geometry-and-trigonometry

[upper karma]

Yes

[obsidian harness]

hmmmm give me some time

https://proofwiki.org/wiki/Equal_Alternate_Angles_implies_Parallel_Lines

the proof is absolutely horrendous if you use Euclid's axioms

but I think yes, the approach would be by contradiction, as in assume lines l and m meet at a point

then deduce a contradiction from this

[obsidian harness]

still thinking a bit

ah if you assume angle EHB = angle EJD, which is our given

then you must have angle JHB + angle HJD = 180 degrees by angles on a straight line, contradiction

so lines AB and CD never meet at a point, implying they are parallel

(this is Euclidean geometry so we can use the parallel postulate)

no need for congruent triangles

[silk jacinth]

length of AC = 12, length of BC = 19. the assignment is to determine the radius of the circle.

I solved this by first making use of the fact that the center of the circle (O) is where the perpendicular bisectors of each side intersect, then created a equilateral triangle ABO, then used the cosine law to determine the length of its base (AB) with its apex being 140 degrees (as central angle is 2 times the angle on the perimeter), divided ABO to two right triangles and solved for length of AO which equals the radius.

I'm pretty sure there's a way to do this without using the information of central angle being 2 times the angle on the perimeter, but I can't figure it out. any tips on that?

[obsidian harness]

another way would be to use the extended sine rule

the radius of the circle is the circumradius R

so you could find AB using the cosine rule and then you can divide by 2 * sin(70 deg) to find R

[silk jacinth]

judging from the context of the assignment and previous material in the textbook, I shouldn't be able to use that either

[obsidian harness]

https://proofwiki.org/wiki/Law_of_Sines#Proof_2

actually it's no different to what you did, here's the proof

that means there's no other way
thanks for confirming what knowledge you can use for this question, by the way

[silk jacinth]

if that's the case, it's odd. the textbook doesn't mention the = 2R extension anywhere, and the inscribed angle theorem is mentioned only in a subsequent chapter. this is why I was so puzzled by this assignment and spent lots of time trying to come up with an alternative way to solve it

[obsidian harness]

yeah that's odd?

which textbook are you using

[silk jacinth]

it's a Finnish textbook for high school level geometry

[obsidian harness]

ah okay

[silk jacinth]

it's for LOPS-2021, which is the latest curriculum for high schools. IIRC there were some legislative issues which required some of the authors to whip up new textbooks in haste, so I've found a variety of mishaps and errors across several books. maybe this is one such mishap

[obsidian harness]

perkele

[silk jacinth]

😄

[obsidian harness]

that's fascinating, I never knew too much about the Finnish education system

[silk jacinth]

I might be mistaken so take it with a grain of salt

[obsidian harness]

well there are a lot of news reports saying your school days are shorter but your standardised test results are very good internationally speaking

but yeah I never thought about what you guys learn in classes

[silk jacinth]

we've two math programs in the curriculum - "short" and "long". short is less abstract, less demanding and more practically oriented, while long is the path taken by those who want to study STEM fields

[obsidian harness]

it's nice you're still doing Euclidean geometry like this

in many Western countries it's been removed

[upper karma]

Ohhhh

Tysm

[obsidian harness]

no worries!

[neat wigeon]

i realized it was impossible triangle but ig it specifically wanted me to use Pythagorean theorem
I've encountered a lot of these impossible triangle problems in my school textbook and they all have an "answer" if u use a specific technique

ya ur cooked

[lyric ocean]

Haha

It got over😭😭

[cinder raven]

how'd you actually do that?

[neat wigeon]

?

[cinder raven]

Fun exercise

[fallow palm]

are you looking for people to do your homework

[cinder raven]

no

i can do it

just to let other people look at it

Its quite easy

[flint marlin]

Quite easy ? It's baby maths -_-

[granite kraken]

i havent done trigonometry yet

im gonna do it this year

[kind jungle]

where can i find advanced trigo questions for free

[tiny sundial]

maybe it would help being more specific...

