geometry-and-trigonometry

[distant crypt]

ima draw it real quick

[distant crypt]

well i think they chose a harder way to solve the problem

find the sides of the base ABCD

[timber cargo]

They're co-functions, so yes

[distant crypt]

A1B1CD is 205

ABCD is 360

but i think i got it tho

the sides are 40 and 9

correct me if im wrong tho

[distant crypt]

yeah i know

i did it again and got it i think

?

[timber cargo]

(a+b)^2=a^2+2ab+b^2

[distant crypt]

yeah

area times 2

i got very high numbers at first

ah

[lapis glade]

does anybody know how to explain sin and cos, im in 7th grade

[opaque panther]

Recommend you start with some YouTube videos and then come back with specific questions

[lapis glade]

ok

[sacred trench]

can someone help me get x for this equation

[nimble fossil]

in an isosceles triangle
an altitude cuts the opposite side in half

so 2x+24 = 5x-30
and then 3x = 54
hence x= 18

[sacred trench]

thank you

@nimble fossil do you know how I can get for this one?

@everyone

[nimble fossil]

here also same way

both the angles are equal

[sacred trench]

I also only got half right on this one was one of my angles wrong?

[nimble fossil]

wait
if both are equal
then answer should be 3 degress

then 58 is not coming

is 58 given in question?

[untold topaz]

can someone help

i said 3 and 3 on this

it was wrong

so idk what it is

[runic beacon]

centroid divides each median in a ratio of 2:1

[rancid tundra]

I forgor cosine rule

Was it a^2=b^2+c^2 something

[zealous pivot]

When exporting tikz in geogebra, is it possible to assign names to the colors you are using so that when you export it you will get the names for the colors you usually use?

Instead of something like \definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1.}

having {ududdf} changed by a readable name

[fickle canopy]

trig is literally worst subject in math

[real oar]

Lemme throw a shot, since it's an isosceles, the height (SU) will bisect the base (TR), So TU = RU = 2x + 24 = 5x - 30
$\therefore 2x-5x = -30 -24$

$\therefore -3x = -54$

$\therecore x = \frac{54}{3} = 18$

[somber coyote]

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

[real oar]

Okay we're good.

Actually I should've replaced OX and OC with x and y respectively and prove x ≠ OX and y ≠ OC as they don't add up to 6, then prove 2x = OX and 2y = OC.

Deleting this I'll try providing something better.

[real oar]

Are you supposed to give any explanation?

[upper quarry]

When using law of cosines when you have all 3 sides, no angles

We can just plug and chug for the angles individually for each of them

Right?

Not just one and convert to law of sines

[nocturne remnant]

Shouldn’t make much of a difference

[upper quarry]

Idk I'm trying to do the same problem with a different to find a different angle

And still confused

Solve triangle ABC

a= 3.1, b= 5.4 c = 7.2

[heavy shale]

U can use herons formula ig

[somber coyote]

NotMyself

[upper quarry]

How exactly would I find the angles using this

3.2+5.4+7.2/2

7.85

But after that idk

[heavy shale]

oh u said Triangle ABC so i thought u meant area

[heavy shale]

sry thats a formula for area

[upper quarry]

Oh it's alright

This is the same problem but I'm trying to find angle B

I already found angle a

But just trying to see and I'm starting to get stuck

[heavy shale]

nvm lol i am sleepy

[upper quarry]

:0 does it look right

[ocean ridge]

hey guys, how can i solve:
cos(x) = cos(3x)
For the range 0<=x<=360

nm, i think i figured it out by sketching the graphs onto one

[wintry saffron]

lmao nice

[pure birch]

#help-6

[twin ember]

Would this be correct?

i guess this is more of an algebra issue, but i kinda forgor some parts of algebra

[north heart]

thats wrong

also #❓how-to-get-help

[wet agate]

My best guess would be to treat it like the 1+2+3... +98+99+100 thing, where sin90+sin1 would be 1.02 then multiply that by 50 because there are 50 pairs of them

[wet agate]

Wait it's sin^2(1) + sin^2(90), then just multiply that sum by 50 and you'd have your answer

[digital tendon]

in the numerator, you should factor out sin theta

think of it like when your dealing with algebra

so if it was like x+2x/x^2, it would become x(1+2)/x^2

then you can cancel out a value of x

so it would become 3/x

try apply that method and see what you get

[digital tendon]

does that help?

[pearl light]

hello, I'm not the smartest person but I'm fairly sure my assignment question makes no sense, it goes "an angle is 2 rays that intersect at a common point, find a contradiction", I dont even know where to start can anyone help, then it asks me how i would change the definition of an angle to make it more accurate as well.

[heavy shale]

in an angle the rays dont intersect

they start at a common point not intersect

[hasty karma]

[pearl light]

sorry i wrote it wrong, it says "an angle is two colinear rays with a common end point, find an example that contradicts this definition"

i cant think of anything that would contradict that definition

[heavy shale]

start point rays dont have end point

they start and keep going on forever(in one direction)

[grave pond]

That sounds like a very pedantic distinction, and might not be the wording convention in Hazashilu's context is.

[heavy shale]

idk i can only find that wrong

nothing else

[grave pond]

I'm more skeptical about which sense the two rays can meaningfully be said to be "colinear".

[sand silo]

guys any help with this?

this is very early stuff iknow

but im still bad

[grave pond]

Do you have any thoughts about it yourself?

[sand silo]

i saw a video on yt that shows 4:3 is the answer but i still dont know how to work things out on my own

[grave pond]

That would be the answer if there were only one cut, but here we have three. That's actually a simpler situation!

[sand silo]

NICE

i would love the help :)

[grave pond]

Suppose we paint the original cube red before we start cutting it apart. The eight small cuboids we're left with after cutting will have some of their sides painted and other sides not. What can we say about the relation between painted and non-painted sides?

[sand silo]

the inside parts that have no paint would be more right?

[grave pond]

What do you mean by "more right"?

[sand silo]

so for every 1 cube theres 4 inside parts that arent painted

no 3

[grave pond]

Yes, 3.

But we see in the diagram that not all of those sides have the same sizes, so simply counting them won't be enough. However, we can still say something about the sizes of each new side compared to a painted one.

