geometry-and-trigonometry

[obsidian harness]

The technique is always to convert the angle into a 1st quadrant angle
Otherwise you have to draw the unit circle every single time

[sage igloo]

Hello, how do you get the value of x?

[native pier]

Have you tried anything?

[sage igloo]

I did 180-70-65 = 45

And then I got stuck

[native pier]

OK. Let's try a different approach

give me a sec I'm pulling up a pic

[sage igloo]

Oki

[native pier]

can you find this angle?

the one in red

-# (and maybe next time I should make it thicker)

[sage igloo]

65?

[native pier]

hmm…not exactly

[sage igloo]

Oh

[native pier]

we don't know that the big triangle is isosceles

in fact, it isn't

but can you use the fact that we know the two angles in the big triangle to find out this one?

[sage igloo]

Ohh so its 45

[native pier]

yeah!

[sage igloo]

Isosceles triangle has 45 right?

[native pier]

the small triangle is isosceles, yes, and so you know two of the angles already

you can use the exterior angle theorem

and you get x=?

[sage igloo]

What's that

[native pier]

give me a sec, pulling pic

[sage igloo]

Oki

[sage igloo]

Ahhh that one

[native pier]

mhm

[native pier]

^^ ?

[sage igloo]

So 45+45-180?

[native pier]

why -180?

[sage igloo]

90°

[native pier]

yeah, the answer is 90º

just 45º+45º

[sage igloo]

Because of the straight line thing, from what I remember its angle is 180

[native pier]

yeah, but here x is angle d, and angle a and angle b are both 45º

[sage igloo]

Is angle c also 45?

[native pier]

that isn't possible, because 45º+45º+45º=135º, and the sum of angles in a triangle is 180º

[sage igloo]

Oh

[sage igloo]

So its 180-90 = 90°

[sage igloo]

Then angle c is 90° as well?

[native pier]

and then 180-90=90 again, but you can just do it directly by adding the two angles

[native pier]

mhm

[native pier]

the idea of this is that the angle outside of the triangle is <a+<b

[sage igloo]

Oh that equals to angle c?

[native pier]

no, it equals angle d

[barren tundra]

some help?

[sage igloo]

Ahhh oki I got it, thank you so much 🫶 , I've been having a hard time with this question

[native pier]

which exact question are you having trouble on

one at a time pls

[barren tundra]

srry im not accustomed

[barren tundra]

IDK how to resolve second problem

[fast pawn]

is there a proof as to how $\sin{(x)}=\sin{(\pi -x)}$ or say $\cos{(x)}=\sin{\left(\frac{\pi}{2}-x\right)}$?

[somber coyote]

parabolicinsanity

[fast pawn]

i never really understood why, and just remembered to ask

[native pier]

you can use the unit circle

suppose you have a point on the unit circle

what happens if you added π? where does that point go?

[fast pawn]

the other side, anti-parallel position or something

i'm not sure of the exact wording

[native pier]

yeah, I get what u mean

so we know that cos is the x value, and sin is the y value

what is the relation between the new y value and the original one?

[fast pawn]

it becomes negative, i think

[native pier]

yeah, and so that's the proof for sin(pi+x)=-sin(x)

u can do something similar for sin(pi-x)

[fast pawn]

oh, i think i understand now

[native pier]

and for pi/2 as well

[fast pawn]

i just remembered, perhaps the sin(A+B) and cos(A+B) expansions could help too...

😔 i forgot about those...

anyhow, thanks

[native pier]

oh, that works too

[native pier]

,tex .sum diff trig

[somber coyote]

astraea 💫

[fast pawn]

i meant like before that but thanks for the refresher

[native pier]

welcome to the mathcord btw

[lime shard]

AB is the diameter
P is the midpoint of CB
O is the center of the circle
PO=8
R=9.6
ACE~OKE
is it true to say EO=3.6?

Just had my hs finals and would like to know if I was right or wrong

[upper echo]

yes

[scenic belfry]

So $sin(\theta) = 2sin(\theta)cos(\theta)$?

[somber coyote]

Iotavian

[obsidian harness]

no, $\sin 2 \theta = 2 \sin \theta \cos \theta$

[somber coyote]

south

[mystic umbra]

semantic gripe but it's true if you treat it as an equation rather than an identity

[obsidian harness]

0 = 1 is true in the trivial ring

[scenic belfry]

I don't know why $sin \theta=sin \theta cos \theta$?

[somber coyote]

Iotavian

[grave pond]

It's not, unless the cosine is 1.

[civic rock]

sin 2theta you mean?

[scenic belfry]

No sin theta only

[civic rock]

^

[stoic mango]

sin(2x) =/= 2sin(x)

[quasi crystal]

May I have lessons on my ball cancer

[civic rock]

use chatgpt haiyaa

[dark sparrow]

!nogpt

[lime crown]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[civic rock]

knew it

[dark sparrow]

where are you seeing anybody say that sin(θ) = sin(θ) cos(θ)?

[scenic belfry]

Oh

[grave pond]

You can see this because it's possible for 2sin(x) to be 2 (such as when x=pi/2), but sin(2x) is never 2.

[scenic belfry]

Oh

[scenic belfry]

So ugh....Is this applied to prove the initial equation?

[static sapphire]

hi

am new to this server

[worthy eagle]

@static sapphire welcome to the mathcord

[stoic mango]

which equation?

[static sapphire]

yes sir

[static sapphire]

thx shubham

as in the guy from inside

[fathom dirge]

Please solve 4th and 5th

[dark sparrow]

is this a current test?

or

well actually the grades are already placed on it

so whatever

share your progress or working on each one

[fathom dirge]

No

[full sundial]

use the standard tan(a-b) identity for 4th one

[full sundial]

for 5th one take out cos(x) common and substitute 4+2sqrt(3) again and solve for x

[stoic mango]

4th

[fathom lynx]

can i ask question here

[civic rock]

sure

[fathom lynx]

https://tenor.com/view/but-nobody-came-gif-12359516821941866500

[dark sparrow]

do you still need help with this

[fathom lynx]

yes

[full sundial]

you re given one spacing subtends 6 degrees and total spacing to be 17 and a half. You can calculate total subtended angle and then use the formula pi radians = 180 degrees to convert

[dark sparrow]

ok, can you express the angle they ask for in degrees for a start?

[fathom lynx]

dawg I just want the solution

[fathom lynx]

this the entire question

[dark sparrow]

please do not call me "bro".

and no, we will not give out solutions.

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[dark sparrow]

!noans

[lime crown]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[dark sparrow]

@fathom lynx please edit the word "bro" out of your message!