[worn scroll]

wdym by advanced trig

[fierce nimbus]

hi

bye

[acoustic pumice]

Can anyone help

[floral linden]

?

[acoustic pumice]

how did u get 60 for angle Q

[floral linden]

MQR = 60 ?

MQP should 15 from 75 - 60

[obsidian harness]

yes and yes

and now what is angle RPQ?

so then how long must side MQ be?

great, now you just have the right-angled triangle MRQ to solve

[flint marlin]

Easy question

[fallow palm]

who sets orthocentre as T

that is so cursed

[flint marlin]

Me ;)

[fallow palm]

you should be sent to geometry jail or something

[flint marlin]

I love geometry, I have made the jails

Also jk I didn't , some doomed person committed that crime

[fallow palm]

yeah some guy in MODS

[flint marlin]

Orz

[maiden brook]

loll

[maiden brook]

wait what’s the shape of a geometry jail

[neat wigeon]

9

[buoyant rivet]

Anyone have tips for memorizing the unit circle?

[silent plank]

for Q1,
sin(0) = sqrt(0)/2
sin(30°) = sqrt(1)/2
sin(45)° = sqrt(2)/2
sin(60°) = sqrt(3)/2
sin(90°) = sqrt(4)/2
the rest can be determined from symmetry

[limber tide]

idk if this will help, my writing and labeling could be better, but i've color coded the patterns that could be observed. i use these in familiarizing the unit circle

[buoyant rivet]

Thanks

[limber tide]

for the radians, you can see that every denominator has 6, 4, 3 with 6 being the one closest to the x axis

for the numerators of the radians, Q1 is just pi
for Q2, the coefficient of pi is 1 LESS than the denominator (idk if i'm stating this right lmao, by coefficient i mean the number next to pi)
for Q3, the coefficient of pi is 1 MORE than the denominator

[finite cave]

can anyone help me pls?

[obsidian harness]

Note that DB = DC as D is on the perpendicular bisector of BC

This tells you that triangle ABD is isosceles

Can you continue?

[finite cave]

yes, thank you!

[obsidian harness]

Np!

[buoyant rivet]

That helps

Using the formula a = sqrt(c^2 - b^2)
What if I just decide that 2.74 was B and 2.3 was C

That would change the answer

[obsidian harness]

c is defined as being the hypotenuse

[buoyant rivet]

Ah

Ic

[obsidian harness]

actually if you try that, you will be square rooting a negative number

and that gives you a non-real answer

[obsidian harness]

and a, b don't really matter

it's like you're tilting the right triangle to lie on its shorter leg or its longer leg

the hypotenuse doesn't change

[buoyant rivet]

Makes sense

[limber tide]

are you tryna find s?

[buoyant rivet]

Is this correct? does tan always equal 0 or undefined when its at a quadrantal angle?

[buoyant rivet]

Yes

[limber tide]

tan is 0 when it's on the x axis, and undefined when it's on the y axis, since tan = sin/cos which would be 1/0, 0/1 -1/0, etc

[buoyant rivet]

Oh because we're dividing by zero?

[limber tide]

yeah, yeah

on the unit circle (x, y) = (cos, sin), if the coordinates are (0, 1) that would make cos = 0, and sin = 1

making the tan value 1/0 or undefined

[limber tide]

that makes this right actually yes

[buoyant rivet]

👍

[obsidian harness]

yes in fact sin theta = y and cos theta = x

y/x is the slope

when the slope is undefined, the line must be vertical

so those are at (x, y)= (0, 1) or (0, -1)

or theta = 90 deg, 270 deg

[buoyant rivet]

Thats cool

So when the slope is zero

The line must be horizontal

[obsidian harness]

yep!