[sand silo]

would this be a 1:1 because the cut on the inside have 3 faces and the outside would also have 3 faces?

so its equal

[grave pond]

I agree that they're equal, but as I said, simply counting faces is not enough to be sure of that when the faces don't all have the same size.

[sand silo]

i dont think the teacher's gonna go that deep into it, idk i missed the class and everyone is getting mixed results

[grave pond]

You should be going deep enough into the problem to understand what's going on.

The point I'm trying to get at is that even though the faces have different side, each unpainted face is on the opposite side of a cuboid from a painted face of the same dimensions. They pair up exactly two by two in that manner.

[sand silo]

2 by 2 sounds like 1:1

yea i dont think its that deep, this is grade 9 maths

[grave pond]

The problem seems to explicitly say "surface area", not "number of sides". ¯_(ツ)_/¯

[sand silo]

oh true idk

[real oar]

Extremely late but I think this can work
j is XC, (j/3)h is XO, (j/3)i is OC
I find this very trivial though.

Can be helpful for finding OX and OC.

[silk mist]

Hello I'm currently in engineering, and I do not understand how to do this. Can anyone help me?
Sorry if it's blurry.

[spice tapir]

#26

[foggy furnace]

can anyone explain this

oh is it because sqrt(3)/sqrt(3) is just 1, so you're just dividing the whole thing by 1?

how does the 1-1/sqrt(3) become sqrt(3)-1 though?

[crimson pawn]

i can help

to get from the second to the third step you use KCF

Keep change flip

can never divide a fraction by a fraction

[foggy furnace]

how does this become this though?

[crimson pawn]

Multiply the left one by the denominator. I don’t know the rule but ik it’s right

1 x sqrt 3

[empty ore]

I know this sounds dumb

But why does a sphere look so much smaller at the top and bottom than at the equator?

Even though it’s not

[crimson pawn]

You talking about the globe?

it’s not a perfect sphere

[foggy furnace]

sorry i don't understand

oh wait

ohhhh

i get it

ty

[empty ore]

No

I’m talking about a perfect sphere

The tops of it look like smaller circles than the circles at the equator

But I’ve been hearing that it’s not the case and that they are the same

[crimson pawn]

Not exactly sure what ur asking

if it’s a perfect sphere than its probably just your eyes deceiving you

[empty ore]

Like for example here the circles and spaces look considerably smaller than the circles and spaces at the middle

Could just be my eyes or the way it’s drawn though

[inner kayak]

Hey guys I haven't actually done trigonometry but I'm looking at my friends work, and can't seem to agree on a answer. Do you think you can help?

[worn dust]

Hey, does anyone know how to prove that if two angles are congruent, and they're both bisected, then one bisected angle from the first angle is congruent to one bisected angle from the 2nd angle?

[nocturne remnant]

if a = b then a/2 = b/2?

[chilly blade]

hekp

[amber quiver]

how would I solve for angle *d when the question says <d = (placeholder)+(placeholder)

[timber cargo]

Angle d is the sum of angle c and a

[amber quiver]

Fount out a bit ago, but thank you lol 😂

[bold smelt]

As a rule of thumb in these types of identites i should multiply so i get asq-bsq in denom right?

[slender bolt]

@bold smelt is ur education system uk based

If so what year are u in I wanna know what level ig trig this photo is

[sinful remnant]

What’s a good book to get started in geometry and trigonometry? Or is it enough with the material that is covered in any precalculus book?

[bold smelt]

Im in 9th grade in india this book in doing is 10th grade

[dusk mountain]

Hello everyone

[dusky basin]

6 exponent -6

[upper karma]

im confused on this

[swift fractal]

Answers?

Anyone?

[timber cargo]

S=r * theta, since you have the length of the sector and the radius, just do 3pi/5 and that will be your angle. (3*180)/5, which is 108

degrees

[swift fractal]

And this?

[timber cargo]

Now, are they asking you to input the answer in radians?

or degrees?

[swift fractal]

It doesn't matter much

[timber cargo]

3pi/4 is 135

degrees

[timber cargo]

45 degrees

[swift fractal]

@timber cargo how bout this one

[timber cargo]

14pi

[swift fractal]

@timber cargo can you do two more?

[timber cargo]

5/2 pi

[swift fractal]

Last one

[timber cargo]

36 degrees of pi/5

[swift fractal]

Thank you

[timber cargo]

You're welcome

[timber cargo]

Do them yourself next time, practice the questions, and you'll get used to the technique and you'll become fluent.

[royal cape]

Could anyone help me with proving the following trig identity?

tan^3A/1+tan^2A+ cot^3A/1+cot^2A =1−2sin^2Acos^2A/sinAcosA

[timber cargo]

Can you write that out on a piece of paper

instead

[royal cape]

sure! give me a minute

Does that work?

[timber cargo]

Okay, so, to simply things, I'll turn a into x

Let me work all that out

[royal cape]

Alright!

[timber cargo]

Yeah, sorry, I can't help you with this one right now, I'll see if I can tomorrow

[royal cape]

That's alright! Thanks anyways!

[dark sparrow]

@swift fractal no

we don't give answers here

[swift fractal]

?

[dark sparrow]

@swift fractal are you waiting for somebody to just give you the answer?

[timber cargo]

Solve it yourself

[silk mist]

Can anyone explain what to do for this? I know how to do a bit of it, but these 2 problems are confusing me

[timber cargo]

I'll explain to you you how to do these questions when I get home

[silk mist]

Thank you so much

[heavy shale]

In the 7th one u need to find x

and u are given a value of base

[silk mist]

Okay how would I go about that

[heavy shale]

so u have to use height/base = tan

[somber coyote]

NotMyself

[heavy shale]

Now when u take tan 10 the base is 200 + y

[somber coyote]

NotMyself

[heavy shale]

now u need to use basic algebra to find value of x

,w tan 10

[somber coyote]

Results provided by WolframAlpha

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

Requested by NotMyself#5342

[heavy shale]

,w tan 40

[somber coyote]

Results provided by WolframAlpha

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

Requested by NotMyself#5342

[heavy shale]

the values^

just use decimal to second place ofc

by the way height of hot air balloon from ground would be x + 5.5(height of the person)

[silk mist]

I'm a idiot lmao

I'm still a little confused 🥲

[heavy shale]

where?

