classes

[long geyser]

i think i saw this in a calc textbook

[wanton yacht]

Kinda

[long geyser]

Makes sense

[wanton yacht]

They use matrices to represent camera transformations

[queen adder]

idk but like alternaste current systems use imaginary numbers

[long geyser]

Ah, like when the camera moves forwards for example?

[long geyser]

i think thats interesting because AC is something physical but you can use math that uses complex numbers

i dont see a reason why that wouldn't make sense though

[wanton yacht]

Yeah. You use the several matrices to transform every point onto its correct position on the 2d monitor. There's like counterrotation matrices that rotate the point into the proper orientation, that move the point relative to the camera's view frustum, then there's the actual 3d -> 2d transformation matrix

I haven't implemented it in code in a while though, so I can't remember exactly the right order

[long geyser]

How long does it take to do all of this by hand compared to a computer?

[wanton yacht]

I should probably go back to doing that since I know lots more about vector math and matrices

[wanton yacht]

Too long, lol

[long geyser]

i wanted to make minecraft from scratch when i was young, i thought u could just code it simply instead of having to use linear algebra i didnt know about that until like 2 years ago

[long geyser]

Makes sense

[wanton yacht]

I mean, you'll do it with variables 'by hand' when you go to put it in the computer for the computer to do, but just think about it, the computer has to transform every point. If you have high poly models with thousands of vertices, that's going to be a LOT of computations, which is where GPUs come in. They're specialized in highly parallel computing, essentially having thousands of threads that can compute these matrix results.

This is also why GPUs are important for AI, because those usually involve matrix multiplications and vector space and that sort of stuff

[wanton yacht]

Lol. Little bit more than that

[long geyser]

When do you learn physics geometry with time as an axis in 4d or something like that? Leibnets?

[long geyser]

Yeah

[wanton yacht]

If your class is in relativity then yea

[long geyser]

Ah

[wanton yacht]

Otherwise if you take a more classical physics class, you separate space and time

[long geyser]

i feel like that's quite close to real life, because the size of an object stays the same but it's relative to observers

[long geyser]

i see

[wanton yacht]

But in relativity you talk about them as the same thing, and so your 4-velocity, the speed you travel through (x,y,z,t) is a constant magnitude. The faster you move through space the slower you move through time. Light wouldn't move through time, it's moving at the maximum magnitude through space.

[long geyser]

my hand near my eyes appears huge but when it's an arms length away it's smaller, but it's still the same size in both positions

[wanton yacht]

Yup

That's the type of stuff you have to account for in 3d graphics

[long geyser]

interesting

[long geyser]

i see

That's really beautiful

[wanton yacht]

Yeah. And incredibly simple too, huh?

[long geyser]

Yeah!

[wanton yacht]

I mean, if you want tips, my tip is to keep things simple

Calculus comes down to 3 concepts. Everything after that is an application of that

[long geyser]

Yea, at the end of the day algebra is simple it has simple solutions (not necessarily easy though)

[wanton yacht]

All of physics comes down to like 5 ideas, everything else is an application of that, it's super simple.

[wanton yacht]

Yeah

[long geyser]

i see

[wanton yacht]

I mean, they can have simple solutions

usually solutions pertaining to the real world are pretty simple

[long geyser]

Yeah

[wanton yacht]

Though when you get to quantum chemistry they tend to be a little bit more abstract, because you have 3d wave functions that describe where electrons might be found, and they get to be all sorts of shapes

Those use imaginary numbers

[long geyser]

Makes sense. Can you use that to find out what happens at the macro?

[wanton yacht]

To an extent, yes

[long geyser]

Would you need a quantum computer to simulate complex atoms?

[long geyser]

is all of this in 4 dimensions?