[buoyant rivet]

👍

[obsidian harness]

so that means if you want to solve tan theta = 0, that's just when y = 0

or sin theta = 0

so 0 deg or 180 deg

or 360 deg, well we don't usually say that cause it's the same position as 0 deg

[bright python]

@trail tendon I tried the same thing with the interval table that the teacher taught us but idk didn't get the same thing

[finite cave]

can anyone help me pls

[fallen surge]

yo people

is this possible

[sweet socket]

some help with this would be cool

[upper karma]

How did it went?

[valid sandal]

Studying for midterms what are the options

[valid sandal]

Im not sure it might be 27 edc

[hushed halo]

any help?

no idea how to do this

didnt pay attention

[upper karma]

Ye

Can you use google

[hushed halo]

yes

tried ai gave wrong answer

multiple times

[upper karma]

Dont use ai

Look up how to find diagonals of trapezoids

And then read

And then tell me what youve tried

[exotic yarrow]

Tbf you need a general algorithm since this is a right trapezoid

Pythagorean theorem suffices

[hushed halo]

cant find what i need

really im looking for an answer since i cba to research maths

[trail tendon]

can you find CD?

[hushed halo]

ah

i knew id need that

i

i tried

and still got no clue how to find even that

[trail tendon]

if I drew a line like this, do you know what length L is?

[hushed halo]

7?

[trail tendon]

yeah

would you know how to find the length of the red line i drew?

[hushed halo]

nope

[trail tendon]

do you remember how to get the third side of a right triangle if you know two sides...

[hushed halo]

hypoteneus?

[trail tendon]

well the hypotenuse is 16

one of the legs is 7

you can find the other one tho

[trail tendon]

remember the pythagorean theorem? 😔

[hushed halo]

yea

[trail tendon]

if the hypotenuse is 16 and one leg is 7, do you know how to find the third side?

the other leg

[hushed halo]

16 squared+7 squared and square root it?

[trail tendon]

close but uh

[hushed halo]

wait

no

thats for hyp

its minus no?

wait

shit

i forgot

[trail tendon]

yeaaa but which is minus

:P

so
a^2 + b^2 = c^2 where a,b are the two legs and c is the hypotenuse (longest side) right?

so if one leg is 7 and the hypotenuse is 16, do u know the other leg? :P

[random nest]

I remember a way of memorizing was, big square, medium square and small square. to get big square (hypnotenus) it's medium square + small square. ect

don't know if it's good tho

[trail tendon]

do you mean like the visual proof of the pythagorean theorem?

[random nest]

yeah

[trail tendon]

ah yea

[random nest]

It was so helpful when first learning about it

[hushed halo]

no clue, im guessing 16^2-7^2 and square root

[trail tendon]

well ur guess is correct XD

[hushed halo]

i remembered something atleast

[trail tendon]

the length of the red line is sqrt( 16^2 - 7^2 )

because a^2 + b^2 = c^2
we can let a=7 and c=16, so 7^2 + b^2 = 16^2 -> b = sqrt(16^2 - 7^2)
where b is the other leg

anyway

the length of the red line is sqrt( 16^2 - 7^2 )
does that give you any idea for the length of CD?

[hushed halo]

14.3874945699

[graceful talon]

,w sqrt(16^2-7^2)

[somber coyote]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[trail tendon]

what length does that represent tho

[hushed halo]

cd

[trail tendon]

yeye ok

so then u gotta find AC

any ideas for how to calculate it? :P

[hushed halo]

ohh

i did it

18.11

thanks man

thanks alot

lets be friends😭🙏 ill need u in life

[maiden brook]

if this isnt what u mean, my favorite is the area of the large square in two ways: (a + b)^2 = ab/2 + ab/2 + ab/2 + ab/2 + c^2 gives u straightaway that a^2 + b^2 = c^2

[random nest]

Might sound ridiculous but I never looked at this visualization before ; my mind is blown ! this is beautiful what the hell ? I've found my new favorite representation now :')

[agile bough]

what is this for, is this proving the pythagorean theorem

[maiden brook]

yep

[maiden brook]