[silk mist]

Uhh with the height part

[heavy shale]

can u reply to the msg so i know exactly

what part

ur talking abt

[silk mist]

Sorry

[heavy shale]

the point from where the person sees(eyes) is above ground

so x was how high hot air balloon is from the persons eye level and not ground

and we need to find how high its from ground

[silk mist]

Okay how would you do that

The height of the person was messing me up since I didn't know what to do with it

[heavy shale]

and since distance of eyes from ground is almost equal to height of person

so we just add height of balloon from eyes and height of person

so i.e. x+ height of person = 5.5 + x

[silk mist]

I'm starting to regret my job choice now

But thank you

[heavy shale]

no prob ig u could do 8, if u use the same principles just with cos

give it a try

[silk mist]

Alright

[plain ingot]

is there a general formula to calculate area enclosed by a given set of points?

[visual edge]

There are formulas for some special cases, like triange, square, rectangle, etc.
For a general formula, I found this article https://algorithmtutor.com/Computational-Geometry/Area-of-a-polygon-given-a-set-of-points/

[plain ingot]

Oh, thank you!

im assuming this decomposes the polygon into triangles and caculcates the area from that

if not there is probably a way to do tha

that

by findind the center point (using average)

and then creating triangles

pi, center, p i+1

[stray portal]

Help please?

[viscid girder]

I have an upcoming (competitive) exam with some extra topics I rusty over. Can someone suggest some quick reading for - Geometry: Elementary geometric properties of common shapes and figures in 2 and 3 dimensional Euclidean spaces (e.g. triangles, circles, discs, spheres, etc.). Plane analytic geometry (= coordinate geometry) and trigonometry.

[real basin]

yo, anyone can tell me how to calculate the angular velocity of a delta quaternion?

i can get the difference with qDelta = q0 * inverse(q1) , but i dont know how to go from there

[slate mauve]

how would i translate this

[gusty umbra]

Shoelace thm.

[atomic orchid]

https://cdn.discordapp.com/attachments/778319432874721319/1039014046076248084/8190D6E1-D031-423D-B8A7-F41577DFAB74.jpg

[lofty girder]

use the examples to get each point then use the points and one by one graph it

u dont know how to do it?

[upper karma]

whats the most comprehensive trig book i can get

that is also suitable for self studying

[smoky jetty]

An imperfect square is an irrational number (i.e it has no pattern to say it's repeating and it is non-terminating), and denominators must not have an irrational number, thus it must be rationalized (i.e remove the radical)

essentially, u multiply the fraction by the fraction of the denominator (screw my ugly terminologies)

[timber cargo]

By multiplying the whole expression by the square root of 3

[jaunty hound]

how do you determine this length pls

[vagrant wraith]

so I'm doing a brilliant course about geometry fundamentals (super-duper-simple for the moment) and obviously I got the answer correct. My point is why did they explain it like that? Can't we just consider it as 1 rectangle of area 3*6 instead of 2 rectangles of area 1*3 and 5*3? Does Brilliant think we're that dumb?

even simpler 6*5-5

they're overcomplicating it, right?

[timber cargo]

That problem is designed for middle schoolers.

When they haven't developed the necessary thinking

[vagrant wraith]

ok I get it for the 6*5-5 but like why breaking down the 6*3 rectangle in two parts?

[foggy furnace]

I just realized I've been using the ln button on my calculator instead of the Inv button

[weary harbor]

probably simple ass question, but is there a way to find a right triangle inside a rectangle?

[nocturne remnant]

Any right triangle?

[weary harbor]

yeah 1 sec

basically wanna carve out the red part

it would just be nice if it was a right triangle

[upper karma]

you mean so this part is a right angle?

[weary harbor]

yes

the big rectangle is a wooden plate, I want to cut out a right triangle

the smaller rectangle is a guidance for size

[upper karma]

right

what is it you're having trouble with? do you not know what measurements to use?

[weary harbor]

its just that I want a triangle with an hypothenuse thats the same length as the rectangle

and has around the same height

was wondering if there was some formula or other way to go about it

[upper karma]

i can really thing of a general formula unfortunately

if you give me values i might be able to work something out

[weary harbor]

150*50

[nocturne remnant]

For any given rectangle and base side there are at most 2 ways to “inscribe” a right triangle in it:

Like this

By drawing a semicircle with diameter being the base side

[weary harbor]

yeah but how to determine which points they are exactly?

[nocturne remnant]

If you are given l and h, you can find a with pythag

[weary harbor]

I mean in practice I could just draw a semicircle and a rectangle inside and get the same results but find it interesting

[weary harbor]

I see

ooh right its l/2

thanks a lot

[worldly solstice]

can someone help me with the second question

i dont understand The transformation of [...] according to the vector LJ is [GB].

[upper karma]

frequency, and wave speed. these two graphs. is there a way of describing this that ties the two together better?

[sullen magnet]

Question 4. I dont know how to solve

Please help asap

[upper karma]

start with pythagoras

[sullen magnet]

If you can tell me the answer I’ll know if i got it right

[upper karma]

nice try

tell me ur answer and i'll tell you

[sullen magnet]

3

X=3

[upper karma]

x=−2 or x=6

how did you get 3?

[somber coyote]

MyMathYourMath

[sullen magnet]

a^2+b^2=c2

(x+2)^2(x+4)^2=x

Oh waot

Wait

I forgot to add the exponents

[rancid heart]

can someone send me a course recomendation or something for geometric proofs,

[gleaming coyote]

hello^^ can someone help me on how ill get x and y?

I tried to calculate it but i think the ones I did were wrong-

[smoky vector]

does anyone know any type of website that can figure out statements for proofs

or proofs generally

[bronze jolt]

A.K.A. cheat

[smoky vector]

yes lmao

its normal to cheat

[bronze jolt]

math.stackexchange.com 💀

[smoky vector]

https://tenor.com/view/the-movie-room-hes-true-mouthfuls-mouthfuls69-youtooz-gif-19825918

[pure sequoia]

i have a friend who needs serious help with proofs, can someone help them please?

[vast vapor]

is the reason we label cosine as co-sine because It's orthonormal to the sine function ?

or are there other reasons

[dark sparrow]

no, it's because its name comes from "complement sine"

namely that cos(x) = sin(90°-x)

[smoky jetty]

yep

cool thing I've learned in trigo a few months ago

[prime totem]

Wtf is trigonometry

You write equations and they somehow become lines

[nocturne remnant]

…not really?