[fathom lynx]

k

[dark sparrow]

thank you

anyway my point stands

[fathom lynx]

[dark sparrow]

this server is not a "do your homework/questions/whatever for you" server

[fathom lynx]

then wut is it

[dark sparrow]

you can read #rules and #info to find out

but basically you're expected to put in some effort

my suggestion in particular was meant as an intermediate step to doing the question

and so it is with literally any question posted on here

[fathom lynx]

I should start reading these when joing agroup

[dark sparrow]

i mean yeah you should

you should always read the rules when joining any server

that is... what rules are for

[fathom lynx]

yes

[fathom lynx]

sorry abt
i just call everyone bro for being friendly

[dark sparrow]

right, some people don't like being called such words though.

so you gotta remember that. and if someone asks you not to call them by some word, you respect it. basic decency.

(and you did that)

[fathom lynx]

btw dont read my status

[fierce monolith]

this shi made me laugh

[winter gazelle]

wat

[fierce monolith]

look at his bio

js funny lol

[fathom lynx]

well I am glad someone found it funny
I almost got banned for having that bio in a different group (r/undertale/deltarune)

[scenic belfry]

The sin 2theta = 2sin theta cos theta

[warped osprey]

man I didn't know this server existed. Time to share knowledge

[fathom lynx]

anyone know why I cant look into members old msg

[trail tendon]

😎

[trail tendon]

into any member's old msgs or just a specific one?

cuz if its specific maybe cuz they never typed

here

[strong frigate]

wait do yall know if for summer courses the high school is gonna give u a placement test to see if ur ready for the next course (example: if we’re already done with biology, will the high school give u a test before allowing u to move on to chemistry??)

also for math (if we’re not doing a summer course on math), will our high school test us on algebra and geometry before allowing us to progress onto the “advanced” algebra 2/trig course?

just wanted to ask cuz im going to a public hs this eyar

[obsidian harness]

uh, that's not the function of a placement test

usually you just need to pass/achieve a certain grade in the previous course to take the next course

I don't know your school specifically

but placement tests are for if you want to take a course earlier than your school's timetable, so you have to demonstrate knowledge of the prerequisite course material for that class

[edgy cargo]

dm me i need help on trig

[obsidian harness]

why not just ask here?

[edgy cargo]

idk

need help with memeorising the identity for mulas except for the pythagreas one

[obsidian harness]

okay, so if we start from sin^2 x + cos^2 x = 1

what happens if you divide everything by cos^2 x?

[edgy cargo]

tan

of x

bro idk

im lost

im cooked

dont teach me

[stoic mango]

is actually a consequence

try sin(a + a)

[strong frigate]

thanks so much for replying so quickly!!

just wanted to follow up with another qs: how does the high school evaluate a summer course (as u mentioned, I am completing a course before the actual timetable suggests - biology), and I already took alg 1 and geometry in 7th and 8th grade respectively. What im asking is if they will give me another placement test for biology (to see if im ready to move on to chem) and geometry to see if im ready for advanced algebra 2

[obsidian harness]

mm they'll usually correspond with your middle school, say ask your teacher about how well you were doing in those classes besides your grades

but yes they could equally give you a placement test covering material from those classes if they can't be bothered to do that

your best bet is to ask your high school directly

[strong frigate]

ohh ok

[obsidian harness]

just email them and they'll answer

[strong frigate]

yup

thank u so much

[obsidian harness]

it's great you're thinking about how to manage your educational options and make the most of your time in school though!

when I was your age I certainly wasn't as proactive

also schools give some very clichéd advice about subject options, like "don't pick a subject just cause your friends are also doing it"

they're treating you like babies when they say stuff like that

there are definitely going to be people with the same maturity that deserve much better advice

[obsidian harness]

cause it's not just about "what are you going to do after high school? are you going to college and what are you going to be studying?" either

[strong frigate]

Yes indeed

[strong frigate]

thank u lol

i prob have forgotten everything in geo over the summer lol

so i have to study

[strong frigate]

very true

[obsidian harness]

if I could say one thing, it'd be don't be afraid! you're going to have a lot of choices but that doesn't mean you have to get everything perfect right here, right now

[strong frigate]

oh that means a lot! Thank you!

[obsidian harness]

yeah honestly I hope you can just get through everything
I experienced a lot of injustice as a teenager that I didn't quite have the words at the time
so being in your early 20s can be a new start

[strong frigate]

ohh i see; well, i hope ur new start is gonna be/is perfect!

[obsidian harness]

it sounds like you could do a lot of good things in the world
but equally don't be surprised if life just kind of rolls you over either

[obsidian harness]

thank you!

[strong frigate]

yup that's true

[scenic belfry]

Thank you!

[obsidian harness]

fml I should have just said why

[snow tide]

why am i missing solutions in this isnt this the best method

help

[fathom lynx]

actually the problem was with my account, but it got fixed by simply reloging

I thounght it was a new discord update where ppl cant look in older msg for privacy but it simply a glich or smth

[obsidian harness]

right, you need to check the case where $\tan^2 x \tan^2 3x - 1 = 0$

[somber coyote]

south

[obsidian harness]

otherwise you're dividing by 0 and that step is not valid

dividing is fine: you don't always need to factor it to avoid dividing

you just need to check when it equals 0

[night basin]

Good morning, everyone. Uh, sorry to interrupt, but do you have any tips for getting started with trigonometry and geometry?

[obsidian harness]

have you tried looking through Khan Academy?

[night basin]

No

[obsidian harness]

go do that and come back
there's videos and quizzes

I say that cause it's hard to help if you don't post a specific question/exercise

so I've just referred you to a place where you can both learn and practice

[snow tide]

oh right mb but then the solution becomes too long cuz write general formula and take intersection or am I dumb idk

[obsidian harness]

in fact no, cause by subbing in you get $0 = \tan^2 x - \tan^2 3x$ or $\tan^2 x = \tan^2 3x$

but $\tan^2 x \tan^2 3x = 1$ so $\tan^2 x = \tan^2 3x = 1$

the intersection of both equalities is hence $\tan^2 x = 1$

[somber coyote]

south

[obsidian harness]

it's a coincidence that tan^2 x = 1 doesn't introduce any new solutions

you're actually not missing solutions

[snow tide]

ty

[regal kraken]

yo chat

what is descartes theorem

?

[spiral lodge]

Google it?