🙂

[finite cave]

its 57

[finite cave]

can someone help me to solve this

[maiden brook]

your answer is 57 degrees. im trying to figure it out

(i got it through geogebra)

[silk gorge]

Hello, I would like to ask how can you answer this? I have been having a hard time + i keep encountering this

char

[maiden brook]

what progress have u made

why is the pythagorean theorem what u have to force yourself to remember of all things (its kinda ubiquitous)? i dont remember like the tangent half-angle just thinking of something random but thats not bad to derive

[silk gorge]

okay na guys

[maiden brook]

what are “index laws”

u don’t have to drill them but dont u kinda have to remember them?

like ok if m and n are positive integers u can “prove” them (but some of them not that rigorously), if not, u can’t rlly prove them easily

yeah. it’s only half their fault, the format of the school curriculum and the tests students are given greatly encourages it

index laws makes me think of summation. The summation rules u rlly don’t have to memorize

[bleak blade]

who actually remmbers tangent half angle

[maiden brook]

yeah. I think the proofs can get kinda hard (compared to how basic the concept is). If I recall to do it correctly u need definition of the exponential (with calculus) and it shouldn’t be too bad

[maiden brook]

I had to (for school)

[maiden brook]

what do u think of my teacher who said this (it is a quote)
“One of my former students forgot the sine double angle formula. We never spoke again after that.”

(I hope this is a joke, in actuality he’s a decent teacher like one of my best)

yeah. I think it’s probably one of the most difficult (relatively-speaking) proofs for some in arithmetic

[bleak blade]

my math teacher had a good way to remember how the cosine sum formula works

basically you know how its cos * cos - sin * sin

"pizza pizza"

[maiden brook]

this is probably my favorite proof of the addition / subtraction ones (it feels much more natural than the geometric setup one), and then it’s easy to get the double angles

https://mymission.lamission.edu/userdata/sargsye2/docs/Math 240/Proof of the difference formula for cosine.pdf

yeah u nicely get the distance in two ways using a rotation

but that’s only for acute angles

yeah I know I’ve seen that

but then u have to extend it for non-acute angles

sen lol

[abstract sparrow]

chat help

or not

thanks

[maiden brook]

Be patient

Are u stuck with everything?

[slender rain]

In phytagoras
$c^2 = a^2 + b^2$
Why we can't make like this:
$c = \sqrt{(a+b)^2}$
So that
$c = a + b$

[somber coyote]

カザミ

[maiden brook]

because sqrt(a^2 + b^2) is not (generally) equal to sqrt((a + b)^2)

or $\sqrt{a^2 + b^2} \neq \sqrt{(a + b)^2}$

[somber coyote]

hockeydude85

[maiden brook]

example: a = 3, b = 4

Most importantly, just because both expressions have pluses and squares does not mean that they are equal. Things are equal for a reason.

[fallen surge]

anyone pls ans?

[silk gorge]

hello again

i computed everything and subtracted it to 360 but my answer is a negative number

omsdajfkdbcasfasc

[lilac nebula]

$-64x^\circ + 122^\circ + 110^\circ &= 360^\circ \
-64x^\circ &= 360^\circ - 232^\circ \
-64x^\circ &= 128^\circ \
x^\circ &= -2 \
\
\angle LNK &= 1^\circ - 22x^\circ \
\angle LNK &= 1^\circ - 22(-2)^\circ \
\angle LNK &= 1^\circ + 44^\circ \
\angle LNK &= 45^\circ$

[somber coyote]

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

[mellow merlin]

do you divide or multiply using the ratio

you divide

just learned you also multiply if its cos

[silent plank]

what you do depends on what's given

start with setting up your equation

whether you divide or multiply will be clear from there

[autumn heron]

Completely lost at 7.2

If BD = xsin(a) due to BD being opposite angle a and x being the Hypotenuse, how am I meant to solve 7.2?

