geometry-and-trigonometry

[foggy swallow]

though i still feel something is wrong

no nothings wrong

mb

it correct

was this correct?

way?

is this the way you were talking about?

as the tan thing u said i didnt get understand it one bit Ann

[dark sparrow]

gonna show you what i meant when i get home

[foggy swallow]

ok Ann!

[lost lichen]

my way:
u take cos(t)-sin(t)=k

then sqaure both eqn

square*

add them

[dark sparrow]

oh yeah lmfao i completely forgor about this

[lost lichen]

and boom u get k

[dark sparrow]

@foggy swallow

[sly urchin]

Sometimes I see people "bash" geometry problems with complex numbers, what would I have to study to be able to do that?

I know what complex numbers are and how to do basic operations on them, but that's about it

[warm shuttle]

I think https://en.wikipedia.org/wiki/Euler's_formula is the main culprit

[dire jackal]

wdym by 'bash' geometry?

[sly urchin]

Like overkill, idk how to say it, bash seems to fit

Like if a geometry tells you to calculate a length of a segment, but you just use coordinates to calculate it without really using many geometry properties

https://brilliant.org/wiki/complex-numbers-in-geometry/

This wiki shows what i'm talking about

[grave pond]

Know 2D vectors; complex numbers are a premium version of those. Be sure you're familiar with the geometric interpretation of the complex multiplication (rotate the plane and then scale it), and you can move between that and the algebraic viewpoint without getting confused. Together with Euler's formulas that should be all you need for bashing geometry.

[sly urchin]

Thanks

[foggy swallow]

took me a while to realize how finding tan proved it , what you did was find tan on both equations if its value were to match then H.P , Though I dont understand why did you rationalize it? it changed the value shouldn't that be against the rules?

[dark sparrow]

H.P

what

also no? rationalization doesn't change the value (if done properly)

[foggy swallow]

i mean that if tan's value were to match we could say the equation if valid hence proved

right that's what you were aiming for right Ann?

but i dont understand why did that (root2 + 1) become 1/(root2 +1)

explain how you converted it

[dark sparrow]

oh so i guess H.P. is indian english for QED

[foggy swallow]

ig maybe yeah

[dark sparrow]

i do not see where you found $\frac{1}{\sqrt{2}+1}$ converted into $\sqrt{2}+1$ though.

[somber coyote]

Ann

[foggy swallow]

step 7

[dark sparrow]

i wrote $\frac{1}{\sqrt{2}+1}$ as $\sqrt{2}-1$, note the minus sign --- and these values \textbf{are} the same.

[somber coyote]

Ann

[foggy swallow]

uh my pc shut down

could you explain these steps?

[dark sparrow]

divide by (sqrt(2)+1)cos(t) on both sides

then rationalize (with a bit of un-clarity on my end)

$\frac{1}{\sqrt{2}+1} = \frac{\sqrt{2}-1}{(\sqrt{2}+1)(\sqrt{2}-1)} = \frac{\sqrt{2}-1}{(\sqrt{2})^2 - 1^2} = \frac{\sqrt{2}-1}{2-1} = \frac{\sqrt{2}-1}{1} = \sqrt{2}-1$

[somber coyote]

Ann

[foggy swallow]

Ann its going completly over my head what i dont under stand is the conversion of (root2 +1)sin(t) to a fraction

i might seem dumb but im not smart enough to just understand things in one go especially when i started trignometry today morning

[dark sparrow]

divide by (sqrt(2)+1)cos(t) on both sides

[lost lichen]

tell me what part do u not get?

[dark sparrow]

from $$\cos(t) = (\sqrt{2}+1)\sin(t)$$ divide both sides by $(\sqrt{2}+1)\cos(t)$ to get $$\frac{\cos(t)}{(\sqrt{2}+1)\cos(t)} = \frac{(\sqrt{2}+1)\sin(t)}{(\sqrt{2}+1)\cos(t)}$$ cancel (or in your words, ``cut'') common factors on each side to get $$\frac{1}{\sqrt{2}+1} = \frac{\sin(t)}{\cos(t)}$$ then follow what i've already written

[somber coyote]

Ann

[dark sparrow]

[LHS cancels cos(t); RHS cancels sqrt(2)+1.]

[lost lichen]

did u actually type this?

[dark sparrow]

yes

[lost lichen]

mad respect

[foggy swallow]

ok Ann I get it I will improve my vocab

T-T

tho thanks i got it

hey is it possible

that if i were to divide both sides by cos

and then cos/cos =1 and (root +1)tan

and than send root2 +1 to the dinominator

[dark sparrow]

you swallowed like half the symbols there mate 😭

[foggy swallow]

to lhs

[dark sparrow]

i mean sure you could do that

[foggy swallow]

num num num

[dark sparrow]

you do in 2 steps what i did in 1

nothing fatal about that

though i dont like "send to denom"

[foggy swallow]

i think your way was more proff

so imma stick to it

thanks alot for the whole day

also Ann we probably live like on the other sides of the hemisphere

dont you sleep?

[dark sparrow]

it is 18:30 here at the moment.

[foggy swallow]

9 pm

damn

[dark sparrow]

ok so you are 2.5 hours ahead of me.

in india, by the looks of it.

[foggy swallow]

yare yare

[dark sparrow]

i am in eastern europe, so we're not really diametrically opposite.

[foggy swallow]

true

should have known when u said mate

um sorry but i have to i sleep at 10 pm and blue light bad so i cant use my pc

bye and thanks alot "Ann of Maths" 🥷

hope you can help me more in future

[pale sentinel]

tbh I think this is the only country with that UTC, so...

[foggy swallow]

do you by chance hold a prejudice towards india?