Another name for it is "law of cosines", if this helps

[rough hound]

so uh I'm learning abt trig using this YouTube video and I don't know why but I entered the same problem in the YouTube video in this calculator and the YouTube video got different answers than my calc so idk why someone help please

[storm sparrow]

Hiii guys, I'm new to this server, and for math too :P, if anyone wanna study with me, I will be really grateful. I'm currently studying deeply sines, cosines, tangents, all their inverse functions and inverse values

[storm sparrow]

You calculated the cot of 5/4, which is equal to (tan(5/4))⁻¹, that has nothing to do with the atan of 5/4, which is tan⁻¹(5/4)

[upper echo]

you should press inv+tan buttons to get arctan

[warped osprey]

Y=(X+Z-1)!/(X-1)!Z! {X≥0} {Y≥0} {Z≥0} (Integers only). This is Pascal's triangle, X is the dimension, Z is the term, Y is the output

[civic rock]

geometry indeed

[warped osprey]

by dimension I am referring to the dimension of the triangular sequence, like 2d is n(n+1)/2 (triangular number sequence) 3d is n(n+1)(n+2)/6 (tetrahedral numbers) ect

[warped osprey]

Well it is graphing

[regal kraken]

uhh no, law of cosines is different I think

i beleive it is used in triangles

[pale sentinel]

LMGTFY - https://en.wikipedia.org/wiki/Descartes'_theorem

[regal kraken]

aight thanks

[pale sentinel]

(there has to be a Wikipedia version of JFGI...)

[foggy forge]

Hi

[spiral lodge]

Oh yeah lol i mixed up Carnot with Descartes 🙈

[spiral lodge]

IGNORE this, my bad @regal kraken

[regal kraken]

aight

[indigo nexus]

its right

it was actualy

tan^-1

not tan(5/4)^-1

\documentclass{}
\usepackage{}

\begin{document}

Given:
[
\tan(\theta) = \frac{\text{opp}}{\text{adj}} = \frac{5}{4}
]

The angle (\theta) is:
[
\theta = \tan^{-1}\left(\frac{5}{4}\right)
]

Calculating:
[
\theta \approx 51.34^\circ \quad \text{(or } 0.896 \text{ radians)}
]

\boxed{\theta \approx 51.34^\circ}

\end{document}

[somber coyote]

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

[snow tide]

is there any other way except cauchy inequality to find the range of this function?

[dark sparrow]

,rccw

[grave pond]

It doesn't make much sense to say "for all x, find the range of the function". The range of the function is what it is; it doesn't depend on x.

[dark sparrow]

it's an abuse of notation

they definitely mean "find the range of f: R -> R given by ..."

[snow tide]

yeah it's an imprecise statement but widely found in textbooks ig to specify that the domain is R in a simpler way idk

anyways my sir said there is another good solution but i don't seem to find it

[rough herald]

Hey all!
I'm looking for 3 teammates for HMMT (November & February)!

I’ll be focusing on algebra, so I’m looking for others who are strong in:

• Geometry
• Number Theory
• Combinatorics

looking for extremely skilled individuals with serious dedication!

[warped osprey]

what is HMMT?

[rough herald]

it is a maths competition that Harvard & MIT host

it is for high school students

I'll participate but looking for teammates

[warped osprey]

I could try to join, I'm in high school as well

and I'm great at math

[rough herald]

great!

you can DM me if you want to join the team

I'll give u 3 questions & if you answer well, we can work with each other!

[solid anchor]

Are none of these right?

[silent plank]

how are you reaching that conclusion?

[solid anchor]

Oml I got the answer -2+sqrt3 and I glanced to quickly over sqrt3-2

Im just lowk stupid

[wanton arrow]

how can prop 3 be used to say BD is equal to AC if the only place that you can use prop 3 to do the cut is from vertex A? also im i supposed to assume that constructing DC doesnt change the angle at vertex C?

[dark sparrow]

constructing DC chops the angle at C into two smaller angles visually but you dont care about it

im not sure what your objection to prop 3 is. can you show how euclid states it?

[wanton arrow]

the only way to chop the less from the greater would be at vertex A on prop 6 and yeah i would think it would split the angles thats why am asking if you assume the vertex C angle stays the same

[dark sparrow]

wait

do you claim that such a cut is ONLY legal if the two lines you're talking about already share a vertex

y/n

[wanton arrow]

yeah i am

[dark sparrow]

ok you're wrong about that then

you can cut off from either end

[wanton arrow]

i cant for the life of me figure out how to do that

[dark sparrow]

even in this prop 3, "Draw red = blue" already assumes you can copy segments by length

which is proposition 2

and, if you really want to spell out the construction in full,

[wanton arrow]

yes

[dark sparrow]

it's allowed to place the red segment on EITHER end of the white line.

no privilege is given to one end of it over the other.

[dark sparrow]

do you want the dumb/non-proofy explanation

[wanton arrow]

sure

[dark sparrow]

if you have a 10cm rod and you want to cut 7cm off of it, you can cut off that length from either end of the rod. by your logic there could be a situation where one end of the rod is privileged over the other, and only it can have 7cm cut off from it, while from the other it's somehow like cosmically or divinely forbidden to do the same

so it just makes no sense that you'd somehow be able to cut a given length off from one end only

capisce?

[wanton arrow]

how could you know you wanted 7cm cut off a line if you have no way to measure the 7cm unless you transfer a length, collapsing the compass

[dark sparrow]

ugh.

okay fine, forget the measurements.

[dark sparrow]

in this picture, you could, if you wanted to, follow the construction of prop 3 and draw a circle centered at B with radius AC.

do you agree or disagree?

[wanton arrow]

no you cant without collapsing the compass, unless it was an equilateral triangle then you could

[dark sparrow]

??

[wanton arrow]

you are measuring the length of AC with the compass then picking it up and setting it on B

[dark sparrow]

yes? is that forbidden?

[wanton arrow]

yeah forbidden

euclid claims to do it without

im going to have a stroke

[dark sparrow]

The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so it may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem.[...])

so says wikipedia

[fathom lynx]

better than ai

[dark sparrow]

.....

[fathom lynx]

did i stutter

[dark sparrow]

can you show prop 2? @valid zinc

that one seems to be the one to do w/ transferring lengths

even when our compass is collapsing

oh

fucking hell

i pressed up arrow and pinged the wrong person

[fathom lynx]

where u get yr pfp from

[dark sparrow]

this is off-topic. if you want to ask me off-topic questions, then go to #chill or #discussion or #serious-discussion.

[wanton arrow]

this might be hard to follow its old

[cunning lion]

you can use a newer translation if you want

[dark sparrow]

ok, so you agree that transferring lengths is still possible even when the compass is a collapsing one?

or do you want this spelled out every single time in every single proposition with every single circle drawn every single time on every single diagram

[wanton arrow]

thats how i want it but i can agree that you can transfer lengths without picking up the compass i just dont see how to do it on prop 6

[dark sparrow]

you want to spell out the full details of the construction within the setting of prop. 6?