Do i attempt to use the sin rule with side BD? The angle opposite BD is not given either so I'm not sure

[junior wigeon]

guys what do I input on my calculator to make cos 30 = root 3 over 2?

[autumn heron]

What do you mean?

[hoary totem]

change to degrees
or press S <=> D

[valid sandal]

Just failed midterms i think

For geo trig

[mellow merlin]

im confused

what does tan65 rlly mean

like what number r u multiplying by 5

[obsidian harness]

tan 65

tan 65 is the ratio of the opposite side to the adjacent side of a right triangle with a 65 degree angle

if you think about this definition a bit further

tan 65 is also the slope of the line that makes a 65 degree angle with the positive x-axis

[quaint ibex]

you

yo

can sum1 help m

e

[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.

[tepid heart]

guys i got a test tomorrow can someone send me a yt link to good videos on these subjects

[void hearth]

Right Angles?

SOH CAH TOA?

and Cosine law + sine law

[delicate cove]

is there any connection between the golden ratio and the power of two or doubling in a circle inside a circle pattern?

[finite cave]

can someone help me pls?

[slender maple]

Let <J = 2a and <K =2b

and then find all angles most of them will be in terms of a and b,After that i guess you will form 2 equations which you will solve simultaneously consider sum in triangle JMK and polygon MPNK

then play around with some algebraic manipulations and then you will find x

[finite cave]

thank you!

[slender maple]

👌

[finite cave]

sorry, but I dont understand how to find other angles

[slender maple]

Use your euclidean geometry properties e.g angles on a str line sum up to 180 degrees and so on...

[finite cave]

thank you so much

[wise zodiac]

why can i draw a triangle

-pi/2 <= y <= pi/2

it'd be a weird triangle right....

not to mention [0,pi/2] tan(y) is positive whereas [-pi/2, 0] tan(y) is negative

i know how to do it the "algebraic" way. I'm just curious why the "right triangle" method works here

[slender maple]

Note that i think x can be positive or negative so you have to provide a response for both cases

[slender maple]

Sin is positive in the 1st and 2nd quadrant where an assumption that x is postive

use the CAST method to remember which trig func is postive

[wise zodiac]

yeah so split as 0 <= y <= pi/2 and -pi/2 <= y <0?

@slender maple

people just draw one right triangle tho

with angle y and opposite that angle we have side length x

and the hypotenuse is 1

and then get tan(y) from there

tbh doesn’t make sense

[wise zodiac]

we’re looking at 1st and fourth quadrant

not 1st and 2nd though

[slender maple]

I am referring to sin being positive and not tan

read my previous message again plz

[wise zodiac]

but it has nothing to do with the 2nd quadrant

so idk what you're point is

sure sin is positive in 1st and 2nd quadrant

but that's literally not related to our question?

we're working on 1st and 4th quadrant

[autumn heron]

Am I allowed so cancel the sin(a) on the left hand side?

[slender maple]

The question you provided is partial incomplete

it says nothing about the domain of y

[wise zodiac]

domain of y????

u mean range?

and no it isn't "partial incomplete"

we know that arcsin(x) has a range of [-pi/2, pi/2]

so y has range of [-pi/2, pi/2]

[slender maple]

Assuming that then you right

[wise zodiac]

yes

[autumn heron]

Perfect, thank you!!!!

Bro no better feeling than finishing a sum after sitting with it forever

Assuming my solution is correct, otherwise...

[wise zodiac]

it's because if alpha = 0 or pi then then sin(alpha) = 0 [ which u may have guessed is not allowed ]

but alpha can't be 0 or pi because u wouldn't be dealing with euclidean triangles anymore

[wise zodiac]

uh yeah

[gleaming ruin]

and arcsin is a function defined from [-1;1] to [-pi/2;pi/2] so the cos should be positive

[wise zodiac]

thanks for the help but like answering the question wasn't my concern

sin(y) = x and cos(y) = +- sqrt(1 - x^2) but since y in [-pi/2, pi/2] then cos(y) > 0 so cos(y) = sqrt(1 - x^2)

hence tan(y) = x/sqrt(1 - x^2)

[gleaming ruin]

yes i said it here

trying to do it with a geometric way,you will end up using this

[civic dune]

hey can anyone help me with my khan trig hw ill screenshare

[hoary prism]

js ask in chat bro

[burnt eagle]

can anyone help?