[storm loom]

could somebody help me out with this

i havent seen this type of triangle before in class

and it wasnt covered in our notes

[heavy shale]

Since N is midpoint of LQ and PM

u can find that mn = np and ln = nq

u can also equate angle using vertically opposite angle

[storm loom]

oh

so i can conclude that it is congruent by SAS?

[heavy shale]

yes

[upper karma]

this is more fucky

[sonic willow]

how can triangle's side be negative?

[muted abyss]

You only take 6 as solution

[sonic willow]

ye

[muted abyss]

because a negative distance doesnt exsit

expect maybe

if the point is before the origin

[sonic willow]

yes Ik

[upper karma]

you can form a second triangle by considering them as vectors. but for that problem you're right, positive solution

[sonic willow]

Is this correct?

[sonic willow]

Im not 100% sure if I got this correct

[sonic willow]

Have I got this things correct?

I mean I just wanted to test my geometry skills

[storm loom]

i think so

reflexive property proves those right im pretty sure

or i have zero clue what im talking about

[sonic willow]

also what grade are you in school

[storm loom]

[storm loom]

grade 8

[sonic willow]

oh, Im first grade of highschool in poland

but I also had this kind of questions at 8 grade in school, or at 7 I forgor accualy, bc I don't remember anything from grade 7

[sonic willow]

also you are from america or where?

[storm loom]

america

U.S.A

[sonic willow]

isn't american maths easy?

[pliant roost]

it's mostly algebra iirc

as my friend told me

[sonic willow]

ohok

and how much grades USA has?

[pliant roost]

12

first grade is like pre-school

[sonic willow]

oh ok

[pliant roost]

poland has 11 right

[sonic willow]

8 grades is early and middle school combined into one plus then you choose highschool 4 years, technikum(Idk how to translate) 5 years or school that turns you into worker, but you dont learn any subject 3 years or less

[pliant roost]

we have the same word for it

[sonic willow]

so it's 12, 13 or 11

[pliant roost]

ok ig

is 1st grade 7 year old?

[sonic willow]

I think 6 years old if I remember correctly

but I accualy forgot

[pliant roost]

oh, then it's the same as USA

[sonic willow]

ok, and your from?

[storm loom]

is this supposed to be slander

or like trash talk

[pliant roost]

sadly russia

[sonic willow]

nu, I've just seen this videohttps://www.youtube.com/watch?v=jyWjvXR7niI&t=77s&ab_channel=ColfaxMath

[pliant roost]

probably it's some minimum test idk

for all students

[sonic willow]

and this questions are jokes

[pliant roost]

probably

[sonic willow]

I mean ok polish minimum test also has easy questions, like

it's litterally maths from 1st grade of highschool

[pliant roost]

well in ЕГЭ there is the fourth task that is also some simple simplifications

you can take either basic or professional math though

the basic math is prob as easy as polish

[sonic willow]

oh, we also have basic and expanded maths

the question I copied was from basic

[sonic willow]

Can you write an example of professional math test question?

[pliant roost]

there are two parst

one is no solution and the other is yes solution

[sonic willow]

like you have questions that can't be solved?

[pliant roost]

no-no

you don't have to provide the sol

[sonic willow]

we have things that can't be solved without computer simulation in physics olympiad

[pliant roost]

an equation from the first part

[pliant roost]

it's the state test

[sonic willow]

at least according to my friend

[pliant roost]

like gaokao

but easier

[pliant roost]

very simple, right? just use some basic log properties

or you have to evaluate this

[sonic willow]

You have a lot logarithms?

[pliant roost]

no

[sonic willow]

ok

and can you tell me the hardest question you've seen in this test?

[pliant roost]

the second part

number theory

[pliant roost]

actually idk because we didn't have it yet

I've just read the math books that are used to study math

[sonic willow]

accualy Im bad at logs for some reason so I probably wouldn't be able to do this, or solve the quation

[pliant roost]

it's just the properties

[sonic willow]

and can you copy and paste one of the questions

[pliant roost]

let me translate

[sonic willow]

ok

also mine mathematician is a chad

he writes topic of the test "test."

and doesn't explain what will be in the test

[pliant roost]

The first term of the arithmetic sequence that is made of 3-digit natural numbers is equal to 368. It is known that the sequence has strictly more than 2 terms.
A) Can 575 be a term of such a sequence?
B) Can 920 be a term of such a sequence?
C) What is the largest numbers that can be a term of such a sequence?

this one is actually easy

typing a harder one...

[sonic willow]

bruh I didn't knew that there are limits on the test

in this question you need to calculate the limit and type 3 digits after , in the "kratki"(my english sucks)

[pliant roost]

An integer triangle is such a triangle that all its sides are integers.
A) Find all right integer triangles, whose sides form an arithmetic sequence.
B) Do right integer triangles, where height, bisector and median drawn from the right angle, exist?
C) Find all right integer triangles, whose area is equal to the perimeter.

[pliant roost]

cells

[sonic willow]

ye

[pliant roost]

are cells kratki on polish? interesting

on russian it's "short"

[sonic willow]

also is this question hard?

bc Im bad at maths

I mean I don't know how to calculate limits

[pliant roost]

just perform long division and combine fractions

apply l'hospital then idk

[pliant roost]

it's not needed prob

[sonic willow]

I don't know long divistion

[pliant roost]

it's a technique to divide polynomials

google it

[sonic willow]

ye Ik what it is but I don't know how to do it, I haven't got polynomials in school yet

[pliant roost]

what grade are you in

[sonic willow]

integer was?

[sonic willow]

1st of highschool

[pliant roost]

oh

[sonic willow]

and you?

[pliant roost]

integer is cały

[sonic willow]

oh ok, but is this something with calculus or no?

[pliant roost]

no...

it's just algebra

[sonic willow]

oh integer, not integral

the name is so simmilar

in polish too

cały and całka

sounds nearly the same

[pliant roost]

the word calculus exists

we have pervoobraznaya

[pliant roost]

rachunek calkowy

[sonic willow]

Accualy Im bad at geometry

Im worse in geometry than in algebra

and Im not really good in algebra as well

[sonic willow]

Also guys do you know some webside to train geometry and trigonometry skills

[timber cargo]

Since the exponents are the same for the left part of the expression and for the right part, that whole expression becomes (9/7)-(1/3)

[timber cargo]

68 and x are complementary angles

68+90+y are supplementary angles

[static nacelle]

help

[thin heart]

You would use cosine for this question

Right??

