geometry-and-trigonometry

[charred zephyr]

thats personal information but use whatever you want

[eternal crag]

lmao ok carry on i dip

[charred zephyr]

what

=

[silent plank]

for small $\theta \text{(in radians)}, \
\sin(\theta) \approx \theta \
\tan(\theta) \approx \theta \
\cos(\theta) \approx 1 - \frac{\theta^2}{2}$

[somber coyote]

ramonov:

[silent plank]

also in future

[cosmic pebble]

From

#❓how-to-get-help

Rule 5

While asking questions, make sure you mention all relevant details, including the context, what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.

[charred zephyr]

Ok thanks my boy

[upper karma]

;-;

that was a w e i r d conversation

"prove that cos(sin(tan(1))) = 1"
(it's false)
"how can i prove it? can i use tan = sin/cos"
bruh

[long shale]

@upper karma im pretty sure that cos(sin(tan(1))) = 1!

[upper karma]

approximated but

uhh

not exactly

[long shale]

if you work in degrees it works out

[upper karma]

0.99984 is if it is degrees

0.99985*

[keen aspen]

Yeah because tan and sin are close to 0 when the input is small

So cos(0ish) gives something close to 1

[upper karma]

but not exactly 1

[keen aspen]

Yep

[upper karma]

yerp

so how y'all doing?

[keen aspen]

I'm crying

[upper karma]

that's nice

[long shale]

but i think they are looking for you to take the arccos of both sides @upper karma

[upper karma]

that is perhaps possible

then again it still isn't exactly 1, is it

[long shale]

ya its not, i messed it up with as x-> 0, mb

[upper karma]

ahh. well no problemo

what kind of math r u studying?

[long shale]

all over the place, just finnished grade 8

[upper karma]

same 😄

what kind of typo

welp I'm trying to finish some precalculus... got a book with 1001 practice problems and I'm relatively close to finishing.

[long shale]

but i am really intruiged by group theory and that kind of stuff

[upper karma]

wait you're doing abstract algebra?

[long shale]

ya

[upper karma]

so you're saying you've done calculus and that such

[long shale]

ive done multi variable, but kinda turned elsewhere after that

[upper karma]

well, that's impressive, to say the least...

I might be starting HS doing calculus

[long shale]

nice 🙂

[upper karma]

🙂 thx... in comparison with some of the really bright people here, it's a small thing, but i am moving forward.

anyway, good luck to you.

(we should probably move channels lol)

[long shale]

thx and ya we should

[upper karma]

lol k

[sleek thistle]

starting hs with calculus..

what am i doing with my life

[eternal crag]

wrong channel also we don't care

[wary wind]

Lol

[upper karma]

Lol

[tawdry pivot]

Lol

[upper karma]

Lol

[leaden bridge]

Lol

[weak shoal]

Lol

[smoky lichen]

Lol

[upper karma]

Lol

[wooden current]

Lol

[dusky surge]

Lol

[wraith drum]

Lol

[arctic forge]

THe moon's distance from the earth is 324000 km and its diameter subtends an angle of 28' at the eye of the observer. the diameter of he moon is ;

[upper karma]

Have you drawn it? @arctic forge

how can i prove this o_o

[paper vale]

cosine

[upper karma]

What have you tried

[arctic forge]

Have you drawn it? @arctic forge
@upper karma yh still nt able to understand

[upper karma]

Post it

[arctic forge]

i really drew it

[paper vale]

do u know cosine law

it is just that

[arctic forge]

but am nt understanding how are u suppose to find the diameter

[paper vale]

draw the distance between the ends of diameter to point on earth

with 28 degrees betweeen them

[arctic forge]

okk

ohhhkkk

get it

[dark sparrow]

28 arc minutes

not 28 degrees

[paper vale]

@upper karma, multiply numerator and denominator by 1+sinx

[arctic forge]

yh

[upper karma]

yee i got that, thank u :d @paper vale

[arctic forge]

i get that

[upper karma]

conjugates should stick out, given 1+sin(x) and 1-sin(x) are conjugates.

When ya see them, and you have no idea what else you can do, use em.

[still meadow]

Hey

I tried solving it but I just need help

[long shale]

@still meadow do you know any angle theorems?

[upper karma]

@still meadow Do you know how many degrees are in a circle?

@still meadow maybe this helps:

[charred zephyr]

6^2

ABC is a triangle. M mid of BC. show that AB+AC>2AM

any indications please

[long shale]

do you have a figure @charred zephyr

[charred zephyr]

no but its like

             A

C M B

[novel flax]

try using triangle sum inequality

[silent plank]

axioms of a triangle / triangle inequality

[charred zephyr]

what is it

what is triangle inequality

please

[long shale]

the sum of any two sides is greater than the third

[charred zephyr]

i dont believe you

proof?

[wary wind]

[silent plank]

https://lmgtfy.com/?q=how+do+i+google+the+triangle+inequality%3F

[charred zephyr]

i mean thats how things work

[wary wind]

[long shale]

so if the sum of two sides is less then the third the sides wont connect @charred zephyr

@silent plank i love using that 🤣

[charred zephyr]

lol did you send a gif

[long shale]

@charred zephyr just graph it and you have a proof

[charred zephyr]

AC + CM > AM
AB + BM > AM
AC + CM + AB + BM > 2AM

i told you this inequality doesnt work

[wary wind]

Please go through something like Khan Academy from scratch and with an open mind, please

[charred zephyr]

i will try to

[silent plank]

applying the inequality:
AB+AC > ?