[ivory rain]

Since it's a parallelogram MP=PQ so MQ = 16.4

[hot vault]

https://discord.com/channels/268882317391429632/1333890913629634622

[opaque anchor]

can anyone can solve this question

[chrome token]

super cute problem

[ivory rain]

Tan of 90 and 270 degrees is not equal to infinity right it just approaches it from the positive direction

[graceful talon]

i think it does

but i think infinity isn't a number anyway

so maybe it's implied that if something equals infinity, it approaches a very large number

[ivory rain]

But isnt it similar to 1/0 in that it approaches positive infinity from negative but approaches negative infity from positive

So no limit

[graceful talon]

I'm not really sure. I'm not knowledgeable in these

[ivory rain]

I mean it seems similar

[graceful talon]

i tried it in wolfram alfa

,w tan(90°)

[somber coyote]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[graceful talon]

that symbol is a complex infinity

,w complex infinity

[somber coyote]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[graceful talon]

idk what's the difference from just infinity

same result with 1/0

it's not really related to your question but yeah

it might lead to it

idk stuff. my knowledge are just duct taped pieces of information

ok wikipedia says complex infinity is a complex number $r\angle\theta$ where $r$ is infinity. Just that. Nothing special

[somber coyote]

0_א

[graceful talon]

nvm idk i didn't read the whole page yet

[graceful talon]

so ur saying 1/0 = infinity is incorrect to say?

shut up

<@&268886789983436800>

i think this is the 2nd time

[ivory rain]

Yeah?

[graceful talon]

yeah

btw idk if u misinterpreted it i wasn't saying shut up to you. there was an advertising spammer here

[dreamy nimbus]

undefined is a better term bc infinity isnt a number

as the denominator for 1/x increases you approach infinity

so it'd be better to just say tan 90 and tan 270 are undefined

cause they're asymptotes on the tan graph

[dense carbon]

I made a silly little formula to calculate the perimeter of any given regular polygon assuming it’s circumradius is equal to 1 but you can also adjust it

Desmos only allowed me to plug radians into trigonometric functions so yeh

[restive abyss]

So long story short, I have a huge unit test tomorrow and I need at least an 88% on the test if I want to finish my class with a 90, the test is on the whole unit for trigonometric identities and I’m hoping someone could help me study for tonight. There’s a few things I still don’t get

[dense carbon]

What are trigonometric identities

[dense carbon]

Ok

[restive abyss]

like sinx = cosx/cotx

[dense carbon]

I looked up what trigonometric identities are

[dense carbon]

Cot is uhhh 1/cos right

[restive abyss]

no, cot is 1/tan, cot is the inverse of tan

here, lemme send a pic of some of the stuff that would be on my test

[dense carbon]

Ok

[trail tendon]

reciprocal of tan, wouldnt say inverse 😔

[dense carbon]

Because i self taught myself trigonometry because I was bored and middle school math was boring

Well the basics

[restive abyss]

oh yeah that, im not the best at math 😭

that’s basically what my test is on

plus solving for stuff like “sin3x = 1/2”

[dense carbon]

Do you get to use a calculator

[restive abyss]

yeah

but it really wont do ya much good

[dense carbon]

How

[restive abyss]

a lot of the test is really just based off of knowledge of formulas and creativity with solving algebra based questions

[dense carbon]

Ah then I can’t help you

[restive abyss]

also cuz hes not expecting any answers with decimals or anything, hes mostly expecting fractions

[dense carbon]

I only learned sin cos and tan and how the work in the past 1 month

In my free time

And also I use Desmos which idk how to put degrees in

So I only know how to use radians

How unfortunate

Give me a few months and I’ll probably learn more

[restive abyss]

wait im confused, are you in middleschool, highschool or college?