[wanton yacht]

Ehh. I've seen simulations done of like proteins in biological systems, and I've also seen thermodynamical simulations and simulations of salt dissolving in water with like dt = units of picoseconds, so 10^-15 seconds or something like that. I don't know how they make those calculations, but

I'm not really too sure. I've always kind of wondered that as well

[long geyser]

i see

[wanton yacht]

I'm pretty sure these are time independent wave functions, so 3 dimensions

[wanton yacht]

No

[long geyser]

is the color gradient because it's a 2d image?

[long geyser]

ooh

[wanton yacht]

The color gradient here describes the probability. The more to the right it is, the higher the probability, and as it fades off the lower it goes

[long geyser]

i see

[wanton yacht]

The idea is, the electron could be found anywhere in space, but it's more likely to be found in some locations than others depending on the energy of that position in space.

And so, it's more likely to be found at a lower energy postion

[long geyser]

Makes sense

[wanton yacht]

So as you go from right to left, you push the atom closer and closer, the energy goes down when they're at the perfect length, and if you push them too close it shoots way up

Kind of like that

[long geyser]

do you recommend i learn on khan academy

[long geyser]

i see

[wanton yacht]

Transformations of things like functions? I mean, you could

Desmos will be a great teacher for that, lol

[long geyser]

i've spent over 170 hours studying algebra 1

[long geyser]

no i mean the whole of high school geometry

[wanton yacht]

Oh you're talking about all of it

[long geyser]

Yea

[wanton yacht]

Well I recommend you learn it, Khan Academy is probably a good resource for that

[long geyser]

Okay!

[wanton yacht]

But learn it in whatever way works for you

[long geyser]

Right

Tyssm!

have a wonderful weekend! ❤️

[wanton yacht]

Mhm. You too. Not many people who seem so passionate about math like you do, at least in the real world.

And there's plenty of people here who can help you with your studies

[long geyser]

Ty!

[chrome cargo]

trig is like the study of certain functions that tell you how the ration of the sides of a right triangle behave based on the angles between the sides of that right triangle

[obsidian sonnet]

Thank you

[shut thorn]

8 is not wrong. Why? Well because if you look closely then you see that
TWV = TWU + UWV
And TWX = TWY + YWX
Now. UWV = YWX (Vertically opposite angles)
And TWU = TWY (TW bisects angle YWU)
-> TWY + YWX = TWU + UWV
-> TWX = TWV

Just li,e know that uh

I did not mention them as angles.

Fuuu

[shut thorn]

Well CPCT is jist a result of proving two triangles congruent.
How?
Well by the definition of congruency.
If two triangles are congruent then EVERYTHING in the is equal to each other. Every angle is equal to the corresponding angle and every side is equal to the corresponding side
So. If we prove that a triangle ABC ≅ triangle PQR
Then AB = PQ (because the triangles are congruent)
And so on.
(CPCT stands for Corresponding Parts of Congruent Triangles). And because of that. When saying that sides or angles of two congruent triangles which we haven't proved equal or were given equal are equal. We denote the reason to be CPCT

Idk if you had that part but uhh

I have written it now so yea

👍

[obsidian sonnet]

Tysm

[shut thorn]

did it help?

[obsidian sonnet]

Yes

I hate ixl bro

It takes 20 points away from you if u get 1 wrong

[onyx owl]

bro im in calc and i physically die whenever i have to do something like cos(0) or sin(pi)

i refuse to learn the unit circe

but i have to

💔

[shut thorn]

suprise for me considering how shit my explainations are

[obsidian sonnet]

It was really good

Helped me more then teacher

Love that you bold the importance parts

[dark sparrow]

don't call me "bro", please.

[shut thorn]

Just a question out of curiosity. How do the following.
x² + y² = r² and x² + y² = r {r ∈ N}
Make a circle?

[dark sparrow]

yeah that's like saying "i refuse to learn the times tables"

it's signing yourself up for spending upwards of 80% more time on any question that remotely smells of trig

[dark sparrow]

this feels kind of redundant, but x^2+y^2=r^2 making a circle has to do with the distance formula.

do you know how to find the distance between two points on the plane

[onyx owl]

???

wait why

[dark sparrow]

i do not like being called "bro", or "dude", or anything else masculine like that.