[pale sentinel]

As I mentioned, it's a deduction from your timezone, nothing more to that

[dark sparrow]

no i dont

india just famously has a half-hour timezone

[foggy swallow]

Ann clearly guessed it from my HP XD

[dark sparrow]

australia has half-hour timezones too, but they're further east

i have experience seeing indian people here

a lot of indian people in fact

[foggy swallow]

lmao

[pale sentinel]

We all do

[dark sparrow]

so it is just accumulated observations

nothing more than that

[foggy swallow]

um if you dont mind

i saw your profile and you seem like a well achieved person(my bad habit of guessing a person by their personality, tho im mostly right)

and yet your solving petty queries of fellas like me

is it ok for you to use your time on my doubts?

if yes what good does it do to you

(im not trying to be aggressive its just i like to have information)

oh it seems I might been too straight forwards apologies for that never mind my interrogations

hehe bad habits : D

[calm juniper]

I'm sure you are confused about what you're saying! 😂

[marble oriole]

Okay there’s the normal way of creating a parallel line above line l

Okay and then there’s this

How is this not simpler

Instead of having to draw 3 whole circles just to get a line

Draw one. Extent BC and AC

By definition is must be a parallel line since the extension is equal to the length of AC and BC because a perfect circle from the middle has equal distances to the outside from the whole way through

[stone latch]

Gyat

[marble oriole]

Gyat wat

[ancient flame]

What’s x?

[scarlet swan]

30

I think

@ancient flame

[sharp oracle]

Going in for math 2 and math 3 for hs 9th grade next week

anything i should know

[ancient flame]

Thank you

[foggy swallow]

today i will study trignometry for 4 hours wish me luck

[dark sparrow]

don't burn yourself out

[jovial beacon]

hi chat

[azure rivet]

inverse trigno?

[foggy swallow]

its alright i have today off

also i like studying maths

as its hard

[midnight wolf]

dont stress on it those maths are fine if you pay attention in class

for math 2 memorize everything

lot of proofs

[dark sparrow]

not sure i would get behind the advice of "memorize everything"

[simple vigil]

Memorizing everything?

In maths

Each question is a new one apart from formula we can't memorize anything

[obsidian harness]

you can memorise procedures to answer certain types of questions

figuring out what the question is asking is half the battle

[simple vigil]

That's for like question which are very hard

[simple vigil]

It takes time to map how you are going through ratios

How you convert them

[obsidian harness]

what?

[simple vigil]

No i want to say

You have to create a map first how you are going to solve a question

[pale lance]

.

[marble oriole]

If you understand something you never have to memorize it

[dark sparrow]

memorizing formulas is also something you should be very careful with

ie dont do it blindly

[simple vigil]

is x = 60

? (my answer)

[grave pond]

Hmm, is it clear that the A1-A13 chord goes through those two internal points exactly?

(The lower one yes, by reflection in A5-A14).

[distant wedge]

Is this grade 10 level geomtry or harder?

[obsidian hornet]

Its not clear, but can be easily proofed using trig cheva and monotony of the acute sine function

[grave pond]

"Cheva"?

[obsidian hornet]

Yes

[young osprey]

is this where i get help for geometry

or no?

[spiral lodge]

Yes

Or also in the single help-channels if you want

[ancient flame]

It's 30

[ancient flame]

What is something wrong?

[mild quartz]

yo guys, i have a summer geometry finals in a few days, its 50 questions all multiple choice (thank god), what main topics do you think i should study (by priority or hardness, etc.)

i have attached an image of the topics, thanks, also, i really struggle with transformations, anyone have some helpful resources?

we get a formula sheet for all the perimeters and areas of shapes so i dont think i really need to be studying that but yeah, thanks for the help

and by a few days i mean like 3 days 😬, i have practically studied most of the things but i just want to review and i thought it would be a good idea asking you guys

[jovial beacon]

hi chat

how do yall memorize trigonometric relations quickly

like sine of x is equivalent of minus cosx in certain quadrants

[scarlet swan]

idk

[grave pond]

Either by visualizing the unit circle or visualizing manipulations of the graphs.

[twin depot]

Mostly practicing

Like the more questions you do the more it will be on your head

[grizzled lion]

them fuckass proofs 😭 those actually suck so bad maybe sohcahtoa if needed

just get papers w all the formulas it’ll help a lot

[topaz vapor]

I found ways they’re similar to each other and just wrote every single one on paper repeatedly till I remembered them

probably not the best method if u wanna remember them fast, but I got them down in like 1.5-2 hrs

Double, half, Pythagorean, sum/differences

I think those are all I did

[upper karma]

is there more information?

[obsidian harness]

see if you can follow this unit circle derivation

the y-coordinate of a point on the unit circle is the sine of that angle
the angles theta, 180 - theta have the same y-coordinate (height)
hence sin(theta) = sin(180 - theta)

similarly, cos(theta) = -cos(180 - theta), cause to the right is positive but to the left is negative

[visual sapphire]

if anyone can come help me in #help-36

that would be amazing

[obsidian harness]

about to be resolved

[lusty jay]

Hello, can anyone recommend good study material for Math CSET subtest 2 and Multiple Subject CSET 2?

[arctic magnet]

Hello. Don't know if it seems silly. Can anyone please help mw to solve this?

[worthy eagle]

If you find the red angle, you can get green angle, then you can get ACB

you have to think how to get the red angle DHC

[simple vigil]

68 is answer

[pale badger]

How to check it, i forget it

[simple vigil]

End of the book

Which book is this

?

[obsidian harness]

,calc 360-90-35-106

[somber coyote]

Result:

129

[obsidian harness]

,calc 180-129

[somber coyote]

Result:

51

[obsidian harness]

,calc 180-61-51

[somber coyote]

Result:

68

[obsidian harness]

checks out

[arctic magnet]

Can you explain it please?

[simple vigil]

Rn

Can I do tomorrow I am on bed and just going to sleep

[upper atlas]

So. Angle DEF + angle EFD + angle EDF = 180. You get ang EDF

And you get angle DGH as angle DGH + 106°=180° (straight lines)

Now you know the red dot. Rest is up to you. Focus on triangle DGH

[short forge]

Hello

[worthy eagle]

I was having physics lecture and suddenly got enlightenment I somehow got understanding of i(iota) and searched physical meaning of i, multiplication (like 2i), addition(like 2+i). It all makes sense now , previously I thought we just invented i to satisfy some equations.