[wanton arrow]

yes please \

[dark sparrow]

hm

ok i admit even i can't quite follow this diagram for prop 2.

not sure what the "describe [triangle] (prop 1)" means

maybe you will have to show me prop 1 too

[wanton arrow]

can i dm you?

[dark sparrow]

no

[wanton arrow]

prop 1 is just an equilateral triangle

[fathom lynx]

then y do u have yr dms open?

[cunning lion]

more modern translation of prop 2

[dark sparrow]

honest to god it is none of your god damn business.

also maybe you should remove the transphobic joke frrom your status.

[wanton arrow]

remove jokes????

[dark sparrow]

yknow what im gonna take that to #discussion my bad

[wanton arrow]

dont look at jokes you dont like nut job, you would say some weird shit like that in the middle of a math conversation

[dark sparrow]

ok, if i'm a nutjob then i'll just leave this convo outright, bye

[wanton arrow]

bye

[dark sparrow]

i am not a "mr".

and no, i don't have euclid's propositions memorized by number.

if you could correct the honorific, that'd be nice.

[civic seal]

they've been banned for DMing another user with homophobia

[dark sparrow]

lmaooooooo

[fierce epoch]

who was it

[civic seal]

eudoxus

[fierce epoch]

no i mean who is the other user

[civic seal]

doesn't matter

[fierce epoch]

ok

[fierce epoch]

who reported

[civic seal]

we do not discuss moderation details with uninvolved users.

[civic seal]

Are you an alt of the banned user

[fierce epoch]

no

my account was created like years ago

[civic seal]

I'm aware. that doesn't preclude the possibility

[fierce epoch]

I joined to seek advice

[fierce epoch]

am just a curious little guy

[civic seal]

Please keep this channel on topic

[fierce epoch]

mb

[worn comet]

yo

[crystal narwhal]

can someone help me with this

[worn comet]

is that the BYU class?

[crystal narwhal]

huh

[worn comet]

independet study for byu

?

[crystal narwhal]

no just middle school algebra

[worn comet]

aww

I need help with mine to dw

[crystal narwhal]

i can do this in eighth grade so i dont have to do this in high school

[worn comet]

smart

well

Im stuck on mine rn

[main plover]

How do i solve these types of questions

If i see its solution its gomma be so obvious

But i cant solve it

i got it

nvm

[zealous pike]

Is it possible to find the length of the sides with the given information?

In the image there is a Rectangle ABCD whose area is 36 and the diagonal line BC length is 5

I've tried an equation of systems like

Let the sides be a and b

ab = 36
a² + b² = 5

But i don't think this is the way 😭

[main plover]

This is what gemini says

[rancid cobalt]

Could I try and help?

[rancid cobalt]

This starts by referencing pre-algebra with area formulas, it seems

[zealous pike]

AI????

[main plover]

hey bro

[zealous pike]

AI for math?

[main plover]

were in the same boat here

the blind leading the blidn

[rancid cobalt]

Isn't ai specifically mentioned against in the rules-

[zealous pike]

Sure

[main plover]

oh

[zealous pike]

Don't trust AI for math, it isn't good for it

Mainly LLM like chatgpt and gemini

[rancid cobalt]

You have the length of the hypotenuse and twice the area of one triangle

So the question now is whether you have enough information to figure out one side

[zealous pike]

Indeed

[rancid cobalt]

It's too large of an area to be a 3-4-5 triangle

[zealous pike]

A right triangle with hypotenuse 5 not necessarily is a 3-4-5 triangle

[rancid cobalt]

I just thought it'd be better to check real quick just in case

Are there any other method options you've crossed out?

[zealous pike]

If we use a system of equations, we have:

ab = 36
a² + b² = 25

a = 36/b
b² + (36²/b²) = 25
b² = (-1296 + 25b²)/b²
b =sqrt (1296+25b²)/b

No, this system seems not solvable

Hmmm

Wait a minute

[rancid cobalt]

?

[zealous pike]

b = sqrt(25 - a²)

asqrt(25-a²) = 25
a²(-a² + 25) = 625
-a⁴ + 25a² = 625
-a⁴ + 25a² - 625

yeah

[rancid cobalt]

yeah, and on a graph the two lines don't collide

[zealous pike]

Therefore

I wanna cry

I think that there is no solutions for this one

[rancid cobalt]

yeah, I agree there

[zealous pike]

The question asks: given the cylinder of radius r inscribed in the circle of radius 5, find the largest value of x such that its volume = 72π.

What I've tried is to find a relation to the information given.

The formula for the volume of a cylinder is hπr², where h is the height. We have that h = 2x. We want to find a value x such that 2xπr² = 72π. With some manipulation, we have:

xr² = 36

Maybe I'm overcomplicating this

[rancid cobalt]

Give me a moment to follow your thought process...

Okay, I see where you're going. I'm assuming there's a second equation we're making a system out of

[zealous pike]

Stop reading my mind

If they would only give me some other angle for that triangle 😭

Hmhmh

Hmmhmgm

[rancid cobalt]

Oh wait

We have something to go off of for every line of the triangle

[zealous pike]

What's it?

[rancid cobalt]

x, r, and 5

[zealous pike]

Yes

[rancid cobalt]

What equation loves having all 3 parts of a right triangle, at least as variables

[zealous pike]

I've thought about x² + r² = 5 and guessing values for x, but I don't want to guess

[rancid cobalt]

Don't forget that c is squared too

[zealous pike]

Yea

[rancid cobalt]

So you have two equations now, right?

[zealous pike]

xr² = 36
x² + r² = 25

r² = 25 - x²

x(-x² + 25) = 36
-x³ + 25x - 36 = 0

[rancid cobalt]

and now we just gotta solve that!

[zealous pike]

[grave pond]

That graph strongly suggests there's an integer root ...

(Which you were probably expected to use the rational root theorem to find).

[zealous pike]

What's that theorem

Lemme search

So

The largest possible x is 4?

[rancid cobalt]

Yes, it seems that way

I might be further out of my lane here than I realized, so I'll just hope someone else comes to help with the next question

[zealous pike]

Is there a faster way to solve this?

[rancid cobalt]

I usually use graphing to solve two-variable systems of equations

desmos graphing calculator is my best friend

[zealous pike]

I can't use a calculator in an actual test though

[rancid cobalt]

oh. That's annoying.

Most tests I get have desmos built-in

You can't even use physical calculators?

[zealous pike]

No

[rancid cobalt]

rip

[tough vapor]

Thats strange

Even the simplest one? Thats bad

[zealous pike]

no

it is a test where I have to solve each of 90 questions in less than 3 minutes

hmm

[upper karma]

Guys i want to know more about
Astc rule

[grave pond]

I don't think so.
I suppose you could have metagamed it and said, if the solution is nice perhaps everything will turn out to be integers, so let's see what happens if the x/r/5 triangle is actually a 3-4-5 or a 4-3-5 triangle.
But that feels like it depends a lot on hindsight.