[charred zephyr]

BC

Yes

someone helpnm . please

[long shale]

use the fact the BM = CM

AC + CM > AM
AB + BM > AM
AB + AC + 2BM> 2AM
BUT AB + AC > BC so we are done!

[charred zephyr]

what?

AC + CM > AM
AB + BM > AM
these are the true inequalities

[long shale]

ya mb, i really only cared about the third one

[charred zephyr]

how did you conclude the thurd one

third

[long shale]

since BM = CM

its a property of the median

[charred zephyr]

AC + CM > AM
AB + BM > AM
AC + CM + AB + BM > 2AM
@charred zephyr i wasnt wrong

[novel flax]

AB + AC + 2BM> 2AM
how do you know AB+AC > 2AM

[long shale]

do the exact same thing just with AM in mind

[novel flax]

what

[charred zephyr]

wdym

[long shale]

use this figure

[charred zephyr]

its okay guys i got it

no need

[novel flax]

ok

[charred zephyr]

actually no i didnt get it.

i got AB+AC>AM

not 2AM

[wary wind]

[charred zephyr]

use this figure
@long shale ok

[long shale]

oh lmao i always though it was AB + AC > AM

[charred zephyr]

uh can the question be false??

has anyone found the answer???

[rich wolf]

,calc sqrt(20/3.2)

[somber coyote]

Result:

2.5

[long shale]

well i using my figure we can say the following
AD = DE
DC = BD (midpoint)
angle(ADC) = angle(EDB)
This means that there are congruent triangles ADC and EDB by SAS
BE = AC
AB + BE > AE
AB + AC > 2AD

@charred zephyr

[charred zephyr]

okay, thank you!

[long shale]

are you sure its not 2AM?

[charred zephyr]

what about?

[long shale]

the question, my proof shows it greater than 2AM not greater than AM

[charred zephyr]

yes it's 2AM but it's also AM

[lyric meadow]

Can you calculate the dot product angle in degrees by simply multiplying by 90?

[wide onyx]

no?

$a \cdot b = |a| |b| \cos\theta$

[somber coyote]

crypthes:

[wide onyx]

not sure what you're multiplying by 90

[charred zephyr]

the answer of your question lies in eulcidians mind praise him

(just kidding lol)

[arctic forge]

(cos@+sin@)^4-(cos@-sin@)^4/sin@cos@=??

[upper karma]

Expand it if you have no ideas

[arctic forge]

not working

[silent plank]

parentheses

[weak shoal]

why're you using cancerous symbols for the angles?

[upper karma]

cosx+sinx can be expressed as a single function

[silent plank]

and proper spacing to indicate what's part of the numerator and denominator

lazy alphas

[arctic forge]

😑

[weak shoal]

jesus

why not just use x or y or literally anything less stupid

[arctic forge]

Will make sure next time

[silent plank]

$\cos(\alpha) + \sin(\alpha))^4 - \frac{(\cos(\alpha) - \sin(\alpha))^4}{\sin(\alpha)}\cos(\alpha)$?

[somber coyote]

ramonov:

[arctic forge]

Noo🤦‍♂️

[silent plank]

[upper karma]

$(\cos(\alpha) + \sin(\alpha))^4 - (\cos(\alpha) - \sin(\alpha))^{\frac{4}{\sin(\alpha)\cos(\alpha)}} $?

[silent plank]

because that's what you're implying

[somber coyote]

HoboSas:

[upper karma]

Correct?

[arctic forge]

No

[silent plank]

make a serious attempt to represent it in plain text properly

also serves as training for general algebra

[arctic forge]

(cosx+sinx)^4-(cosx-sinx)^4 whole divided by sinxcosx

[silent plank]

use parantheses to wrap the numerators / denominators

$\frac{(\cos(x) + \sin(x))^4 - (\cos(x) - \sin(x))^4}{\sin(x)\cos(x)}$

[upper karma]

||difference of squares ||

[somber coyote]

ramonov:

[silent plank]

that?

[arctic forge]

yeahh great finally we did it

[silent plank]

can be represented in plain text as: \
$\verb| ((cos(x)+sin(x))^4-(cos(x)-sin(x))^4)/ ( sin(x)cos(x))|$

[somber coyote]

ramonov:

[silent plank]

anyway, consider difference of 2 squares

[arctic forge]

okay

[upper karma]

||difference of squares ||
If you have no clue

$a^2-b^2=(a-b)(a+b)$

[somber coyote]

HoboSas:

[arctic forge]

(cosx+sinx)^2-(sinx-cosx)^2= (cosx-sinx)^4

[upper karma]

Wot

[silent plank]

where are you getting that?

[arctic forge]

i saw the solution and thats what written 😓

[upper karma]

...

We are trying to help you and you betray us

:(

[arctic forge]

😑 No

[upper karma]

anyway, consider difference of 2 squares
^

👻

[rich wolf]

@upper karma what you having trouble with

[upper karma]

Everything

[wary wind]

@upper karma ooof. Why do you think you are struggling on everything here? Were you not able to understand the concepts in the chapter at all?