[onyx owl]

yeah u are right

[onyx owl]

okay

[shut thorn]

Pythagoras theorem?

[dark sparrow]

indeed

but more specifically the expression sqrt(x^2+y^2) gives the distance between (x,y) and (0,0).

[shut thorn]

Yeah.

[dark sparrow]

when you require this value to be fixed, you get all the points at distance r from the origin.

sqrt(x^2+y^2)=r is usually written x^2+y^2=r^2

[shut thorn]

Because they change such that sqrt(x²+y²) = r?

[dark sparrow]

i would not say anything "changes"

[whole root]

how are you in calc without knowledge of trig wtf

how did u do it

[warm shuttle]

There really isn't much to learn. cos is the x-coordinate and sin is the y-coordinate.
The special values are 30, 45, and 60 degrees and the values of cos and sin for them are sqrt(1)/2 sqrt(2)/2 and sqrt(3)/2. (sin in that order, and cos backwards. You know that because sin should be increasing and cos decreasing)
Everything else you can get by just mirroring and geometric intuition

and if you need to convert between radians and degrees, just express them as a fraction of 2pi.
E.g. (1/3) * 2pi is 1/3 of the full rotation is 120 degrees

tan = sin/cos
sec = 1/cos, csc = 1/sin, ctg = 1/tan

[long geyser]

How do you rotate objects forwards and backwards in a 2d plane? I know that you can rotate clockwise and counterclockwise

[rustic girder]

Elaborate

[long geyser]

When you rotate a square for example, you generally rotate it along the middle of it right?

Center

Now that I think about it, would rotating that square forwards and backwards essentially make some of it disappear? To the point that when it’s orthogonal to you that it’s just a 1d line?

[rustic girder]

Yes

[long geyser]

I see

Why does this happen? Is it a limitation of eyesight in the graph?

[rustic girder]

You can say eyesight that is what would happen if you keep your pov fixed

[long geyser]

Yeah

I suppose if you could see with an X-ray you would see that there are multiple points orthogonal to you and that it’s not in fact 1d

If you get what I mean?

[rustic girder]

Eh then we are moving to 3d

Ig

[long geyser]

Well I mean that’s where the points would exist right?

I suppose in 2d there would be no real values for the extra bit that went off into another dimension?

[rustic girder]

Wrt to those 2 dimensions

[long geyser]

Yeah

[long geyser]

Does linear algebra use this stuff all the time

Rotations?

[rustic girder]

Idk

Perhaps yes

[long geyser]

Ty for talking with me!

I realize now how intuitive this is when I’ve spent years in 3d programs and looking at objects in real life

When you take a cube and point it towards you, all you see is a square

In real life

[warm shuttle]

I'm not sure what you mean by that

If you are in a plane, there is only one possible axis of rotation

Anything else would be rotating it out of the plane?

[lost lichen]

cinema

[onyx owl]

bro idk

ik sin is opp/hyp

soh cah toa

[short obsidian]

close enough welcome back al khwarizmi

[velvet crypt]

hello guys i m new

[worthy folio]

In question 14. Is it even possible to have tan A + cot A = 4

I guess the max will be 2 for A = 45 degree

[obsidian harness]

A will be a complex number

but tan^4 A + cot^4 A will still be real

[worthy folio]

Oof. Haven't studied complex nos.

[obsidian harness]

really, it's the same question as "x + 1/x = 4; find x^4 + 1/x^4"

x might be complex in this situation but 8th graders still know how to do it regardless

[warm shuttle]

Will it?

[obsidian harness]

ah wait, for a similar problem such as x + 1/x = 1

got the inequality direction mixed up for AM-GM

[upper echo]

sure, for A=15°, but you don't need to use it. Just use t^2+1/t^2=(t+1/t)^2-2 two times

[dark sparrow]

why wouldn't it be possible

the MINIMUM of tan+cot is 2