So cos^-1 (12\15)= angle of inclination then use angle of inclination to find the height using sine function.

[hasty karma]

@next mantle found someone who says that axis matter

so there is only one right axis orientation

yeah, when i invert axes, suddenly cube becomes a ball and and angles become right

its the same as saying that world has only one origin, some point where all positions are 0;0;0

or when you go from hex to bin number value changes

[open karma]

does anyone know

[hasty karma]

all?

or some specific one?

[open karma]

yeah all lmao

im lost

[hasty karma]

ok i suck at english math, let me go to translator

[hasty karma]

1)<H = <I (<GIH = <GHI)
2)DC=BC, AC - common side, <DCA = <BCA so tri ACD = tri ABC (why there is wave above equality symbol?)
3)AC=DC, BC=EC, <ACB = <DCE (vertical angles) so tri ACB = tri DCE
4)AC=CD because C is a midpoint, BC=CE, <ACB = < ECD (vertical angles) so tri ABC = tri DCE

[open karma]

tysm i luv u

[hasty karma]

if triangles have two sides equal and angle between equal too, they are equal

if you try to change value of third side or other two angles, you will break known equal sides

so there is only one case when triangles have two sides with angle between equal - they both are equal triangles

[burnt wasp]

something I was wondering was why did they square root side PQ in this problem?

[stray vigil]

Because cosine law gives the square?

[burnt wasp]

literally 2-3 minutes after I asked I realized pffft BUT THANK YOU

[worn sun]

Can anyone help pls ?

[dark sparrow]

,rccw

[worn sun]

I drew out the diagram but I’m not sure how to solve for the shaded region

[dark sparrow]

it's the circle minus the triangle inscribed into it

[worn sun]

How do I solve for the area of the circle and the triangle

I only have coordinates

The diagram is basicly everygint I have

[nocturne remnant]

You only need coordinates

What is the radius of the circle?

[sonic willow]

I guess

[timber cargo]

Area shaded = Area of circle minus the area of the traingle

[timber cargo]

Here you go

[upper karma]

x = 22 and y = 112

you need to know about vertical angles for this one too

[upper karma]

a wave means congruent

there is a difference between equal and congruent

the wave is also sometimes called a tilda symbol

[upper karma]

first one you are correct

i am almost done doing the last one then I will post the picture

please note that you always put your prove statement at the last and give the reason

here you go

[upper karma]

Please mark on your drawings as they help a lot

[worn sun]

Thank you so much !!

[granite radish]

Thanks!

[vernal surge]

does anyone know this please

<@&286206848099549185>

[muted abyss]

Hm guys if I got vec(AC) how many vec(AB) I need to get vec(AC)?

What's the method for knowing that

[thin heart]

Step 1: identify that the triangle is a right triangle ( meaning one of the side is a 90 degree angle). Step 2: use pythagorean to find the length CB. Step 3: identify which trigonometric function applies to triangle CBD to find length CD (Answers Sine). Step 4: apply CB to the trig function sine of 55 degrees. Answer to the whole question is 12^2 - 6^2= CB. CB\sin55 =CD.

[thin heart]

Does x need to be in fractions form??

[coral crypt]

Hence why I don't like geometry

[limpid flint]

No idea. It says to express as a single rational number

[coral crypt]

I am so lost on how to prove the Pythagorean theorem

Wait a minute

MAYBE I DO KNOW

I JUST FIGURED IT OUT LEEEETTSSS GOOOOOOOOO

[nocturne remnant]

What did you get?

[coral crypt]

I got 33

[nocturne remnant]

Oh that’s correct

[coral crypt]

Woooooo

[nocturne remnant]

Nice

[coral crypt]

The sad part is it had taken me 2 weeks to figure that out lamo

[nocturne remnant]

At least you figured it out

Now if you see a similar question you won’t take 2 weeks

[coral crypt]

It didn't 🙂

I managed to get it pretty quickly and managed to finish the lesson

[vague radish]

friend told me teacher said it takes 9 steps

is that correct

cant you do this is 4-5

[chrome kelp]

Dam

I feel sorry for you

That you have to do proofs

[vague radish]

nah nah im a senior now

[chrome kelp]

Oh

[vague radish]

my freshman friend is dying

[chrome kelp]

I’m a softmore

😭

[vague radish]

and he's telling me that his teacher told him its 9 steps

[chrome kelp]

I don’t see why it would take so many steps

[vague radish]

maybe i just havent done it in a while but i did it in 4

[chrome kelp]

You could do it in 4-5

[vague radish]

EXACTLY

[chrome kelp]

I’m not very good at proofs so idk

[nocturne remnant]

Multiply sin20° to the product and use double angle and see what happens

@limpid flint

[limpid flint]

Ok

[limpid flint]

I used cofunctions to make it all sines

Was that the right thing to do

It feels easier because it’s all the same but idk

[nocturne remnant]

hm idk

what i did was that sin20cos20cos40cos80 = sin160/8

by double angle formula

but notice that sin20 = sin160

and cos60 you can find separately

[robust finch]

how is this true

[limpid flint]

You’re right

[robust finch]

in order for it to be perpendicular there would have to be a 90 degree angle at the point of intersection right?

[robust finch]

omg

that says AB

not AD

sigh

[limpid flint]

(Sin(160))/8

Or

Sin(160/8)

??

[nocturne remnant]

(sin160)/8

[smoky vector]

what did i get wrong here?

[upper karma]

for triangle mnp you messed up on the side

you were supposed to add 6 and 3.2

as it is asking for the whole triangle

then you see that one of the side is 6, the other is 8.1, and 6 + 3.2 is 9.2. So since these are all 3 different side lengths, the answer would have been scalene for sides

and you were correct on everything

[sonic willow]

You had a question to solve for a=sqrt(x) or you had to prove why a^2+b^2=c^2?

[coral crypt]

I was trying to figure out on how to prove the Pythagorean theorem but once I looked at it a little differently I managed to figure it out lol

[sonic willow]

oh ok, but the question that you pasted on the photo was a question to solve in head in 20 seconds ye?