[upper karma]

Welp I has question

Well sorta

Anyways I’ve been spending some time with a formula I derived... it’s for area of a triangle. It works perfectly like heron’s but looks nothing like it, and up until now there’s been no issues. In fact, this formula for me was much much easier to derive and prove than herons is. Anyway, there’s this problem I came across and it’s being a dingus... I have resorted to using heron’s specifically because it works better with this specific problem, but I feel it’s unfair for me to use a formula I haven’t proved. (Much like when I ‘proved’ e^pi i without proving e^pix).

So anyway, I would just like a hint on how to prove Heron’s formula. make it a small hint if any.

aaand ping me when response.

[wary wind]

@upper karma hint - Use Law of Sines.

[upper karma]

thank you very much

I had suspected so... but thank you

[wary wind]

You're welcome

[upper karma]

I shall tackle the proof tomorrow and then proceed to deconstruct and solve the issue that relies on it...

ahh this server is amazing.

[wary wind]

Good.

[upper karma]

well I’d best be heading to bed now, thanks you for the hint. G’night epic math server.

[wary wind]

G'night Squid

[upper karma]

Find area of triangle

Need someone to verify if my solution is correct

[quartz prism]

Maya Angelou in Math huh

[upper karma]

I wrote it in my English booklet

[quartz prism]

bruh your internet must be slow

it's ok

I didn't pay attention in circles, how do I do these kind of problems
I have a test next Monday

@upper karma your method seems right btw

[upper karma]

Thanks!

[quartz prism]

np

[urban egret]

Need help with this practice problem I forgot what to do when i am given a negative angle. I added 360 to get the coterminal but the problems stated it was wrong

[upper karma]

when it's a negative angle you use 180 - angle

(instead of angle)

[warm verge]

Would anyone be willing to help walk me through this Trig problem?

[upper karma]

@warm verge go with it

Also

[cosmic pebble]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[warm verge]

Oh ok sorry

Ok so #61

[upper karma]

Do you know the identity of tan(2x)

[weak shoal]

Don't doublepost

Your question was literally in #help-8 and i gave you a possible way to do it

At least have the fking courtesy to respond

[upper karma]

Yeah lol i triggered the rule

@warm verge

[warm verge]

alright yeah i wasn't trying to be rude

The bot kind of chewed me out and I thought I was abiding by the rules lol. Sorry!

[weak shoal]

Do you still need help?

[graceful narwhal]

ya the bot is pretty cruel

[weak shoal]

what does the bot actually do lol?

does it message you as well?

[graceful narwhal]

it judges you

with its little text box

[weak shoal]

how do you trigger the rule, though?

[graceful narwhal]

just ping al3dium

[weak shoal]

kek

[versed river]

Exclamation mark r(rule number)

[weak shoal]

oooh

[upper karma]

how do you trigger the rule, though?
@weak shoal yeah i did

[weak shoal]

nice

[upper karma]

!r3

[urban egret]

@upper karma I figured it out thanks for your help. I did do the inverse on my calculator@to get the correct angle but it was completely different from the ones on my paper I think I inputted numbers incorrectly some how

[upper karma]

This is about to anger me but I am going to give up on proving heron’s.

ugh why am I so dumb

Ugh screw it I give up

I’ll just accept it as an axiom until I’m smart enough to prove it

[eternal crag]

what have you tried?

[upper karma]

staring at it for 3 hours and using the law of sines

It’s as if he pulled the thing out of thin air and babam

I have absolutely no idea how it works and I w a n t to know

[eternal crag]

i know it's lame but if you want to "accept it as an axiom," you should just read a proof offered on wiki

the proof with pythagorean theorem is really really elementary

[upper karma]

😦 alright.

[upper karma]

Anyone else taken this long on some easy proof like heron’s?

[upper karma]

Yes proofs are hard in general

For me

Someone please help.

@upper karma Yes what

Please help

Help with what

@upper karma Do you understand what a midpoint is?

Yes

The midpoint is the middle point

Do you see how a midpoint splits the line into halves

1/2 1/2

Equal lengths

@upper karma

Yes

Ok what are you having trouble with then?

What don’t you understand about the 1st problem?

@upper karma

What is x

Well the whole line is Uv right

And w is the midpoint

If you know w is the midpoint then what do you know about UW And WV

@upper karma

X is A Variable

The unknown variable you are solving for

Do you know simple algebra

Yes

@upper karma Hello

Yes

You plug it in

Once you find x

Ya ok but do you know how to find x

In this specific problem

Nooo

What

I’m sorry

I’m dumb

The whole line is UV right

And the midpoint is W

Yes

If the midpoint is W then what do you know about segments UW and WV

@upper karma

Read the explanations

Omggg that makes sense

Thank you

So much

@upper karma Do you understand what to do tho

Or was that sarcasm

What

Do you understand what to do

Why would I be sarcastic

Idk

Yes I do

Tell me

@upper karma What do u do

The midpoint is w

So you basically

Basically...

Waitttim typing

K

UW AND WV IS what helps us find the variable. Which we can use to plug in. Yes??

Ya it helps you find the variable yes

But what do you need to do to find the variable

@upper karma

Do you see how UW = WV

Since W is the midpoint

Since a midpoint splits a line into two congruent segments

Hello???

@upper karma You got it man I believe in you

Thank you

I’ll watch more videos on this

But thank you

Ya sure

Your welcome

[upper karma]

welp

I have decided that I am capable of doing this proof, but because I’ve been on a whiteboard for 3 hours now, I have decided to put it off until my mind clears.

today I think I logged... 5 hours of math?

good exercise for the mind. Very fun subject.