[zealous pike]

yea

gotta get myself used with polynomials then

[round charm]

Bro, that's the vertex. You can clearly see 4 getting intersected by the line.

So, that's the ez way x = 4.

[round charm]

HEY how about we use the pythagorean triplet formula?

Guys I found an easy way

[viscid nimbus]

zawg i'm just using differentiation for ts

[round charm]

We know that 2m, m²-1, m²+1 are pythagoream triplets. And the equation xr² = 36 suggests that x is a perfect square.

[viscid nimbus]

🙏🏼

[round charm]

Then, when I try to keep the known pythagorean number (5) in all the 3 expressions, we can see this:
m²+1=5
m²=5-1
m²=4
m=2

Then, 2m = 2*2=4

m²-1= 2²-1 = 3

Then 3, 4, 5 are the pythagoran triplet

put x = 4 and r = 3, then:
r² = 9
9 = 36/4
9 = 9

Hence, x = 4

👍

[autumn briar]

People

Is anyone here

[dark sparrow]

http://nohello.net/

http://dontasktoask.com/

if you have something to ask then ask it; otherwise the answer will be "no, this server has been deserted for many years now"

[autumn briar]

:/

I see

I've test tmrw of trigonometry
I gotta do 9 exercise
[ I missed the theory classes of this chapter due to health issues]
So I'm kinda cooked rn

I mean what could be the best way to study if you are in that situation
[Pls don't be like js study]

[dark sparrow]

review SOH-CAH-TOA and/or trig identities as applicable

if you're gonna get tested on the sine law and/or cosine law, review that too

know your basic trig values (0, 30, 45, 60, 90°)

these are the most important things to know

[autumn briar]

thankyou so much ive already reviewed it at all

Actually i sometimes sucks at math

how should i approach the questions of my book

Like the exercise

[viscid nimbus]

all of us do

[viscid nimbus]

what questions is it asking

[autumn briar]

Demonstrate understanding of trigonometric functions synthetically, graphically, and analytically.

Compute and manipulate trigonometric expressions confidently.

Apply knowledge of angles, quadrants, and signs to solve for unknowns.

Represent trigonometric functions visually.

Use trigonometry in context, especially with respect to measurements and problem scenarios.

summary of Half of the exercise

[viscid nimbus]

1. learn how to graph trigonometric functions, 2. learn your trigonometric identities, 3. learn the unit circle and connect it to 1., 4. is just 1. and 3., 5. apply your knowledge

2. will usually include proof of trigonometric identities using given trigonometric identities

such as pythagoras', reciprocals, sum, product, double-angle and half-angle

3. will usually include solving trigonometric equations, how to convert radians to degrees and vice versa and what an angle is in terms of radians according to the unit circle

[autumn briar]

Damn thankyou so much for all of it

Should i consider watching lectures?

Any yt channel or something you would like to include

[viscid nimbus]

i learned via the organic chemistry tutor

but you also need to do more challenging exercises outside of the ones he includes in his videos

because they are "introductory" and aren't the full scope of the exercises you will encounter

[twin depot]

Not the person but I really like this community college professor: math with professor V. She goes into detail and i like how she teaches https://youtube.com/@mathwithprofessorv?si=M-K9NEQrREhe4hf9. She has pretty much everything on a playlist including trig so you can see what you’re struggling with and there will be in depth explanations and a lot of examples.

[split lion]

is geomertry bad or good

THERE IS SO MUCH MATH

[dark sparrow]

geometry, just like all other fields of math, is morally neutral

[obsidian harness]

also there's the view that mathematics exists independently of our culture and society

so you can't really apply the labels 'bad' and 'good' to something that doesn't come from this world

[signal vapor]

Except for the fact that most people hate euclidian geometry

[grave pond]

I don't think so.

Perhaps Americans who (though a tradition for misleading schooling) have gotten the impression that Eucliean geometry inherently means two-column proofs and a ban on intuition.

[wispy whale]

Truth

Geometry is a simple topic yet when taught rigidly to an early student, becomes very unappealing

[zealous pike]

I'm trying to learn the intuitive part but for me it's being harder than the rigid/proof based one

[wispy whale]

https://cdn.discordapp.com/attachments/1333055289909313596/1396510515815120936/togif.gif

[pale sentinel]

I mean, #info message kinda states that the whole purpose of this server is to encourage learning

[that said, I do find it funny that the THINK poster's been sent three times in just over an hour ]

[wispy whale]

yo we're joking

😭

jokes aside avoid saying stuff like that in a channel like this, it may deter other learners if they see that someone has breezed through a topic they have a hard time understanding

[lone trellis]

hello, what do i need to know/learn for high school geometry

topics etc

[silent plank]

you can get a decent structure from khan

algebra,
definition of perimeter/area and the respective formulae for common shapes

parallel line theorems

[lone trellis]

alr

[silent plank]

coordinate geometry / basic graphing

[jovial maple]

Whats a free website that'll solve math all free

[autumn briar]

Thankyou so much

[autumn briar]

I really needed this tysm 🙏🏻

[autumn briar]

Alright

Ty

[warped osprey]

http://www.chatgpt.com

[viscid nimbus]

https://tenor.com/view/facepalm-soprano-really-gif-8277415

[patent dirge]

Guys need help with graphing sine and cosine functions rn 😇🙏

I don't understand a thing from my book

[restive solstice]

please provide the question

[dire jackal]

like you want to make the graph? or want to see the graph?

[patent dirge]

Naur

It's more of a discussion thing because I don't understand anything from the book

[patent dirge]

See the graph

Wait

Idk

[dire jackal]

use desmos for the graph

[vague current]

does the book explain using a unit circle or general function?

[patent dirge]

I will know how to graph

Once I understand the whole thing

[patent dirge]

Idk

Waot

Wait

1 and -1

Highest and lowest so like

90 and 270 that's what it wants me to remember

Anyway I'll send the pages

https://drive.google.com/file/d/1tiyIz1JYVSWX7lq3KUjoUlCp2WuX5vvS/view?usp=drivesdk

Y'all pls explain each pages cuz like

Also be wary of the terms.. I'm unfamiliar

[dire jackal]

need access

make it publiv

like anyone with link can view

[patent dirge]

Wait rlly?

[restive solstice]

seems like a unit circle

[patent dirge]

https://drive.google.com/file/d/1tiyIz1JYVSWX7lq3KUjoUlCp2WuX5vvS/view?usp=drivesdk

Try it again

[dire jackal]

same thing

[restive solstice]

access denied

[patent dirge]

.