[coral crypt]

You could say that yeah it ended up being 33

[sonic willow]

ye Ik, also I remember when I had a problem with square roots

[coral crypt]

Honestly it wasn't the fact it was a square root it was how I was going to apply the Pythagorean theorem lol

For me anyway

[sonic willow]

bc it seemed wierd to me that the answer was like 5*sqrt(2) or something

bc in the lower grades answers were all rational

[sonic willow]

accualy I have no problem with this now, now I have a problems with logarithms

[coral crypt]

Never heard of them lamo

[coral crypt]

What are logarithms?

Looks complicated

[sonic willow]

it isn't in most of scenarios but I couldn't solve some questions with them

[coral crypt]

How are they used?

Or how are they applied?

[sonic willow]

Idk if they are used by themselfs a lot

[coral crypt]

Huh, neat

[sonic willow]

I mean I know that natural logarithm(log with base e) is used a lot in calculus from what I know also they are used in some functions

[sonic willow]

oh ye I forgot ph scale in chemistry uses negative logarithm

so accualy they have some use

[coral crypt]

That's pretty cool

[sonic willow]

and how they work is writen in there

I can give an example of question with them

[coral crypt]

Reminds me of two step operations

[coral crypt]

Sure

[sonic willow]

that's an easy example

[coral crypt]

Welp I'm lost

[sonic willow]

nu it's easy

proving something using this shit is worse

[coral crypt]

Seriously?

Wait yeah it would be lol

Wait I just realized that you solved it -_-

[sonic willow]

ye

really you didn't see

[coral crypt]

I thought the whole thing was the problem 😅

Yeah lamo

[sonic willow]

no this was a solve

the problem was first line

[coral crypt]

Yeah I realize that now

[sonic willow]

prove this shit is rational
(I had problem with this)

[coral crypt]

What do you expect me to do? lamo

[sonic willow]

I was just puting an example of a question

not asking you to do this

[coral crypt]

I know I was making a joke lol

[sonic willow]

ok, accualy this isn't hard, sadly I wasn't the one to solve this, bc some girl in my class did this before

[coral crypt]

So the base would be 4, 5, 6 and 7 right?

Would you multiply the bases as if they were an exponent?

@sonic willow or am I wrong?

[sonic willow]

Idk I don't remember how to solve this

[coral crypt]

Lol

[thick summit]

Hello I am new

where do we post doubts

[coral crypt]

Wassap yeet

[sonic willow]

I think you just do a tower like
log4(5)^log5(6)^log6(7)^log7(8)
you use the formula a^loga(b)=b, so
log4(5)^log5(6)^log6(7)^log7(8)=log4(5)^log5(6)^log6(8)=log4(5)^log5(8)=log4(8)=log2^2(2^3)=3/2

ok I remembered it accualy

accualy it was solved a little bit diffrently but this works too

accualy it wasn't hard I remembered it harder

[coral crypt]

?

[pliant roost]

probably change of base formula

[bright rover]

How should I solve this ?
All curvy lines are arcs with w as radius, with a circumference of either A B C or D

(You have to find the area in the middle

[sonic willow]

Idk

like really Im probably bad at geometry(and yes I'm) but I don't have any idea about solving this

[bright rover]

Its okay me neither

Do you think the question itself is unsolvable ?

One of my classmates gave this so I’m not sure whether itself is solvable or even logically correct

[sonic willow]

no, I think that it requires knowledge about some law that I don't know

[sonic willow]

oh it was made by your classmate, it isn't from book, or made by teacher, then Idk 50/50 depends on how good your classmate is in maths

[sonic willow]

I think this might have too Small amout of data

Just maybe

[bright rover]

No I thought the same

But eh

He said he has the solution

[sonic willow]

Also The drawing isnt precise

[bright rover]

And tht he’ll give it on monday

[bright rover]

No Ik tht
I just wanted to represent it

[sonic willow]

Are you math dueling

[bright rover]

Nah not rlly
He just said it was a challenge question

He went from simultaneous equations to that

[sonic willow]

Eh I Dont really have a lot of geometry knowledge

I can do some basic questions, but you know how it is

I prefer algebra

But Simple geometry questions are fun

Accualy I will try to solve this

[bright rover]

Same

[bright rover]

Go for it
But sorry if I’m wasting your time

[sonic willow]

I think I have an idea

Also The fact that Im active on this server means that I have nothing to do

[bright rover]

Go on

[vast vapor]

I'm shooting in the dark here and this does sound tedious but consider rotating the geometry by 90 degrees and putting it in the center of a Cartesian coordinate system
then complete the circle of each arc
and try to derive a formula with the current information and w for the 4 circles

then take the integral of each circle over the whole domain and set each of the 4 integrals equal to each other

[bright rover]

Im sorry but would you mind explaining how I could do that ?

[vast vapor]

very hard over text but I'll try

so imagine this structure you made but rotated 90 deg so It's a diamond

then place is on an x-y coordinate plane

where the center of your structure is the center of the plane = (0, 0)

now you have 4 arcs right

complete each arc's circle

you'll get 4 circles on your plane

I'll try to draw it

[bright rover]

Can you try using desmos (https://www.desmos.com/calculator) ?
I cant fully understand it

[bright rover]

Oh okay

[vast vapor]

excuse the quality, I used an online paint tool

[bright rover]

Yea its fine

I see

But how did you obtain the equations for the circles ?

[vast vapor]

one sec I think I'll try desmos

[nocturne remnant]

To find the blue-shaded area, first find the purple-shaded area and subtract the area shaded in purple but not blue (which is the sum of two triangles)

The 60° angles should make the trig a bit easier

[vast vapor]

I can't see how that'll get the area

[bright rover]

Yea

[vast vapor]

I understand the area will be the blue part * 4 but even then trig is good with triangles

the shape we want to get the area of isn't a square

It's sides are sections of arcs

[nocturne remnant]

The blue shaded part isn’t a triangle and neither is the purple shaded part

But the purple shaded part is a circular sector

And you can find its area

Pardon my typos

But the answer is probably quite ugly

[bright rover]

I think I understand what you’re saying

But how do u find the area of the blue shaded region ?

Its base is curved

[lyric mango]

do all geometry courses allow scientific calculators

[bright rover]

Did it work ?