Yes awesome

Math is fun

I agree.

And since setting my time goal, as advised by you guys, I have been moving faster and understanding much more since I’m more thorough.

anyway

proof of heron’s has been fun... but it’s taken a while so I will resume later.

Yes good luck 👍

Thank you. You too 😄

[wraith drum]

guys, how do i prove sin^-1(x)+cos^-1(x)=pi/2

[dark sparrow]

take θ = arccos(x), prove that arcsin(x) = π/2 - θ

[wraith drum]

wait, so i got sin^-1(cos(θ))-θ

what do i do after

[dark sparrow]

sin(π/2 - θ) = x

[wraith drum]

ye

[dark sparrow]

and π/2 - θ is in [-π/2, +π/2]

[wraith drum]

yeah...😕

nvm i got it

[still meadow]

Ok so I need help

360-47 = 313

But I need the x and y

[silent plank]

consider angle sum on a line and size of a right angle

[weak shoal]

Don't doublepost

[upper karma]

!r5

!r4

Uh

[obtuse current]

may someone help me with some goe proofs

I am doing struggling to understand to understand them

[upper karma]

Yep it’s alright, everyone struggles with proofs

Every geo student hates them

[obtuse current]

Ok, are u willing to help me solve me once?

one*

[upper karma]

Nah I suck doing proofs, I just came here to comment that

Lol bye

[obtuse current]

bruh

come on

[upper karma]

@obtuse current Ill take a look tho

[obtuse current]

kk

here the question

@upper karma

[upper karma]

Thales theorem could help

[obtuse current]

hm?

[upper karma]

Did I say it right

Idk if on eng is the same

[obtuse current]

mhm

[upper karma]

But i get what you mean

E is the middle point of CB

Clear?

I think its known as similar triangles

[obtuse current]

yes, I get that, however im not looking for advanced theories

im looking for starter level ones

and I don;t think I have learned thales yet

[upper karma]

D is the middle point of CA

[obtuse current]

,hm

[upper karma]

Thales theorem => DE // AB

Do you know what the formula for the middle point of a segment is?

[obtuse current]

midpoint

[upper karma]

Yes

Do you know it?

Yes

[obtuse current]

yes

[upper karma]

$M(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2}) $

[somber coyote]

HoboSas:

[upper karma]

Ok?

Notice how E is midpoint of CB

[obtuse current]

yes

[upper karma]

C(x_1, y_1) and B(x_2, 0)

[obtuse current]

mhm

[upper karma]

If you apply that formula

With C and B

You get E (as stated in the problem)

So E is the midpoint of CB

[obtuse current]

can u just hmu with that proof.

[upper karma]

No

[obtuse current]

its easier for me understand

[upper karma]

This is not how it works

[obtuse current]

to be honest

🤷‍♂️

[upper karma]

Rip

What's better than being guided through the proof...

[silent plank]

uh...you could just apply slope formula for the lines AB and DE (for non-zero x_2)

[upper karma]

That's a good one

[upper karma]

Should be 0

[obtuse current]

hi hobo

@upper karma Well, I found my solution it was based of @silent plank lmao

I just used slope theorms

😂

[upper karma]

Mine was more Euclidean

[coral dagger]

Can someone help me with this

What I did so far was

Convert 150 into Radians in order to graph it

So like I set my Y=2.62 and my Y=200x

And Im trying to see where they intersect but to no aveil

[coral dagger]

I've reverted solving this algebraically by subsituding 140=Y

140=200tanx

However Im still curious on the graphing method

[upper karma]

hey all, what is the name of the technique I would use to solve this? or is it purely knowledge based

[dark sparrow]

maybe consider rewriting the arcsec as an arccos

[upper karma]

thank you, @dark sparrow

[obtuse current]

anyone help

[eternal crag]

no

[azure reef]

help urself

[versed river]

If you're looking for help on this then cant you just conpute the slopes of AB and DE and see theyre both 0?

uh...you could just apply slope formula for the lines AB and DE (for non-zero x_2)

Which is exactly what ramonov said before too lmao

Do that

Idk what thales theorem had to do with it but what ramonov and i have said should work

[wraith drum]

Are you comfortable with the section formula

where you find a point which divides the line into 2 parts with a certain ratio

since D and E are midpoints of AC and BC, just prove that CD/AD=CE/BE

then say by inverse thales theorem, AB||BE

Yeah, you could just use slopes, if that is what your teacher is expecting you to do, but if your teacher is expecting you to use thales, then the thing above is what you should do

[versed river]

and I don;t think I have learned thales yet
@obtuse current

Oh sorry for the ping

Itll help you see this anyway ig

[arctic vortex]

how do i do this

[wooden current]

AAS = Angle-Angle-Side
You already have one angle ( SNW = TNW )
and one side ( NW = NW )
Now you have to look at other pairs of angles.

[plucky marlin]

ASS when 😔

[obtuse current]

lol

[upper karma]

what a bullshit question... it's the same thing if you know either angle S or angle SWN

any of them will do, since all angles from a triangle need to add up to 180

if you know one, you know the other

the question says "Select one" but both c) and d) have equal merit

Yes but the question is about AAS

That's why he said it's a bullshit question.