[velvet pond]

since DE an AB are parallel, this means that the measures of ABC and DHC are the exact same, then from the combined angles of the quadrilateral GHEF we get 360-(106 + 35 + 90), which leaves us with 360-231 which gives us the measure of DHG, which is 180-129 = 51, and since DHG = DHC = ABC, this means that ABC is also 51, then by subtracting like so: 180-(51+61), we get the answer, which is 68!
Hope this helps

[simple vigil]

i^2=1 knew this since class 8

[dire jackal]

i^2 is not 1 its -1

[velvet pond]

i = sqrt(-1), hence i^2 is -1, not 1

[mighty arch]

Can anyone message me and help me with my geometry its literally the basics

[quasi eagle]

20

[granite umbra]

blud was misinformed

[inland roost]

https://tenor.com/view/einstein-gif-18349346

[simple vigil]

Typing error

My mistake

i^2=-1

[dark sparrow]

<@&268886789983436800> offtopic/inappropriate image

[green lodge]

How do i draw this? The answer is 1.02m

i only need help with making the diagram, my brain cant comprehend this rn

wait nvm i drew it and still dont get how to asnwer this 💔

[zealous mountain]

How do I find the angles of sin cos tan without memorizing?

Any methods to commit the calculation?

[arctic magnet]

Tysm

[zealous mountain]

Where did you bring the question from?

[quasi eagle]

I made my diagram and ended up getting 3.11m

[simple vigil]

What do you think which class question is this

Should I be able to solve this as a class 10 student

[dark sparrow]

wdym by "angles of sin cos tan"

[arctic magnet]

I got it from my mate

[arctic magnet]

Yess.. It helped me a
lot. Tysm

[velvet pond]

need assistance?

[simple vigil]

you need to remember i think sin only

which is
0 -- 0
30 -- 1/2
45 -- 1/root 2
60 -- root3/2
90 -- 1

cos is just reverse of this

and tan is just SIN/COS

[obsidian harness]

not the inverse

the reverse

[simple vigil]

sorry

my mistake

[obsidian harness]

also sin(0) = 0 and sin(90) = 1

[simple vigil]

my maths just slipped

no that's why i know everything in application chapter

but still got 6/10 in test

[green lodge]

grade 11 math but this is an easy topic

[simple vigil]

as a respected class 10 student

I approve it's not our type of questions

[obsidian harness]

it's creatively worded but the thing they're asking you to do is super simple

this is actually how a textbook problem might appear in the real world

same problem, but you can see why it might be useful now

[whole sequoia]

is there a book w methods on how to get better at word problems

[night holly]

https://tenor.com/view/einstein-gif-18349346

[dark sparrow]

@bitter solstice so you mentioned in #discussion you're having difficulties with trigonometric equations

do you still want some help w/ that or what

if you do: show some examples of questions that you struggle with

[hard fox]

Ronaldo Teaches Math

[dull ore]

Idk where to put this so is saying N ∈ W ∈ Z ∈ Q ∈ R true?

[dark sparrow]

no

you're probably looking for ⊆ (subset) symbols there

also using W and the name "whole numbers" for naturals with zero is stupid but thats a different convo

[dull ore]

like the whole idea of whole numbers being natural numbers but with a 0? if so i think so too lol

[dark sparrow]

i mean like "naturals with zero" is a useful set to talk about but calling it "whole numbers" and reserving an entire letter for it is undeserved imo

[dull ore]

day 1 geometry notes from edwin’s geometry book

[dull ore]

for sure lol

[dark sparrow]

better to write it as $\bN_0$

[somber coyote]

Ann

[dull ore]

i have to gts my head hurts so bad from trying to understand geometry

☹️

all this just made no sense and gave me a headache but i got it down atleast

[simple vigil]

Same here while doing geometry

[simple vigil]

BTW guys how much trigo i should study in class 10

if any indian is here

[vocal quail]

IM INDIAN TOO

CLASS 10 HERE

[outer dawn]

Hello, could anybody help me with this circles question? Two parallel chords of lengths 30cm and 16cm are drawn on the opposite sides on the centre of a circle of radius 17cm. Find the distance between the chords. I really do not understand this sum.

[frail talon]

Does this diagram help?

[manic swan]

enough to understand it

def read about the unit circle

its not there in the ncerts and its a travesty

[dull ore]

Unit circle is easiest thing in trig id say

all you have to remember is 3 points essentially

[distant wedge]

In seven-sided polygon MNOPQRS, segment PQ is parallel to segment MN and all interior angle measures are less than 180 degrees. The measure of angle Q is 98 degrees, and the measure of angle M is 113 degrees. What is the sum of the measures, in degrees, of angle R and angle S?

Good luck

there is two appraoches for this

one quicker tha the other

[meager raft]

any idea how to solve this? dont know where i went wrong. im stumped

[haughty venture]

How hard is Trigonometry?

[hoary gulch]

May I inquire some help with my geometry homework?

I’m stuck on this one problem and I get different answers by doing it two correct ways. (If that makes sense)

It’s number 15

[graceful palm]

i gotchu vro

[hoary gulch]

Thx

[graceful palm]

Alright so what do you think MR is?

[hoary gulch]

I got two different answers

[graceful palm]

There should only be one for MR!

[hoary gulch]

Ik

[graceful palm]

So?

[hoary gulch]

Are you asking for the answers I got?

[graceful palm]

Let's move back a bit, which part are you confused about.

[hoary gulch]

This what I have down rn. But I’m confused abt how I got two different answers depending on if I subtract 2.5 over or if I subtract 1 over.

[stray trail]

r u asking for 15?

[graceful palm]

Here's how you should think about it.

[stray trail]

i got the answer

[graceful palm]

MR = MN + NR

Meaning 5x-3 = 2.5x+x

With me so far?

[hoary gulch]

Yes

[graceful palm]

That will be: 5x-3 = 3.5x

[graceful palm]

Hold up

[stray trail]

dude?

[hoary gulch]

?

[stray trail]

did you get me?