[vast vapor]

elon's approach would be much less tedious than mine

mine will require doing 4 integrals

but I'm still trying

but this all rests on the fact we know the distance across the area

because we need it to put the circles in the right place coordinate wise

idk how to get that rn or whether It's possible

I'm just assuming It's 2/3

[nocturne remnant]

i solved it and the answer involves some pi's and radicals, but not as ugly as i thought honestly
apparently this problem is famous https://youtu.be/8GnyjbUj-eE

[vast vapor]

but if It's not possible that completely crosses out my approach

[bright rover]

Yoooo

Nice

Ill watch the vid and Ill try it

Then I’ll ask it

[nocturne remnant]

Here’s the sol if you’re interested

[vast vapor]

lmao

I'm completely overthinking

[nocturne remnant]

oh it looks cool in colors

lol

[vast vapor]

yea

anyway the idea was taking the integral of each one

[nocturne remnant]

💀

[vast vapor]

call the 4 integrals I1, I2, I3, I4

to get the shared area we do I1 = I2 = I3 = I4 and solve

[nocturne remnant]

sounds like something on a calc 2 final or sth...not impossible tho

probably

[vast vapor]

why not

btw I made them inequalities just to see the shades area

[nocturne remnant]

the integrals themselves are probably solvable with an appropriate trig sub (after the coordinates of the intersections of the circles have been found)

[vast vapor]

just so that we're clear

has nothing to do with my approach

[vast vapor]

yeah lol

I mean

where bot

mf

k cool

so the integral of that will be just pi/2

just because you're integrating the circle formula you get the area under the shape

if you put r instead of 1 you'll get pi * r^2 the famous formula

thing is

shifting the circle on the coordinate plane doesn't change the area

so that raises a problem

that I1, I2, I3, and I4 are actually all equal

so that's a problem

wait no

[somber coyote]

indeterminate form

[bright rover]

Thanks @nocturne remnant and @vast vapor for helping

Appreciate it

[nocturne remnant]

@vast vapor I did end up doing the integral

Kek

[vast vapor]

np but I got to nothing so no need for thanking lol

[bright rover]

Nah thanks for trying
Ur method works too
Its just a tiny tiny tiny bit long

[vast vapor]

ay great too bad I understand nothing LMFAO

like idk how you got to the starting point

[nocturne remnant]

i set the origin as the center of the square and examined the circle centered at the left bottom corner

then i wrote the equation for the circle in terms of y

then calc stuff

[vast vapor]

oh so you didn't rotate by 90 degree

you made it alot harder lol

if you rotated it, It would've been much simpler

[nocturne remnant]

?

you mean 45 degrees?

[vast vapor]

oh yeah my bad

[nocturne remnant]

but that makes it the area under two curves

.

[vast vapor]

how so

[nocturne remnant]

like this?

there are two curves

well technically you just need to compute one of them because symmetry and stuff

but still not a bit tedious with integrals

[vast vapor]

wait just so that we're clear and I have my info right

if you have 2 integrals

setting them equal will get you their intersection

right ?

[nocturne remnant]

?

wdym

[mortal knot]

Prove that (√3 + 1) (3 – cot 30°) = tan360° – 2 sin 60°. how do you do this one?

[vast vapor]

no nvm

I meant something like simultaneous equations

[mortal knot]

k

[bright rover]

Do u mean cos ?

[mortal knot]

yeah

[lucid ingot]

Does anyone know how to do question 10

[mortal knot]

here it is

[balmy bay]

Jojojo, does anyone of you guys have a list of the most important geometrical and trigonometrical theorems?

[heavy shale]

check pins

there is one of trig

[balmy bay]

Ah ok I see, thanks

[sonic willow]

does this require integrating?

bc I might be an idiot, but I can't solve it with just some geometry and algebra

[sonic willow]

oh it doesn't

fuk it I can't solve it

[torn gazelle]

yo

can someone help me rq?

[cinder oar]

can someone solve for Sn(x)?

[pliant roost]

I don't think the Sn(x) formula is possible even

it's probably just very convoluted

[last nexus]

if the diagonal of a trapezoid are equal, the figure is an isosceles trapezoid proof

how can i prove it

i find the distance of both diagonals

then idk what to do next

[grave pond]

It's not necessarily as impossible as it looks, if we can use complex numbers. The arccotangent of f(k,x) is the argument of f(k,x)+i, so we're really looking for the argument of an indexed product of f(k,x)+i. And the k(k+1) factor looks like something that might lead to telescoping somewhere -- but if we're lucky we don't need to find that telescoping from scratch, because answer (A) strongly suggests that perhaps the whole sum is always arccot((1+(n+1)x²)/n). So perhaps if we divide successive values of (1+(n+1)x²)/nx + i, we'll find a real multiple of f(n,x). And if that turns out to be true, we're suddenly in a lot better position to answer (B), (C), and (D).

[upper karma]

IIT JEE ADVANCED QUESTION

I remember this

[pliant roost]

may you please explain the sentence before the last one?

yes, the sum actually turns out to be arccot((1+(n+1)x^2)/nx)

[grave pond]

My idea there was instead of showing that a_1+a+2+...+a_n = S_n by summing directly, show that S_n - S_{n-1} = a_n.

[proven marsh]

can i ask something ? İs logaritm same in all countrys

[grave pond]

But subtracting the arguments is the same as dividing the original complex numbers, except we might not get equality, just "real multiple".

I don't think there's any country-specific differences in logarithms -- but different fields have different traditions for which logarithm is the "default" one. In pure mathematics "log" is usually the natural logarithm; in engineering "log" is usually the base-10 logarithm; in computer science it's usually the base-2 logarithm.

[proven marsh]

so ? i mean example in romania im going to solve logaritm but idk can i watch how to solve logaritm which produced videos by Turkey or ABD etc.

[grave pond]

I don't know what you mean by "solve logarithm".

[proven marsh]

mmm how can i explain

like

log10^10000 (ex) and im gonna find how to solve

[pliant roost]

ah yes

well maybe

[grave pond]

I don't know what you mean by "solve" in that context. There doesn't seem to be any equation.

[proven marsh]

ok im changing

i dont know english so good

[grave pond]

If there's an e^x involved it's almost certainly the natural logarithm, though.

[proven marsh]

to find log a^x

[grave pond]

Though it also says log10, so I'm confused.

[proven marsh]

im confused too

my question is , if formulas is same in every country , i can watch videos in every country right ?

[grave pond]

Um, sure?