Cuz in reality who gives a fuck.

Guys it's a very basic geometry question

Not more than that

there should be one answer

and it's not

both c) and d) have equal merit

they should both count

I think this section comes before proving that A+B+C=180

there's no good reason to pick c) over d), or vice versa

If you don't know that the sum of angles of a triangle is 180, then c) is the only possible answer

why not d)?

it's the same thing

if you know 2 angles and a side, you can solve any triangle

(AAS)

Omg

If you don't know that the sum of angles of a triangle is 180, then c) is the only possible answer

why not d)?

if they only credit you for c), then it's a shitty question

If you don't know that the sum of angles of a triangle is 180, then c) is the only possible answer

you still haven't answered my question

I know there should be 2 correct answers

"Pick one" - I hate it when they add that

I remember studying AAS, the first version was 2 angles and the side between them. Then, when we studied that the sum of the angles of a triangle is 180,we extended this fact to 2 angles and 1 side (any)

[novel flax]

aas means that the side is not included by the angles

this is different from ASA, where the side is included by the angles

so i think it should be D

you don't need to know <SWN is congruent to <TWN, but you do need to know that <S is congruent to <T to use AAS

[upper karma]

AAS, ASA, SAA

exact same thing

it's like saying angle NWS instead of angle SWN

it's the same thing

Why so many abbreviations

Smh

A - angle
S - side

Laziness

it's quite common in trig

[novel flax]

what

AAS is different from ASA

one of them the side is included, the other one the side is not included

[upper karma]

^

[upper karma]

https://media.discordapp.net/attachments/641351291343208448/727625092187815988/unknown.png

I know right triangle is isosceles

So angle on top is also 64

Then I use exterior angle theorem

Set them equal

And x = 9

Right

Someone check my work

[charred zephyr]

wheres m

[versed river]

m<2 means angle 2

So its where the 2 is

[charred zephyr]

ok so i got 9 as well

[versed river]

Me too

Its right

[upper karma]

thanks !

[sleek thistle]

can i get help with a problem?

[edgy quail]

sure

whats the problem?

[sleek thistle]

how do i set up the equation correctly?

[edgy quail]

Wait what is z supposed to be

oh wait

that says x

sorry my bad

yeah it should just be 3x^2+(2x^2 - 16)=180

[sleek thistle]

ohh

[edgy quail]

so yes you are correct

[sleek thistle]

okay thank you

[edgy quail]

np

[sleek thistle]

wait but how would i input the x if it is squared?

[upper karma]

Huh

@sleek thistle What u mean

[edgy quail]

its a quadratic equation

you make everything equal to 0 then factor

actually no

in this case x is the square root of 196

which is 14

it can also be -14

[silent plank]

don't forget about the 2+3

[upper karma]

Yes

[edgy quail]

oh shit wait

5x^2=196

x^2=196/5

my bad

[sleek thistle]

yeah it’s x^2=196/5 but it’s asking to give a single x

[untold bone]

das

[edgy quail]

oh

[sleek thistle]

do i put two answers?

[edgy quail]

do the positive and negative versions

separated by a comma

[upper karma]

Yes

[silent plank]

depends on how the question is worded. it's cut off

[sleek thistle]

it also doesn’t let me put a sqrt symbol so would i have to approximate?

[edgy quail]

it said round

didnt it

so compute both

[silent plank]

the answer box hover text implies they're only expecting one decimal answer

[edgy quail]

i see

[silent plank]

maybe click more for more info

[sleek thistle]

it says round to the nearest tenths

so it’d be 6.3?

or -6.3,6.3

[silent plank]

,calc 14sqrt(5)/5

[somber coyote]

Result:

6.2609903369994

[edgy quail]

yep

umm i would put both separated by a comma

idk tho

maybe it only wants one

if it wants one just put the positive

[sleek thistle]

alright thanks i’ll see if it works

[upper karma]

Help with this question

[versed river]

So what have you got for the expanded LHs?

[upper karma]

1/sin^2 x - 2cosx/sin^2 x + cos^2 x/sin^2 x

Oh that's with the stuff fliped over

Trig identity stuff

[versed river]

It seems youve made some errors expannding out the brackets

[silent plank]

^

[upper karma]

Mmmm

So it becomes (cosecx-cotx)^2 no?

Like first step

[silent plank]

no

[upper karma]

Oh wait

I;m stupid

[versed river]

Nice

[upper karma]

Well I think I can do that then

[silent plank]

consider working with csc and cot

[upper karma]

Yeah I think I know what to do

I don't know why I though that

What I did

[silent plank]

the formatting for i though

[upper karma]

The circle is theta

Like on the LHS

It's just the text book doesn't print it right for whatever reason

So how do you do that one?

I don't understand it either

Wait was there message before?

D'you delete it or was tht from before?

[versed river]

Sorry i thought i did something wrong

[silent plank]

consider pythagorean trig identities

there are multiple directions to approach it

[upper karma]

I still don't know what to do with the left though

I don't know right side either actually

I keep getting different stuff

[silent plank]

show your work

[upper karma]

Well one way

For right side I'll do

sin^2 x/cos^2 x +cos^2 x

And I don't know what you'd do then if that's correct

Would you divide cos^2 x by cos^2 x to get a common denominator? But then it'd equal 1

I don't think that's correct

[versed river]

I would probably work from the LHS actually

[upper karma]

And what do you do with that?