[vague current]

usually I would explain a sine or cosine using a unit-circle with the 90° triangle like this: https://www.geogebra.org/resource/uvJq3wEm/LQpXDRXhqPeAvJC2/[e-mail] then move the point around on the circle and measure the length of sine and cosine. This is where you get the values from for the function graph...

[restive solstice]

I've requested access

[dire jackal]

same

[patent dirge]

Okay done

https://drive.google.com/file/d/1ExnHh1nYcp3st9fc-JQfzIFf9tj_7yM0/view?usp=drivesdk

Hereee

Y'all dm me the explanation

So it wouldn't get lost

🩵

Per page

[restive solstice]

dude this book is wierd

[patent dirge]

.

[dire jackal]

very weird way to teach the graph

never seen it before

[restive solstice]

yeah

i've learnt it from the unit circle

this book starts with physics

[haughty root]

[dire jackal]

same i think

[patent dirge]

Oh-

So like..

[dire jackal]

i dont remember though

[vague current]

we start with the unit circle and then move on to physics... did you understand the unit circle @patent dirge and the other essentials mentioned on page 1?

[patent dirge]

Yesss

Ik the unit circle

Sine and cosine functions at that.

[restive solstice]

the rest is easy then

[patent dirge]

But I'm here at graphing which I don't understand

😭

and I'm supposed to answer something

And I can't answer unless I understand the book

PLS

[dire jackal]

like page 5?

[restive solstice]

the book has made it complicated

with formula and stuff

[vague current]

do you understand the definition of amplitide, domain/range, period, vertical and horizontal phase shift?

[restive solstice]

Do you have a teacher?

[dire jackal]

for range use this formula ig

[restive solstice]

range is easy

[dire jackal]

ye

[patent dirge]

WAIT SOMEONE DMED ME I IGNORED IT ACCIDENTALLY

Whoeger u are pls dm again

U have a dog pfp

[patent dirge]

What

[patent dirge]

No

That's the thing

It's new to me

Help

I haven't read the book yet

[dire jackal]

you need to learn functions in general first

[obsidian harness]

if you understand transformations it should make sense why

[restive solstice]

dude, try to get a physical teacher

because you're struggling with the basics

[obsidian harness]

the range of sin(anything) is y in [-1, 1]
multiply that range by a, when a > 0 and you get [-a, a]
and then add k to both, so [k - a, k + a]

[obsidian harness]

or try Khan Academy first

[restive solstice]

basically, get this basics right first

[dire jackal]

range is basically all the values the function can have

[vague current]

ok, maybe a more visual approach helps... amplitude=how much difference between maximum and minimum divided by 2, period: how long before the function repeats itself, phase shift: how is the function graph moved up/down or left/right compared to the sine you know from the unit circle

[obsidian harness]

yeah the best thing is some textbook/book to go through the material properly

[dire jackal]

and domain is all the values x(in this case theta) can have

[obsidian harness]

YouTube, for instance org chem tutor, isn't a bad source

[patent dirge]

Omg..

[patent dirge]

Tried na

This one I tried

[obsidian harness]

oh because this question is asking you about how to identify the amplitude, domain/range, period, vertical and horizontal phase shift?

[patent dirge]

It's kinda ironic

[obsidian harness]

yeah the question isn't asking you about how to graph trig functions

[patent dirge]

Ik how the unit circle works and cosine functions applying to unit circle

YET

I don't know how to graph

Oml

[dire jackal]

you dont need to make the graph for the questions

[patent dirge]

Yes

For instance

This looks positive

But because of the shift

It's negative

Like what

😭

[obsidian harness]

what is your book using as the reference/default function?

sin or cos?

[restive solstice]

@patent dirge check your DM

[dire jackal]

are you, by any chance indian?

[patent dirge]

Idk Haven read

[patent dirge]

Oh yea this

We mainly use

Sin and cosine

[dire jackal]

since we add na at the end of responses a lot

[obsidian harness]

um, the answer to my question can't be both

either your book starts the transformation from sin(x)

[patent dirge]

Idk

[obsidian harness]

or it starts the transformation from cos(x)

[patent dirge]

I sent the file

😭

[obsidian harness]

and the file doesn't have this information

sigh...

[dire jackal]

@patent dirge

[patent dirge]

No

side eye

[dire jackal]

oki

since if you were i have great lectures in hindi

[patent dirge]

.

[dire jackal]

thats why i asked

[patent dirge]

.

Okay but like

Is the book great for learning how to graph

Cosine functiona

[obsidian harness]

I'd say it's decent, yes

[obsidian harness]

wait, do you understand that if I start with y = x^2

then I do y = (x - 5)^2

the new graph is translated 5 units right and not 5 units left?

[patent dirge]

I-

I'm trying to do it visually rn

[obsidian harness]

instead of trying to follow the whole function, follow the vertex

so the vertex of y = x^2 is (0, 0), do you agree?

[patent dirge]

Do I have a choice

Actually

[obsidian harness]

it seems like you haven't learned transformations of graphs right

[patent dirge]

This is an independent learning thing

Because of the weather issues, classes are cancelled right.. and we are tasked just to read the book and answer the supplementary learning

That's the thing.. without a teacher I'm flopping

And the independent task is due tomorrow

Can I send videos here

[obsidian harness]

yeah

I'm not sure how I can help after all this so I'll just leave you for now

[patent dirge]

Okay I'll send what I understand and giv me feedback

ExcUSE my native language

I'm also like sending these to my friends

[vague current]

do you understand the explanations here? https://www.youtube.com/watch?v=EIS-tWnVWAo

[vague current]

ok, so you did unterstand amplitude and period. Now you have to look at the function f(theta)=1+cos(pi\cdot theta). If you move this around you get f(theta) = 1*cos(pi\cdot(theta-0))+1 which is the same form ad y=Asin(k\cdot (theta-b))+c

[patent dirge]

I'm rewatching organic chem rn

I'll watch that after

[patent dirge]

Will ur video help me with that?

[patent dirge]

Yes ik the explanations from the picture

C is the horizontal phase shift

And d is the vertical shift right

So for horizontal ofc left and right

For vertical up and down

The shift is like the central line

This part is really complicated

Oh nvm

lol got it now

[hollow remnant]

Can anyone help me quickly with a sinusoidal question? I just need the answer also it’s a word problem

[dire jackal]

!da2a

[lime crown]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[proper peak]

I made a simplified proof to solve for the identity sin(beta-alpha) or any other sine subtraction equation. It only uses some basic geometry like congruence, some geometry around isosceles triangles, the d(P,r) formula, sine law, the unit circle.... Basically anything you would see up until your 10th year of school (excluding complex numbers).