[next mantle]

yea math doesnt change from country to country, it is the same in all countries

certain places might have conventions but most of the time it'll be minor stuff for school level things

[ocean topaz]

hi! i'm new here, and i'm struggling a bit in maths, can someone help me with this? thank you so much!

[upper karma]

Struggling is good

And

For the first part

[timber cargo]

Why didn't you just grab a piece of paper and saved yourself some time and energy

[upper karma]

Solve this equation for the possible values of p

[upper karma]

Bro cause I am on bed

And I'm lazy to get Outta here

[upper karma]

And for the second part let me illustrate you, you can calculate it then

[ocean topaz]

omg thank you! i actually did the first part but i didn't know what to do with the square root and the quadratic, thank you so much

[upper karma]

Welcome

[upper karma]

So we know that the both the points in which p is a variable lies on a line

And a line 2x + 3y = 9 is perpendicular to it

So the slope of this line is -2/3

As slope of a line of the type ax + by + c = 0 is -a/b

[upper karma]

Now to get the slope of our actual line on which the points lie we need to use the fact that

M1.M2 = -1

Where M1 and M2 are the slope the line perpendicular to it and the line itself

[upper karma]

So the slope of our actual line is M1 = 3/2, put M2 = -2/3

Now just use the formula of the slope of a line

That is

Y2-Y1/X2-X1 = M1

We already have calculated M1

And the points are already given where you could take (X1, Y1) = (p,1)

And (X2, Y2) = (9, 3p+1)

Then you shall get the answer of p

[ocean topaz]

okay.. it actually seems like a mountain rn but i think it's pretty understandable! thank you so so much, sorry if i disturbed you!:)

[upper karma]

It's actually the explanation that looks lengthy and terrific

But it's easy if you see the core steps

[upper karma]

No worries, I am already disturbed.

[hollow bane]

Now

How do I know the difference between a obtuse and acute?

💀there's literally no one here

[grave pond]

Are you looking for a way to remember which word is which, or for an explanation of the difference in meaning?

[upper karma]

ok, let us take an example of a triangle

if one angle is obtuse, then the entire triangle will be called as on obtuse angled triangle.

this is because if one is obtuse (greater than 90 degrees) then the other 2 sides have to add up to some number less than ninety and all the 3 sides will equal to 180 degrees by the Triangle Angles Sum Theorem.

Any angle less than 90 degree is known as acute

Any angle equal to 90 degree is known as right

However, if there is one acute angle in a triangle, it is not necessary for the triangle to be acute angled.

This is because the one of the other side could be obtuse, making the triangle obtuse OR one of the other side could be 90 degrees making the triangle a right triangle.

And if that one side is 90, the other two sides must be complementary (two angles adding up to 90 degrees) and if two angles add up to 90 degrees then each of them has to be less than 90 (common sense 😉

however, that still will not make the triangle acute

remember, if there is even ONE, like just ONE angle in a triangle is Obtuse or Right, then the triangle will be named as that angle.

Now as per common sense, One triangle cannot have one obtuse and one right

this is because obtuse is greater than 90 and right is 90.

By the Triangle Angles Sum Theorem, all interior sides of a triangle shall add up to 180 degrees.

something above 90 + 90 will be above 180, making the entire shape NOT A TRIANGLE

Now, I hope you understand the difference between obtuse and acute

And a few more points

just please take note if you want (i suggest)

any angle between 0 and 90 degree is called ACUTE

any angle equal to 90 degree is called RIGHT

any angle between 90 and 180 degree is called OBTUSE

and any angle between 180 to 360 degree is called REFLEX

[upper karma]

I explained both for him/her , buddy.

[upper karma]

yes for example in the United States of America, PEMDAS is used and in Republic of India, BODMAS is used. 😉

[next mantle]

No, both PEMDAS and BODMAS are used in both

[upper karma]

I mean like usually

I study in USA and they never used BODMAS and my cousins who study back in India told me, they do not use PEMDAS.

well it might depend on the schools or etc

[next mantle]

different places and different schools in those countries use different things

[next mantle]

yea

[wooden mango]

aren't they the same thing? lol

[upper karma]

did you know it does not matter if you do y2 - y1/ x2 - x1 or y1 - y2/ x1 - x2? Just remember to keep the y on the top and x on the bottom 🙂

[upper karma]

yes

they are

just different terminologies

[wooden mango]

?

[upper karma]

yes, my teacher asked this question and I was the only one in the class that knew the answer. The question was "does do order matter, like does it matter is y2 or y1 comes first in the numerator and x2 or x1 comes first in the denominator?"

[wooden mango]

it does when you don't use parentheses 🥲

[upper karma]

yeah

[sinful forge]

Haiiii
Can some help me with this question
Find the max and min values for y=sin x + cos x

I know that the derivativehas to be 0

To find the crit points

So

0=cosx - sin x

But im stuck here

[upper karma]

Bro while solving someone's doubt why do you wanna complicate stuff

And yeah ofc I know it

Isn't It obvious

I know many things

But it isn't a great idea to show off all your maths and confuse the other person

Keep it simple

[upper karma]

From here we will get sinx = cos x

Or sinx/cosx = 1

=> tan(x)=1

And now x = π/4

So now we know that this function will be maximum at x=π/4

Now evaluate the f(x) sinx + cosx for x=π/4

I will give you maximum value of this function

And you could actually remember this

If f(x) = a sin(x) + b cos(x)

Then max value of this function is √(a^2 + b^2)

And for minimum

We know that the sin(x) and cos(x) should be both negative to produce minimum output

So surely they will lie in 3rd quadrant

And if you observe that too will be more minimum if sin(x) and cos(x) will be same and that is for π/4

So the x should be π + π/4 (getting to the third quadrant)

Now put x=(π+π/4) in f(x) to get minimum value of the function

[tame scroll]

0 = cos x - sin x
cos x = sin x
then divide each side by cos x u get
1 = tan x
solved

[sinful forge]

thankuuuu

[sinful forge]

thankuuu 🙂

[upper karma]

I like to make stuff complex, especially when it comes to complex numbers.

hahaha, get the joke? eh, complex, hahaha

[upper karma]

Haha, very funny 😅

[solar sigil]

Am i missing something? My answer is not correct my i can't seem to figure out what the problem is

[upper karma]

I think you did some calc mistake

[upper karma]

cause I am getting 1205.68542495