[versed river]

Do the division to get 1/cos^2(x)-sin^2(x)

[upper karma]

How do you get that?

[versed river]

I dont wanna type it up since im on my phone but

Sorry for the chicken scratch

[upper karma]

Oh alright

[versed river]

You understand how i got it? So thats sec^2(x)-sin^2(x)

[upper karma]

Yes

[versed river]

sec^2(x)-(1-cos^2(x))

[upper karma]

Yes

[versed river]

You try work from there, remembering to > consider pythagorean trig identities

[upper karma]

Alright I'll see

Oh yeah I see

You get 1+tan^ x -1 + cos^2 x

And that equals RHS

Yeah thanks for that

[versed river]

Could have just noticed that sec^2(x)-1=tan^2(x) too

Yeah no worries

[upper karma]

Oh yeah

[obtuse current]

dude why is the math chat's time of people talking so sporadic

[vagrant stratus]

idk lol

[upper karma]

Someone please help me

[safe cape]

https://en.m.wikipedia.org/wiki/Rose_(mathematics)
How to convert this formula
'r = cos(k¤)' into x and y how it is done on this Wikipedia page? Is this even easily possible to do so?

[dark sparrow]

i mean

what they did up there is the standard conversion from polar to cartesian

x = r cos(θ), y = r sin(θ)

i think if you try really hard you could try to convert that into an implicit equation but i'm not sure if it's worth the hassle

[safe cape]

So you multiply x by cos and y by sin normally?

For every polar fuction to get x and y

[dark sparrow]

.... that's a horrible way to phrase it

[safe cape]

Why

[dark sparrow]

neither x not y themselves are getting multiplied by anything

x = r cos(θ), y = r sin(θ)

[safe cape]

thanks found a nice website explaining it got it now I guess

[brave hill]

anyone can help me with 26) plz asap

[dark sparrow]

wym asap

,rccw

[dark sparrow]

god this is hard to read

[brave hill]

is it blurry

xd

i can retake another one

[dark sparrow]

yes please

it's low resolution as is

[brave hill]

,rccw

[dark sparrow]

much better

ok so where are you stuck

[brave hill]

basically have no idea where to start

i have no clues which theorem to use on this

[dark sparrow]

can you tell me what objects you can see on your diagram

don't overthink it

[brave hill]

it's an cyclic quadrilateral and two triangles

if thats what u are asking

nvm

i got it

XD

f

30 degre

since it's cyclic quadrilateral , 100+ angle DAB = 180

180-100 = 80

70+80+x=180

x=30

yea

this one is harder

,rccw

[brave hill]

woosh u got it

@pure pendant what does the y refer to

which angle is it

how abt the X

oh i see

[charred zephyr]

A ; B ; C are aligned points
What is the angle AEC knowing with Pi~3.14

can someone help please and thanks

[cosmic pebble]

From

#❓how-to-get-help

Rule 5

While asking questions, make sure you mention all relevant details, including the context, what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.

[silent plank]

wtf is E

[upper karma]

What is E?

[charred zephyr]

i think the center of the cercle which the triangle is inscribed it

to

[upper karma]

Which triangle

[charred zephyr]

uhhh wait

ABC

[upper karma]

Please tell the whole problem

[charred zephyr]

i really wrote it

up

the chat

[upper karma]

A ; B ; C are aligned points
What is the angle AEC knowing with Pi~3.14
This?

@charred zephyr

[charred zephyr]

Y3s.

yes*

[upper karma]

Where is the triangle

[charred zephyr]

ABC is the triangle and E the intersection of (BC) with the circle it is inscribed to

[upper karma]

Degenerate triangle?

I'm not following

[silent plank]

copy the problem exactly

[charred zephyr]

ok wait

[torn oar]

someone help and explain please ! i'm struggling so much with this

[upper karma]

Please tell the whole problem
@upper karma this had already happened to me several times, and i already gave up om helping him, every time he words the problem in any way he wants and expects me to help him when there is a ton shit load of info missing.

Even though i keep telling to copy it correctly, keeps missing stuff

Good luck

Thanks I guess

@torn oar let's move to the geometry channel

[torn oar]

okay..

[upper karma]

Oh nvm

Lol

[torn oar]

yeah

[upper karma]

Uh lets move to a free channel

[torn oar]

okay

where?

[upper karma]

Iota one seems free

#help-9

[torn oar]

are you coming?

[upper karma]

Yep

[charred zephyr]

(C') and (C'') are two circles such that :
(C') intersecting (C'') in A and B.
(D1) and (D2) are two parallel lines such that :

• A is a point of (D1) and B is a point of (D2)
• (D1) intersects (C') in A and A'.
• (D1) intersects (C'') in A and A''.
• (D2) intersects (C') in B and B'.
• (D2) intersects (C'') in B and B''.
• A'A''B''B' is a covex quadrilateral.
  Prove that A'A''B''B' is a parallelogram.

also im not a he

are you good now . i copied every single letter its not my fault if im having trouble concentrating while copying , like sometimes my eyes sees another exercise and im sorry @upper karma @upper karma @silent plank

[upper karma]

Is that the same problem

Just askin

[charred zephyr]

no because i couldnt focus on it lol just like ervy other problem i posted . before

thats why im sorry for wasting your time

[upper karma]

Np

[charred zephyr]

👍

do you have any ideas for this problem

[upper karma]

Hold on

[charred zephyr]

okay

[silent plank]

have you drawn a diagram?