[hoary gulch]

How you get 3.5

[stray trail]

2.5x + x

3.5x

[hoary gulch]

Yes but I’m taught to subtract one over to the other

For example 2.5 - 1 = 1.5

[stray trail]

3.5x=5x+3
-5x+3.5x=3
1.5x=3
x=3/1.5
x=2

there you go

[stray trail]

both works

[hoary gulch]

But depending on if I do 2.5 - 1 or 1 - 2.5 I get different answers

At the end I mean

[stray trail]

nah dude

see this

[hoary gulch]

I get 6.5 or -3.5

[stray trail]

2.5x-x
1.5x=5x-3
-5x+1.5x=-3
3.5x=-3
x=-3/3.5 * 10
x=-30/35
x=-6/7

this is wrong

[hoary gulch]

This what I get at the very end

That’s if I go with 2.5 - 1

I then get 2 1/6 if I go with 1 - 2.5

[hoary gulch]

I didn’t get that

[graceful palm]

Guys i'm back.

[stray trail]

x-2.5x=5x-3
x-2.5x-5x=3
-6.5x=3
x=-3/6.5

[graceful palm]

wtf

Did u guys do the problem?

[stray trail]

bro did u minus the coefficient on x?

[stray trail]

i did

[graceful palm]

What did you get?

[hoary gulch]

Yes bc that’s what I was taught

[stray trail]

but he got a diff ans

[stray trail]

2

[graceful palm]

x=2 right?

MN = 5?

[stray trail]

yes

[graceful palm]

ight

@hoary gulch what are you confused on

[hoary gulch]

I got x = 1 1/6 or x = 2 1/6

[stray trail]

he said he was taugyht to minus the coeffient of x

[graceful palm]

[stray trail]

ikr

[graceful palm]

nah ur teacher is cooked for that

[stray trail]

actually dude

[stray trail]

dude do u understand now?

[hoary gulch]

Unless it’s negative

[stray trail]

boi that doesnt work like that!?

yo which class r u

tell me

[hoary gulch]

Nvm I got confused

I’m so dumb

Sorry

I was thinking of switching what sign you use when you move them across the equal sign

Damn I’m dumb

[hoary gulch]

Sophomore

[graceful palm]

Ight so what do you do now.

[hoary gulch]

But I did part of this last year in algebra and I was good at it, but I forgot it all

[hoary gulch]

Start over the problem

[stray trail]

bruh h

[graceful palm]

You can do this vro

[stray trail]

you can do this dude

[graceful palm]

[stray trail]

i wanna meet your teacher btw

[graceful palm]

lol fr

[hoary gulch]

So I’m at 3.5x = 5x - 3

But idk if I sub the 5 over or add it over

[hoary gulch]

Na it was my mistake

[stray trail]

u sub the 5

[hoary gulch]

Thought so bc you switch signs when crossing the equal sign correct?

[stray trail]

ya bro

[hoary gulch]

I got -1.5 then I got x = 1/2 idk what happened

I did 3.5 - 5 and got -1.5

[graceful palm]

ight bro im back

[hoary gulch]

Ok

[graceful palm]

lets start from the beginning

MR = 5x-3 right?

[stray trail]

haahhaa

yA

[hoary gulch]

Ya

[graceful palm]

MR = MN + NR right?

so its 5x-3 = 2.5x+x right?

[hoary gulch]

I have it as 2.5x + 1x = 5x - 3

[graceful palm]

its x

[hoary gulch]

I forgot the x’s in the text here mb

[stray trail]

DUDE SAME THINGG

imma crash out

[graceful palm]

ight so change it and tell me what your left side and right side are for the equation

[graceful palm]

https://tenor.com/view/tornado-twister-kevin-costner-kevin-costner-gif-18107319

[stray trail]

ysst is it 2 or -2?

[graceful palm]

for x?

[stray trail]

ya

[graceful palm]

i got positive 2!

[stray trail]

me too just asking

[hoary gulch]

It’s 2.5x + 1x = 5x - 3

[graceful palm]

LFGGG

[graceful palm]

ight so now add the left side

should be 3.5 x = 5x-3 right?

[hoary gulch]

That’s done

[graceful palm]

ight

so now subtract 3.5 x from 5x

what do u get

[hoary gulch]

-1.5

[graceful palm]

nah

5-3.5 is?

[hoary gulch]

Uh

[stray trail]

dudde 5-35

[graceful palm]

1.5 right?

[stray trail]

5-3.6

[graceful palm]

mb i wrote it wrong for a sec

[stray trail]

okok

[graceful palm]

5-3.5 = 1.5 right?

[hoary gulch]

I had it as 3-5 in my calc

[graceful palm]

lol

[stray trail]

lololoo

[graceful palm]

do 5-3.5 for this one

[hoary gulch]

I’m used to left to right that’s mb

[graceful palm]

All good.

What did you get now that you changed it

[hoary gulch]

One sec

[stray trail]

1.5

[hoary gulch]

-0.5

[graceful palm]

WHAT

[stray trail]

what r u on bout

[hoary gulch]

As what equals X

[graceful palm]

where did c come from vro

[stray trail]

huh

[hoary gulch]

Fat fingers

[graceful palm]

can you open a browser tab

?

[hoary gulch]

I misclicked the c

[hoary gulch]

My bed is alr full

[stray trail]

how is that relevant

[graceful palm]

can you type 5 - 3.5

[hoary gulch]

I don’t have room to bring my computer up

[stray trail]

ohhoh

lolol

[graceful palm]

ight riddle me this

what do you need to add to 3.5 to get 5

[hoary gulch]

I got that alr

[stray trail]

haha

[graceful palm]

what did you get

1.5 right?

[hoary gulch]

1.5

[graceful palm]

YESS

[stray trail]

thank uuuu

yessesess

[graceful palm]

Okay so now you have 1.5x-3 = 0

[hoary gulch]

But I got -0.5 = x

[graceful palm]

How do you solve for x

[graceful palm]

nah chill

solve it with me

1.5x-3 = 0

what do you do

[hoary gulch]

It’s 1.5x = 3 tho

[stray trail]

move the three

[graceful palm]

YES

[stray trail]

THANKNKN YOU

[graceful palm]

What do you do now.