[mystic umbra]

its a nice proof 👍

do you know how to prove it using vectors? it become extra-simplified when you use them

[haughty root]

[ashen sentinel]

i love geometry so much
i got 8/20 in my math test just cuz of not being able to do geometry

[civic rock]

geometry 😈

[blissful cypress]

anyone got any advice to get better at trigonometry

sorry if it's a dumb question

[upper karma]

I know this might not be alot you should master the basics Soh-Cah-Toa
then id suggest to learn the values for sin, cos, tan at 0⁰ to 90⁰ master it by using the unit circle
And just practice some simple problems and remember you should always try to learn not memorize

[random onyx]

oh man where do i even start

[dark sparrow]

do you know your trig identities?

[random onyx]

yeah

[dark sparrow]

do you know any ones to do with cos(A ± B)

[random onyx]

do i want to start with given one or the tan one

[random onyx]

ko i try

[dark sparrow]

you always start with the given

[random onyx]

gow its that easy

[random onyx]

alright

feel so stupid rn

[spring basin]

i have the answer

[random onyx]

im stuck at every single question wtf

where do i start again

[dark sparrow]

well you might wanna expand sin(A-B)

that should give you some ideas for how to proceed e.g. how to get your hands on sin(A)cos(B)

[spring basin]

i think i got it

nvm

[random onyx]

yeah and i got lost immediately right after

i dont recall anything that changes multiplication to addition

[dark sparrow]

ok well your goal is sin(A)cos(B) - cos(A)sin(B) yes?

[random onyx]

ye

[dark sparrow]

so let's set that aside for a moment

now here is a crazy idea that's actually going to cook:

take the equation sin(A) + cos(B) = m

and square both sides.

[random onyx]

ohh shitt

im so rusty what the hell

[dark sparrow]

did you manage to proceed?

[spring basin]

i have a different method

[dire jackal]

what if you multiply m and n?

[random onyx]

yeah

[spring basin]

you'll get a messy expression

[dire jackal]

youd have the terms you need plus some extra

[random onyx]

u get one part thay can be written as sin(A-B)

and some extra terms u really dont want to see

[dire jackal]

ig yea cosacosb and sinasinb

[random onyx]

also not a good approach since its just too random

[dire jackal]

oki

[random onyx]

yeah?

[spring basin]

wait nvm it's garbage

it still depends on B

[haughty root]

[night cape]

going to ask a silly question

but do i need to know my geomatry well before learning trig properly

[obsidian harness]

yes and no

know all your geometry relating to triangles well, because the focus of trig is how triangles relate to the unit circle

so definitely revise the special triangles, the 30-60-90 and 45-45-90 ones

but a lot of the 'proof', like two-column proofs, is totally unnecessary for trig

[night cape]

oh awesome ok

sweet

so which subject teaches the principles of angles

i assume trig

[obsidian harness]

also observing similar right triangles is super useful in trig

[obsidian harness]

geometry, actually

so all of that angles in parallel lines material belongs in geometry

it does help in trig but there's no shame in looking it up if you've forgotten

maths does tend to build on itself like stacking up a brick wall

but those concepts aren't the main focuses of trig

[night cape]

perfection thank you so much

the main reasons i want to know is because of linear algebra

where certrain transoformations require angles and im shit at angles

[obsidian harness]

well if you're talking about linear algebra

it's not about angles specifically! it's about transformations that rotate and stretch the plane (while fixing the origin)

for those rotational transformations yes trig is very important

[obsidian harness]

but it doesn't relate to angles in this context

so honestly just leave geometry behind if you're ready

[night cape]

ohhhh so the sin60 and all that

[obsidian harness]

I think that the book Linear Algebra Done Right by Axler also has a foundations chapter at the very beginning

[night cape]

thats not geomatry

[obsidian harness]

that's trig

[night cape]

oh sick!

[obsidian harness]

it is a part of geometry yes but taught separately

[night cape]

then is there really anything i need from geomatry or can i just focus trig?

[obsidian harness]

just focus trig I'd say

[night cape]

perfect thank you south

[obsidian harness]

if you're really missing anything don't be afraid to look back and revise if you need it

but that's on a "if you need it to understand trig" basis

[night cape]

of course I did that with algebra

[obsidian harness]

np!

[night cape]

went all the way back to 4th grade for that one

and now i understand equations, kinda haha

[proper peak]

For the sine identity I haven’t learned anything that really comes to mind as sufficient enough to prove it, I figure you’re talking about matrices and matrix multiplication or something else of the linear algebra field. I made this proof based only on my current knowledge of mathematics up until the 10th year (here it is 4th year of high school Belgium, mostly ages 15-16). I will be teaching myself some new stuff this summer.

[obtuse moth]

Where is a good place to get a really complete understanding of trignonometey before starting calculus?

I checked the pins but I dont see much

[deft sail]

Hmm

So when I learned Trig, I didn’t really learned it in school so I have no textbook

[obtuse moth]

I bought algebra and trigonometry by sullivan but I think the book is too slow paced for me as I learned a decent bit of trig and algebra from hs

[deft sail]

But I used Professor Dave’s Playlist and an app that has Trig on it

[obtuse moth]

I would also want to get a better understanding of algebra

[deft sail]

Don’t use the app

[deft sail]

Okay

[obtuse moth]

But im decent at algebra, I just want to learn trig better

Before I start learning calc

[deft sail]

Yeah I would just use Professor Dave’s math playlist

[obtuse moth]

Thanks man

Are there any places where I can find practice problems with solutions?

[deft sail]

No prob, and just in case he doesn’t have precalc to my Knowles

[deft sail]

Good question! Give me a sec.

[obtuse moth]

Would be cool if there was a site with practice problems for all branches of math

[deft sail]

On what I know, unfortunately not :(

But there was one website

[obtuse moth]

Thats okay!

[deft sail]

I just don’t know the name

[obtuse moth]

Thank you for the advice regardless

[deft sail]

You’re welcome

[modern wharf]

there is a nice one though, the art of problem solving i think

[obtuse moth]

This is a series of books

[modern wharf]

huh?

[obtuse moth]

AOPS

They are books

If im not mistaken

[modern wharf]

there is a website and a trainer on there

alcumus

i used it quite a bit and it’s pretty nice

[obtuse moth]

Ohhh I see

[green latch]

https://tenor.com/view/sinewave-sineline-sine-gif-22707024

hello fellas

what a great day to be an engineer+math major]

[rich wagon]

not sure if this is the right place to ask for this so please correct me if this is wrong. But is there a way to get desmos to give me this number as the fraction pi/2?