[charred zephyr]

not yet its pretty diffixult

did you?

[upper karma]

I have drawn one

But you first

[charred zephyr]

i did one with a software im not sure if its correct

[upper karma]

I have a trivial solution

[silent plank]

show us

the image

[charred zephyr]

are.you sure

i send my sketch

[silent plank]

that looks fine

[upper karma]

Segment AB is really helpful

[charred zephyr]

ok

[upper karma]

And consider cyclic quadrilaterals A'ABB' and AA"B"B

What's a consequence of being cyclic?

[charred zephyr]

what is cyclic

[upper karma]

Inscribed in a circle

Prove that A'=B" and A"=B'

[charred zephyr]

ptolemys

[upper karma]

Not really helpful here

Prove that A'=B" and A"=B'
This should be enough

[charred zephyr]

what doe sit mean a point equal to a point

[upper karma]

I was referring to angles

Im lazy

[charred zephyr]

oh

did you get how you prove theyre equal

[upper karma]

Yes

[charred zephyr]

ok i ll try

[upper karma]

Now i have to go

I'll be here in 20 mins

[charred zephyr]

thank you

you confirmed my doubts lol

B'A'A + ABB' = 180
ABB'' + ABB' = 180
B'A'A = ABB'' 1️⃣
ABB''A'' cyclic quadrilateral
ABB'' + AA''B'' = 180
IA''B + AA''B'' = 180
ABB'' = IA''B'' 2️⃣
from 1 and 2 : B'A'A =BIA''B''
BB''A" = IA"B"
B'A'A = BB''A"
same goes to prove BB'A' = AA"B"
BB'A' = AA"B and B'A'A = BB"A"
A'A"B"B' is a parallelogram

is this correct

[upper karma]

Correct

[charred zephyr]

ok thank youu

[nova prawn]

which theorem is it?

8 th one. I could not prove it...

[upper karma]

@nova prawn Circumcenter idk

$a_1 + a_2 = a_3 + a_4$

[somber coyote]

leviosa:

[upper karma]

Prove that $a_1=a_3$

[somber coyote]

leviosa:

[upper karma]

@nova prawn Proving these two statements will lead you to the answer.

@nova prawn A hint to prove that a_1 = a_3 would be to prove that DE is parallel to AB. With that, you have two triangles with the same base and the same height. AKA, same area.

Gl ;)

And proving the first statement shouldn't be too hard :3

Wow ghosted

[nova prawn]

Thanks, a lot 🙂

[upper karma]

Np.

@nova prawn Don't focus on "what theorem to use," just focus on "how else can I solve this?"

Theorems will help you solve it, but theorems isn't the answer.

[nova prawn]

I am zero at Geo

So I started with Euclid's elements

[upper karma]

Never heard of it.

[nova prawn]

greek guy

the father of geometry 🙂

[upper karma]

Oh lol.

[nova prawn]

Trying to understand, my focus is how else can I solve this now.

[upper karma]

If you're only seeking to pass the class, you don't have to focus on the... "creative" aspect of math.

But otherwise, it'd be wise for you to do so.

[nova prawn]

I don't have to learn it right now, I have 2 more years. But it is important and geometry takes time i think.

[upper karma]

It takes a different mindset.

Which could include time or not :/

[nova prawn]

Do you think i am doing wrong?

I have plenty of time, and I also want to learn more advanced stuff than school.

[upper karma]

I'm only 16.

Barely certified to give you that answer.

[nova prawn]

I am the same.

[upper karma]

I'm only 16.
Same :)

Smh.

Lol

[nova prawn]

But a huge difference is I am from Turkey.

damn system

[upper karma]

Smh wut

I'm from America. And BOY, the math school system in America is garbo.

[nova prawn]

really?

you sure that is garbo

ahahahhaha

[upper karma]

Well, they teach you the stuff.

[nova prawn]

I wish that I would be there.

[upper karma]

But it's just the method I don't like.

[nova prawn]

Come to middle east than talk.

[upper karma]

Everything I suggested to you did not come from school.

If anything, I had a 69% in my most recent math class.

[nova prawn]

%69 means what?

[upper karma]

Like.

A very bad grade.

[nova prawn]

AH, i score 60 out of 100 🙂

[upper karma]

Schools for me is basically give you math questions.

And then you redo them 100 times.

But the numbers are changed.

I'd NEVER get a problem like the one you posted in school.

[nova prawn]

it is good, you solve math questions in math lesson.

[upper karma]

Nah.

I watch anime in math lesson

I only do challenge problems my teacher gives.

And then shit on everything else.

[nova prawn]

lol, i think we will get banned here it is geometry/trig channel lol

[upper karma]

Nah.

As long as no one else is talking here.

It's fine.

But yeah, you think you got the rest of the problem?

[nova prawn]

i will take care of, was doing the same thing but wanted to check.

[upper karma]

Nice.

[nova prawn]

USA's system is 100 times better than here.

[upper karma]

US' system for English, Science and History is pretty good. But not so good in math.

[nova prawn]

Here people learn to say hi in 12 years.

[upper karma]

Oof.

[nova prawn]

History is half-lie.

[upper karma]

I mean same for us.

[nova prawn]

Science? What is it?

[upper karma]

[nova prawn]

Here we have religious lessons lol.