[hoary gulch]

Divide

[graceful palm]

YEs!

3/1.5 is what?

[hoary gulch]

I get -0.5

[graceful palm]

Nah

It should be 2

[stray trail]

"""22""2222222

[graceful palm]

[hoary gulch]

This is wrong it’s 1.5x = -3

[graceful palm]

its the same thing after u add the 3

[stray trail]

ok move the three

[graceful palm]

lol no

[hoary gulch]

To where?

[stray trail]

how ?

[hoary gulch]

There’s no where to move it

[graceful palm]

just stay with what you had with 1.5x -3 = 0

1.5x = 3

divide 1.5 from both sides, x = 2

[hoary gulch]

I never had that

I never had 1.5x - 3

[graceful palm]

??

u literally did

[hoary gulch]

No I didn’t

[graceful palm]

look at what u wrote bro

[hoary gulch]

I am

[graceful palm]

bro

so u had 1.5 x = -3 right?

add the 3

[stray trail]

yo ysst i think it is -2

[graceful palm]

it could be +2 or -2

both of them make the equation true

ight,

lets go with what u had

[hoary gulch]

yes

[graceful palm]

1.5 x = -3

divide 1.5 on both sides

[hoary gulch]

yup

[graceful palm]

-3/1.5

[stray trail]

nah mb mb

[graceful palm]

= -2 right?

[stray trail]

no no

it two

[hoary gulch]

stop for it a sec

[stray trail]

positive 2

[graceful palm]

lol

[stray trail]

mb

[hoary gulch]

pause

time out

[graceful palm]

ay imma go do my physics hw vro

good luck

[hoary gulch]

i was dividing 3

-3 i mean

done

mn = 5 right

?

[hoary gulch]

mn is 5 correct?

[stray trail]

yes dude

[hoary gulch]

ok

thank you

sorry for making you upset with my stupidity earlier

[hoary gulch]

@graceful palm goes for you too

[graceful palm]

[stray trail]

its ok

actually im so much younger than u any way so sry for being mad at u

[hoary gulch]

na im only 15, plus you should be proud yk more than me. I used to be able to do this stuff last year but forgot this year

[stray trail]

guess my age?

[hoary gulch]

13'

[stray trail]

nope lower

[hoary gulch]

would you mind helping me more? also 11

[stray trail]

ok

could you send it again

@graceful palm yo come back online

[hoary gulch]

16 this time

[sand lion]

i need help with checking if i translated some angles correctly, left is original figure and right is what i drew, im trying to find resultant of forces so ik they have to start from the same point

[hoary gulch]

i dont understand what its asking

[hoary gulch]

oh no is this what i have to do geomitry or is this trig?

[sand lion]

its trig

[hoary gulch]

oh thank god

[stray trail]

sry bro i cant help

i dont even know geometry

[hoary gulch]

some of mine is algerba but i am in geometry.

[sand lion]

its alright dw i was just tryin my luck here

[hoary gulch]

I would help but i barely can do algeriba rn let alone geo or trig lol

[stray trail]

sry bro

[stray trail]

41 yrds

ans to ur ques

16

got it?

[hoary gulch]

i need to show my work

[graceful palm]

vro i cant today i got some free time trw tho

@hoary gulch when is ur hw due

[hoary gulch]

tmmr

first hour

at 8:10

[graceful palm]

https://tenor.com/view/lebron-james-lebron-screaming-lebron-lebron-james-screaming-gif-5629213437781461656

[hoary gulch]

its fine

ill figure it out

[stray trail]

i gave u your ans dude

9 to 24

is 15

yrds

24 to 50 is
26 yrds

26 +15 is
41 yrds

done

anyway gtg bye

[hoary gulch]

i got 28

[stray trail]

got to study rocket science

[stray trail]

dude answer is 41

and i gtg

[hoary gulch]

half so dived by 2

bye

[stray trail]

no 50 -24

[hoary gulch]

yes which is 26 which you need to dived by two which is 13 then add 15 28.

any way im done with hw

[storm sun]

Excuse me what does this mean

The <) symbol

[obsidian harness]

Angle

[storm sun]

It just means angle…

[obsidian harness]

Yeah

[storm sun]

I’m going to go crash out for awhile

Thank you

[rancid pebble]

Angle

m means measure

[rancid flint]

need some source to study solution of triangles textbook seems too boring, any recommendations?

[sterile gazelle]

koobits

[rancid flint]

ill check it out thanks!

[near girder]

anyone got a good explanation of hyperbolic trig, their integrals and derivatives?

[fast widget]

Hyperbolic trig is like the exponential version of regular trig. Instead of being tied to circles, it comes from hyperbolas, so its main identity is “cosh^2 x- sinh^2 x = 1.” The functions are built from e to the x and e to the negative x, which makes them grow smoothly rather than oscillate. Their derivatives follow clean patterns: sinh turns into cosh, cosh turns back into sinh, and tanh becomes sech squared; integrals just reverse those rules. They also show up in real life, like the curve of a hanging cable, which is shaped exactly like cosh of x.

But I might not be best at explaining things honestly, but here’s some resources to use too:

• BetterExplained – "Intuitive Guide to Hyperbolic Functions"
• Paul’s Online Notes – "Derivatives of Hyperbolic Functions"

[sharp root]

hello 👋 i have completed all the questions in the image except for question e. when i checked the solution at the back of the book it tells that angle 1 and angle 3 are complementary. how is that? is there a theorem that i dont know? any help would be appreciated

[haughty panther]

Dude 1 and 3 is in z axis and the rest of the stuff is in x-y plane

You get it?

I mean how else would they even show a line coming straight towards you

[near girder]

thank you!

[sharp root]

yeah i get it now thank you 👍

[haughty panther]

Yeah so am I right?

Or you find any alternatives?

[sharp root]

i didnt really think there would be a z axis since i've been dealing with only lines, angles and triangles

so i've been trying to find a reason in a 2d perspective

[sharp root]

yeah i think you are

[haughty panther]

Great

Can we be friends bro?