[wintry ibex]

great

[pale sentinel]

I don't think so.

[rich wagon]

yikes

why can it convert some decimals to fractions and not others though

but then I add 1 more digit

and it wont work

[pale sentinel]

Because pi is definitionally not rational

So it can't be written as a fraction

Further, it has a memory limit

[rich wagon]

but it can be written in ways like (2pi/4)

[pale sentinel]

Again, PI is not rational

So neither is any fraction a*pi/b where a and b are integers

[rich wagon]

so desmos just isnt good enough to convert it?

because can't like AI calculators do it

[pale sentinel]

All AIs are merely interpolative

[rich wagon]

interpolative?

[pale sentinel]

And further, MLM AIs are just interpolative of written works

As in, they take in shitloads of written works as a corpus of information, then respond to a prompt in a manner that mimics the corpus

[rich wagon]

hmm

ok got it

[pale sentinel]

So if the corpus contains shitloads of "sin pi = 0", then when you ask it to evaluate sin pi, it will give you 0

[rich wagon]

would still be so nice if calculators could do it

[pale sentinel]

This is the crux of using AI here

[pale sentinel]

Also - you gotta remember this - humans built the calculator

It's no divine entity

This is why maths is still a school subject after thousands of years

[rich wagon]

sure feels like it sometimes

[grave pond]

That's why it's important to learn how the calculator does it, to demystify it at least a little.
Unfortunately, understanding how calculators handle trig functions (in the sense of "how can we be sure the results it gives are right") takes a lot more mathematics than it does to learn to use trigonometry for ... um ... "practical" tasks.

[hybrid pivot]

Hey Here is simple task May you solve the problem. That's easy
It takes for two minutes.
a + b = a * b ===>>>> a != b ~~a ,b ??

[native pier]

!topic and also please don't post the same question in two different channels

[lime crown]

Please read the channel description before posting, and stay on topic.

[visual flume]

geometry is so tuff

anyways is this a good idea?

my 7 y/o brother cant hop off roblox
i set his time limit as fibonacci sequence
i told him its the first few terms of the fibonacci sequence (there is no way he is able to spell it out in the next 2 years)
i wrote down the formula for it
if he figures it out by the end of this month he can play whenever he wants
if he doesnt im changing the psw

[native pier]

!topic — this probably belongs in #discussion or #math-discussion

[lime crown]

Please read the channel description before posting, and stay on topic.

[dark sparrow]

did you mean LLM

[knotty quiver]

does LLM mean Large Language Model?

if it does, could there be a Medium Language Model and that's what MLM stands for?

the closest relevant acronym i can find online is Masked Language Model

[upper karma]

yes

[mossy mirage]

hi can anyone help me prove this identity

[dark sparrow]

what's your progress so far?

[mossy mirage]

oh someone helped me solve it already in the help section but thanks

[dark sparrow]

ok then don't multipost

[mossy mirage]

sorry 😭

[agile glen]

IF U DONT MIND CAN I GIVE TELL U MY APPROACH

[edgy wagon]

Why is the altitude of 30*40/50?

[pearl hinge]

Try proving that triangle ABD and triangle BDH r similar

[pearl hinge]

That's how they got what they got

[edgy wagon]

Ahhh,

That makes sense,

Thank you!

[pearl hinge]

Np

[glossy flare]

<@&286206848099549185>

[native pier]

!1c

[lime crown]

Please stick to your channel.

[clear sleet]

what web is this?

[edgy wagon]

Alcumus,

It is on the AoPS website,

https://artofproblemsolving.com/alcumus/problem

[jagged sonnet]

Hi, not asking help for any specific question but more so on like how I'd study this topic, if I needed to learn the unit circle what's the best way to tackle it? I've always struggled with it

To solve like questions like these or anything that needs trig

[silent plank]

start with learning how to derive the ratios for the special angles

that pretty much gives the first quadrant of the unit circle

you can get the rest of the unit circle from reflections

which also gives you the supplementary and odd/even identities

(also learn the conversion between radians and degrees)

[twin depot]

I literally replayed ts for a whole hour and then had it memorized😭

Lowkey a banger

Or you could use the finger trick (if you have 6 your fucked😭 /j)

https://youtu.be/1RJ-DIwxdqQ?si=fZyZstvqj0GRFIbs

Like what Rauomenganato said as long as you know the first quadrant then you can figure out the rest

[haughty root]

[solid needle]

honestly just learning your special triangles and how sin and cos actually work is way easier than memorizing these values

youre just making more work for yourself and not understanding the material as well in the process

oh that is what you're saying, nvm

[dense escarp]

Is this channel for general discussion of geometry? I’m new

[civic rock]

yes

[slow pasture]

the fuck is wrong with yall

i just memorized it

by hard practice

[twin depot]

Same😭

Seeing shit when I needed the most is crazy

[slow pasture]

do what i did

2500 hours of math

[twin depot]

https://tenor.com/view/взгляд-2000-ярдов-война-war-soldier-gif-3632617944134077161

[slow pasture]

will skill you up

[slow pasture]

it was good tho

[twin depot]

Grinding through my precalc book🫩

[slow pasture]

oh no americans

😔

im israeli.

our edu system is at the rubble

[twin depot]

I don’t like being American😢

[snow tide]

yo theres such a short method just divide by cos and u get cosx/(1+sinx) and then rationalise and its done in 3 lines lol

[slow pasture]

just memorize.

i remember 30 and 60 together.

[dense escarp]

Book name please?

[snow tide]

why memorize a identity that doesn't even come many times

[slow pasture]

it does.

[snow tide]

ik like 100 diff identities but the useful ones smh

[slow pasture]

proceed mathing.

[civic rock]

either memorize by experience if you have good memory
or just do the hand trick or whatever trick if you struggle to remember

[twin depot]

You can find a free one by openstax but I am currently learning from this one. I like it a lot lots of practice problems

[dense escarp]

Cool thank you

[snow tide]

oh yeah? bro this is a garbage identity what you on😭

[twin depot]

Do whatever helps you🤔

[dense escarp]

When did you guys start studying mathematics?

[slow pasture]

everyones accepted dw.

[slow pasture]

last year

[dense escarp]

Cool

[slow pasture]

im now doing a degree lmao

[dense escarp]

In maths?

[slow pasture]

mhm.

[dense escarp]

Sounds cool

[twin depot]

When my 7th grade teacher was absolutely terrible at teaching (I barely passed my state exam😭 and many of her students failed and most of them were hard working) I hated math but my algebra 1 teacher the next year made me love it a lot cuz she teached well and I guess now few months later I’m learning something what I hate now I love😂