[upper karma]

For history, they only tell you half of the truth, that's us.

And then they hide the rest of the truth.

[nova prawn]

Never experimented physcics but I study one of the best school.

[upper karma]

Oo nice.

You're lucky lol.

[nova prawn]

Why?

Was born in a country that they will block twitter/instagram tomorrow?

[upper karma]

I don't really have a passion for learning.

[nova prawn]

Why not?

[upper karma]

You're lucky in that respect.

School takes the fun out of it :/

[nova prawn]

I hate school

[upper karma]

I'm learning coding atm, which seems fun.

[nova prawn]

That's why i spend my all time on KhanAcademy and MIT OCW

Same thing, but different ways.

I am learning neurel networks/deep learning. So math is needed.

[upper karma]

Khan Academy math (in particular) only scratches the surface of certain concepts.

I suggest you use openstax.

https://openstax.org/

[nova prawn]

I have

[upper karma]

Much better, for the purpose of actually understanding a concept.

[nova prawn]

never seen it.

[upper karma]

Instead of rinsing and reusing the same concept.

[nova prawn]

i have seen classcentral etc. but it is the first time

thank you too much.

[upper karma]

Nahnah.

[nova prawn]

I just find e-books from Libgen and try to solve&understand them.

[upper karma]

Gl.

Lol libgen is great.

Khan Academy math (in particular) only scratches the surface of certain concepts.
Hmmm do you really think so?

I didn't feel like so when completing courses

[nova prawn]

In USA do you pay money for high school?

or how it is decided to go better one.

[upper karma]

For public, it's paid via taxes.

But they don't tell you that

Scratch the surface, I mean they don't give you a lot "variety" to certain problems @upper karma :/

[nova prawn]

Like do you pay for books etc?

[upper karma]

Oh agreed

Fair

We generally rent from our school library.

And that's about it.

But we do have to pay like 300$ for each textbook if we lose it or anything.

[nova prawn]

Hmm, like how do you go middle school to high school.

do you enter exam.

[upper karma]

Nah.

[nova prawn]

wut

[upper karma]

I go to public high school.

@nova prawn are you planning to move to us or you are curious about it lol

[nova prawn]

I will move

but time is needed

[upper karma]

Nice

[nova prawn]

I don't like people here

[upper karma]

Why not?

Greetings from Spain

American people are... quite

[nova prawn]

They are literally idiot, they don't understand religious, respect...

[upper karma]

OH BOY.

YOU DON'T EVEN UNDERSTAND.

AMERICANS HAVE 0 RESPECT.

TOWARDS ANYTHING.

[nova prawn]

Really?

[upper karma]

They tore down a Jewish statue last week and said it was in the name for justice.

And no one fucking cares.

Okay obv not like that.

[nova prawn]

lol

[upper karma]

Well, the people protesting for BLM killed a black sheriff that was trying to protect a pawn shop.

[nova prawn]

Twitter and instagram are getting blocked here because they have written idiotic things

[upper karma]

And that was in the name of justice.

[nova prawn]

I know, %50 are robbers.

[upper karma]

America, while still a great place, has a society that's slowly rotting to absolute shit.

American minors thinks that adults are wrong, no matter what they say.

[nova prawn]

Here is absolute shit, trust me. I am not american dreamer 🙂

[upper karma]

Hence, the boomer meme, and all that bs.

There's very little respect in what America has to offer.

They either hate you for being successful, or they like you for their own political gain.

[nova prawn]

fuck politics.

[upper karma]

In America, people are now thinking if you're successful, you're robbing from everyone else.

They have no idea what risk management is, and how many employers are making less than their employees.

[nova prawn]

People go to mosques for praying because they don't want covid to come them.

[upper karma]

Oh and if you're successful, half of the money you make goes to the government to be wasted on useless shit.

[nova prawn]

half of the money?

[upper karma]

Yes.

[nova prawn]

If you buy car here

[upper karma]

Literally 50%.

[nova prawn]

tax is %300

literally %300

[upper karma]

Jesus.

That sucks ass.

[nova prawn]

mustang is 200-300k dollars

because it is engine is big 🙂

they take 2 different taxes, and another one for that taxes

[upper karma]

That sounds like pure corruption

[nova prawn]

They earn %100 more money than producers

how do you expect them to make cars, or produce something

[upper karma]

Idk what it's like to live in your shoes, but from the sounds of it, hella worse than the average American.

But if you're looking for any amounts of respect in America, you've come to the wrong place :/

JESUS.

DAILY?

HOLY CRAP.

[soft gulch]

#geometry-and-trigonometry

Suits this

[upper karma]

America is not a respectful country. You're categorized than stereotyped.

@soft gulch No one else using channel lol.

Ig we should stop it here.

[nova prawn]

Lol, it is ridicilous

if i say bad thing, i go to prison for being agent of FETO

[upper karma]

In Kansas University.

[nova prawn]

do you know him?

[upper karma]

The football players are threatening to quit their job (that's hella high paying btw) just cuz some random white kid in the school posted something on Twitter they didn't like.

Americans are turning into weak sauce.

They have no confidence in themselves, and they can't stand their own ground.

[nova prawn]

they go to streets

Do you know how good it is

[upper karma]

Yeah and then loot buildings and burn banks in the name of justice smh.

Eventually, America is gonna be ran by these fools.