[fast widget]

ofc, no problem, I hope it helps!

[deep vault]

Hello, i'm starting trig.

[devout pollen]

guys I do not understand planes

[deep vault]

It's a flat 2D surface.

[upper karma]

C is the only answer that might make sense because those lines dont uniquely determine a plane

[warm shuttle]

upon which lines lie evenly within themselves?

[knotty quiver]

1. 4 and 3 are complementary
2. 1 and 4 are the same angles
3. Therefore 1 and 3 are complementary

[knotty quiver]

how about D) ?

[upper karma]

ABH?

[knotty quiver]

C) are just points. idt points can determine a plane

[knotty quiver]

yes and JGC

[upper karma]

they could just refer to the planes

[knotty quiver]

true

[upper karma]

ABH passes through both planes and not in a straight line

[knotty quiver]

plane ABH isn't drawn but you can form a plane from it

[upper karma]

oh

[knotty quiver]

I looked up the definition and it says

three non-collinear points uniquely define a plane

question asked for two planes only so, maybe D) is the only correct answer

@devout pollen what do u think. how does it compare to your notes

[devout pollen]

That's what I put down so I think it's right?

Thank you guys for helping 🙏

[knotty quiver]

i see. i hope you understand the reasoning behind it

,w collinear

[somber coyote]

Results provided by WolframAlpha

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

Requested by usrcard

[dire jackal]

how can you infer that? they can be just 3 lines on a single plane. also, to prove 1 and 3 is quite simple. we know that 1,2,3 add up to angle of a line which is 180 degrees. now angle 2 is 90, hence 1+3=90 and thus they are complementary

@sharp root

[somber slate]

can anyone help me w this, i already tried to solve this w the law of sines, but im not 100% sure if im correct

[dire jackal]

the third angle of the triangle say A, could be found using the property that angles in a triangle add upto 180 degrees right?

now see if any trigo can be used to find the perpendicular drawn

[haughty panther]

oh yeah my bad, i overthink a lot

i just ignored the geometry part , i am sorry

[dire jackal]

yo dont need to apologize man its fine

[sharp root]

thank you!

[sharp root]

thank you aswell

[dire jackal]

np!

[long yarrow]

And missing side AB

[rose arch]

use law of sines twice
first find the height of the triangle then find the side x

[knotty quiver]

,rccw

[dull ore]

uh so wtf does this mean

$F_{x} = F cos \theta , F_{y} = F sin \theta$

[somber coyote]

yunshul

[dull ore]

$the~magnitude~is~ F=\sqrt(F_{x^2}+F_{y^2})$

[somber coyote]

yunshul

[dull ore]

but

what does that actually mean

imf oncufsed

[cunning lion]

vectors are directed line segments (arrows) which have a magnitude (length) and direction

vectors can be added according to the parallelogram law shown

and all vectors can be decomposed into a vector parallel to the x-axis and a vector parallel to the y-axis, called its components

so the formulas given convert between the magnitude and the components

[dull ore]

so

if you wanted a vector saying for example

45 degrees

and a radius of 10

itd be

$F_{x} = 10 cos \theta + F_{y} = 10 sin \theta~~\theta=45$

[somber coyote]

yunshul

[cunning lion]

yes, those would be the components

[dull ore]

okay i think i got it

[spice fiber]

Hi

Help pls

[echo elbow]

Hi guys can you help me about "circle" because I'm in 9th grade and I lost some basics how should I study to understand and ty

[lime crown]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[spice fiber]

2

[lime crown]

Show your work, and if possible, explain where you are stuck.

[spice fiber]

I don't have ideas

[exotic yarrow]

Try rotating about A by 9alpha?

[tall niche]

hellos

uhhh I’m taking geometry in 8th grade (rn)

what should I expect?

or uhhh

will it be hard

[spice fiber]

?

[dull ore]

@alpine portal what ur trig question?

[alpine portal]

I have this problem and I’m lost in what to do!! I’m not sure how to proceed

I just want to understand

[dull ore]

soo

we have

$h(t)=2sin(pi/6t)+4$

[somber coyote]

yunshul

[dull ore]

first thing you do

is set your hieght

*height

to 5

so we have

$5=2sin(pi/6t)+4$

[somber coyote]

yunshul

[dull ore]

now you subtract 4 from both sides

then divide by 2

@alpine portal

[knotty quiver]

$5=2\sin(\pi/6 t)+4$

[somber coyote]

glass

[knotty quiver]

$5=2\sin(\frac{\pi}{6}t)+4$

[somber coyote]

glass

[simple vigil]

What class question is this

[regal kraken]

can any1 link me to the general chat :/

[glad pasture]

Yo guys simple q

Find measure of angle X

It seems to have two solutions

What do y'all think

[upper karma]

||the quad is cyclic so 110°||

[glad pasture]

Does this work?

Contradict me please, the book says it's 110

[upper karma]

do you have any motivation for this?

[glad pasture]

I assumed the diagram was inaccurate, when I got 110, there was something itching in my brain that i cannot scratch

So i tried other measures

This was from evan chen

His answer was 110

[upper karma]

paranoia is real

[glad pasture]

So ig im wrong, but i need some1 to contradict me

I have OCD

I really cant sleep if i dont know what's wrong

😁

[upper karma]

What is there to contradict

You put random numbers in the diagram

[glad pasture]

Can it be two answers?

[upper karma]

bro

[glad pasture]

Bro

[upper karma]

why would this be correct

[upper karma]

The diagram is uniquely determined there's no degree of freedom

[fresh birch]

The quadrilateral is cyclic, so angle x measures 110 degrees.

[glad pasture]

Ik that if we extend YZ, the angle that would be formed will be 110

[fresh birch]

Ok?

[tender kayak]

I guess something is wrong

[glad pasture]

That was what i was thinking man

[tender kayak]

By X they mean WXY ?

[glad pasture]

Yup

This was my og solution

[glad pasture]

But this also could work

I think

💀

[fresh birch]

Thats wrong

[tender kayak]

Wait its cyclic right?

[glad pasture]

Yup

[tender kayak]

Should be easy then

There is no need for calculations

You already got Z

Its 70

[glad pasture]

Yup

Then 180-70

110

[tender kayak]

Then 180 - 70 = 110

Yeah

[fresh birch]

🫡

[tender kayak]

🫡

[glad pasture]

🥀

[silk jacinth]

ok, I'm stumped. any tips on how to determine what alpha is? or is there some implicit assumption that I should take advantage of?

[obsidian harness]

do you know your circle theorems? the one that's important here is: (external) tangents to a circle have the same length

[silk jacinth]

alright, but I'm not quite sure how I can use that information to determine the length of either external tangent

[obsidian harness]

right, so what's this blue angle in terms of alpha?

the strategy is to write an equation of the three parts that sum to h = 93

[silk jacinth]

all I can think of is 11+x+82-x = 93 but that just cancels the x out

[obsidian harness]

11 is correct

[obsidian harness]

if you can find the blue angle in terms of alpha, you can find the side length using right-angled trig, in terms of alpha

[silk jacinth]

I've no idea how to get the blue angle in terms of alpha

if I extend the hypotenuse from the vertex of the blue angle, then extend a horizontal line from the vertex as well, I can try to visualize alpha there, but I'm failing to see any clear relation there

[obsidian harness]

well, the two right angled triangles with the black line are congruent

[upper echo]

Problems like that can always be solved with kind of brute force, using the sine law. Here you get cos(6a)-2cos(8a)+cos(12a)=0 which factors as
(1-2cos(4a)) (3+4cos(2a)+4cos(4a)+2cos(6a))sin²(a)=0
so, alpha=15°, since all other roots are greater than 20°.

[silk jacinth]

yeah, but I'm unaware how I can take advantage of the congruence if I don't know the length of either tangent line

[obsidian harness]

so 2 * (blue angle) is supplementary to 90 - alpha

[silk jacinth]

just so we're clear, we're talking about the same alpha here, the alpha on the bottom left corner of the image?

[obsidian harness]

yes

[silk jacinth]

oh okay now I think I get it

I mean at least that particular sentence 😄

[obsidian harness]

the sine law on which triangle?

[upper echo]

on both

[obsidian harness]

interesting.....

[obsidian harness]

you mean the two congruent triangles I drew right also

[upper echo]

check the problem I replied to in my message

[obsidian harness]

oh completely different problem LMAo

I was so confused

[silk jacinth]

ok so the blue angle is:

(180-(90-alpha)) / 2 = (90+alpha)/2

but I'm not entirely sure how I can still use this information 😄

[obsidian harness]

right, so if you look at the smaller pair of triangles

you know that opp/adj = tan((90 + alpha)/2)

[silk jacinth]

yeah

[obsidian harness]

but then you know what opp is!

[silk jacinth]

but what is adj here?

[obsidian harness]

that's what we want to find

[silk jacinth]

11 / tan((90+alpha)/2), but if I don't know alpha, how can I proceed

[obsidian harness]

^

[obsidian harness]

so now do the same with the largest triangle, opp/adj = tan(alpha), and you know adj

[silk jacinth]

so if adj is x, then I have a pair of equations:

tan ((90+alpha)/2) = 11/x
tan (90-alpha) = 151/(82-x)

but I'm still not sure how I can solve for x or alpha here

if the input of the tangent were the same, I could do a substitution

(I think?)

there's something terribly obvious I'm missing here, isn't there? 😄

[obsidian harness]

so from this 11 + adj + opp = 93

11 + 11/tan((90 + a)/2) + 151 tan(a) = 93

[silk jacinth]

where does the 153 come from?

[obsidian harness]

wait

[obsidian harness]

my bad I messed up the value of h

[silk jacinth]

ah

[obsidian harness]

are you expected to solve this equation by hand?

like where does the question come from

[silk jacinth]

the assignment is to solve for alpha, nothing else

[obsidian harness]

have you been introduced to double-angle and compound-angle formulae yet?

[silk jacinth]

not entirely sure, my native language isn't English so I'm not entirely sure how those translate to my language

[obsidian harness]

have you seen these before in class?

[silk jacinth]

I don't recognize these. I might've seen them on my own high school classes (which were a while ago), but I'm pretty sure they're not a part of the curriculum this assignment is a part of

this isn't an assignment of any curriculum I'm studying myself, it's my friend's and I'm trying to help them out, but I'll have to check their materials to be sure

[obsidian harness]

oh okay, thanks for clarifying

cause I really don't see how you could do this problem otherwise

[silk jacinth]

shouldn't 151 tan(alpha) be 82-151 tan (alpha) ?

[obsidian harness]

no

[obsidian harness]

^

[silk jacinth]

for the larger triangle, isn't the opp of alpha (93-11-x)?

i.e., 82-x

[obsidian harness]

we want to find the opp not in terms of x

[silk jacinth]

so tan(alpha) = large_opp / 151

but I'm not sure what large_opp should be

oh, I'll just have to solve for it, then form the equation, doesn't really matter how I call it

[obsidian harness]

large_opp = 151 tan(alpha)

simple as that

yeah

[silk jacinth]

was overthinking that one

[silk jacinth]

just realized how silly it'd be to solve for x since I'm not supposed to be adding x another time

so now I've got the equation where I've summed all the lengths to 93 and the only way to solve for alpha is with the formulae you presented?

[obsidian harness]

yeah, I really don't see another way

[silk jacinth]

if so, no wonder this stumped me. like I've taught planar geometry in high school (got a minor in math, this year I'll be starting a new major as an actual maths teacher) but I don't think I've applied those particular formulae

[obsidian harness]

I just feel that something's going to be lost in translation

you not being comfortable with this topic, and you and your friends' best language not being English

[obsidian harness]

RIP, I'm not judging, especially if you'll be teaching primary school but

[silk jacinth]

no worries, I've got a lot of gaps in my general knowledge, so I'm doing this stuff in part to plug those gaps

[obsidian harness]

cool, I know you're just starting your degree

[bitter solstice]

Hey

Anyone here

[dire jackal]

yo

[dark sparrow]

http://dontasktoask.com/ & http://nohello.net/ @bitter solstice

just post your doubts directly

or idk maybe you've already had someone resolve your doubt somewhere else

[mild spoke]

does anyone know how i could get zeta? psi and r are known variables, the big circle has radius 1

this is for research in geometry but i forgot how to do trig lol

[lost lichen]

izzat a tangent or not?

[mild spoke]

the two circles are tangent

at the rightmost point

[lost lichen]

no like the radius of unit circle and the other circle

[mild spoke]

oh no the radius is based off of psi and its intersection with the unit circle

[lost lichen]

so this is not a tangent?

[mild spoke]

not necessarily

yeah there'll exist values for which it is obv

[lost lichen]

ite ite

[mild spoke]

but a priori we can't assume it

[lost lichen]

cool

[mild spoke]

any ideas? i've been so stuck

[lost lichen]

same lel

my idea was to mirror it but then i was like nah

[worthy eagle]

used €, ¥ for zeta and psi.

so, sin€ = (cos€ - 1 + r) tan¥
if you know r, ¥ you can get €

ik i could have chosen better variables

[lost lichen]

so tan(psi)=sin(zeta)/(cos(zeta)-1+r)?

ite cool

[mild spoke]

oh this works tysm!!!

[upper echo]

The easiest is to write the law of sines for the left triangle. You get 1/sin(psi)=(1-r)/sin(psi-zeta). So, zeta=psi-arcsin((1-r)sin(psi))

[mild spoke]

thank you!

[sterile gazelle]

help

[obsidian harness]

!help

[lime crown]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[velvet pond]

wsp?

[short lynx]

pls someone assist me i keep graphing this wrong..?

[upper echo]

Continue CP, it is an altitude too. The same thing with BP.

[dire jackal]

try to find intercepts maybe, like see what values of x you get when putting y=0 and shift the graph such that you get those values on the x axis

[short lynx]

i got two solutions for x

x=5pi/6
x=7pi/6

[dire jackal]

now try to shift the graph around such that the graph crosses x axis at those points

[round granite]

I think amplitude isn't 1

[upper karma]

I think point A is the orthocenter because pbc is obtuse triangle, And the altitude is through A, meaning if B and C go through meet at the point A, it is must be orthocenter (if not then it is unsolvable)

[reef gazelle]

I'm pretty sure it's solvable tho

[upper karma]

even if Point A is not orthocenter??

[reef gazelle]

Point A is a vertex

Wdym

[upper karma]

I mean i try to use law of sines, law of cosines, and other things to find the angle pbc and... nothing happen

[upper karma]

I mean if we make two point meet at orthocenter it is a vertex too

[upper karma]

look triangle PBC is obtuse triangle.

[reef gazelle]

I'm very close to finishing it

How to proceed now

[upper karma]

that what i thought, using s
law of cosine or law of sin is useless here.

we can solve it, if only point A is orthocenter

[reef gazelle]

Bro what do you mean how can point A be the orthocentre

Point A is literally a vertex

Do you mean point P?

[upper karma]

Orthocenter of an obtuse triangle is outside of the triangle

Look, the triangle pbc is obtuse triangle

And i assume A is orthocenter because.... if it is not then we cannot solve it...

Well, let me resolve again

[summer cradle]

extend CP to side AB

call the intersection D

[reef gazelle]

Then?

[summer cradle]

notice that ADP is a right triangle

both AL and CD are altitudes and passes through P so P is orthocentre

thus if you extend BP to side AC it will also be perpendicular cuz it's also altitude

[cold cargo]

<@&286206848099549185> whats the formula for square, Triangle, circle, and long Square

[gilded bone]

How can I calculate the center coordinates of all hexagons that are adjacent to a given hexagon?

[copper hazel]

formula for what about them

[cold cargo]

How do i writte

[copper hazel]

like x^2 + y^2 = r^2?

[cold cargo]

Like

[upper karma]

!15m

[cold cargo]

Let's start with circle

[lime crown]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cold cargo]

I havent pinged here in days 💔

What are all stuff about circles

[upper karma]

HEWWOOOOOOOOOOOOO

[cold cargo]

From. Begining. To. The. End

Later

Me rn

No :3

Thats why i need help

Cuz i know nothing

[mossy crow]

well the circle is basically the set of all points that are a certain distance from a given point

[cold cargo]

So basically, given point is middle?

Im waiting for ur response :3

Yeah i guess, and how is center written as?

O k

Like this

Wait

tOji

Great

Nexwt :3

( ＾ω＾ )

Yes

Easy enough

Btw i aint 12

Im js goofy

16yo

And childish

So i appologize

[mossy crow]

dont apologise, were here to help

[cold cargo]

Yuh

Js rly happy lately

Like i am on coce

[mossy crow]

have more questions?

[cold cargo]

Yeah

How do i calculate all the stuff

Diametar

[mossy crow]

what do you know about the circle?

radius?

[cold cargo]

Pretty much nothing

[cold cargo]

Yeah

[mossy crow]

well diameter is 2*radius

(definitions yippee)

[cold cargo]

But i will never do drugs and its just that so many good things happen to me lately

[cold cargo]

Ok

[mossy crow]

good

[cold cargo]

Ty

So basically

Radius

Is

2 × itself

[mossy crow]

uhh

[cold cargo]

Since you splited it in half right?

[mossy crow]

radius is a segment from the center of a circle to a point on the circle

[cold cargo]

Ive never been good with words and all, but you basically say that radius is point from center to any point of the circle?

[mossy crow]

yea

[cold cargo]

Good

So how we calculate it?

Do we need

Something more?

How do we get Radius

[sinful iron]

I got pinged

[sudden nexus]

Its usually given in task or you can get it by dividing diameter by 2

[cold cargo]

Yeah 😁

[mossy crow]

you dont see helper pings a lot in topic channels

[cold cargo]

How do we get diametar

[cold cargo]

Probably

[mossy crow]

usually you're given diameter or radius, one or the other

[sudden nexus]

Can you share the exercise you need help with? Or tell me more about it