[dense carbon]

Middle

School math is eh

I listen like a tenth of the time

[neat wigeon]

are u in algebra in middle school

[dense carbon]

Yeh

[neat wigeon]

nice

[dense carbon]

I listen in math class a tenth of the time then if there’s a test I extrapolate how to do the test from the tenth

[neat wigeon]

math in general is easy tbf

[dense carbon]

Yeah

[maiden brook]

Nah. just cause u had easy classes doesn’t mean it’s easy

[dense carbon]

Well depending on how advanced you are

I’m doing linear equations in math and I’m bored half of the time

Quadratics is coming soon

So hopefully that’ll pique my interest

[neat wigeon]

quadratics is quite interesting

[maiden brook]

No

[neat wigeon]

LOL

well

[maiden brook]

What’s interesting about quadratics

[neat wigeon]

compared to linear equations it's a billion times more fun

[dense carbon]

First time I come in blind to something

[dense carbon]

Not really fun more intresting

[maiden brook]

Well systems of linear equations can lead to linear algebra (I haven’t taken it yet so I don’t know much about it)

[dense carbon]

I spent yesterday math class in school making a formula to calculate the the perimeter of any given regular polygon

[neat wigeon]

once u get to quadratics u should try to figure out why quadratic formula works for fun (-b +- sqrt(b^2-4ac))/2a

(it took me 3 months to understand why)

[maiden brook]

given what?

[maiden brook]

3 months? not to be rude?

[neat wigeon]

ya but that's college level stuff so idk anything about it

[maiden brook]

My high school offers it

[neat wigeon]

?

[dense carbon]

Assuming it is inscribed within a circle of radius 1

[maiden brook]

it’s just the general case of completing the square

[dense carbon]

This?

[maiden brook]

ah. So then u have to get into a tiny bit of trig

[dense carbon]

I did

[maiden brook]

yeah

[dense carbon]

But Desmos only lets me use radians so it’s a bit messy

I would like to use degrees but I can’t

[maiden brook]

It should be pretty simple. The “central angle” is 360/theta
so by the law of cosines c^2 = a^2 + b^2 - 2ab cos c

so c^2 = 2 - 2 cos(360/theta)

[dense carbon]

I did it in a weird way

[maiden brook]

c = sqrt(2 - 2 cos(360/theta))
(There’s probably a way to denest but whatever)

[dense carbon]

I set 90 degrees to equal pi/2 radians

[neat wigeon]

yes but it's more than that
b is the sum of the solutions, b/2a is the axis of symmetry, and b^2-4ac is the distance of the solutions squared, so by finding the square root u find the distance between the solutions
and dividing it by 2a is the distance between axis of symmetry and each solution because each solution is equidistant to the axis of symmetry

whoever made it is a genius. absolute art.

[dense carbon]

And 180 to equal pi radians

[maiden brook]

And then it’s n * sqrt(2 - 2 cos(360/n))

[maiden brook]

u don’t set it equal it is equal but ok

[dense carbon]

So it’s 180pi/degree

Hold on

[maiden brook]

b is not the sum of the roots in ax^2 + bx + c

[dense carbon]

It’s pi(degrees)/180

[maiden brook]

?

[neat wigeon]

how is it not

[dense carbon]

That converts degrees to radians

[maiden brook]

don’t do work converting u can convert at the end

[neat wigeon]

oh i meant it's the negative of the sum

basically same thing

[maiden brook]

It’s not that either

It’s -b/a

[neat wigeon]

it is

no

[maiden brook]

do u wanna bet?

[neat wigeon]

-b/2a is axis of symmetry

oh wait

Ah

ur right

[dense carbon]

I divided the shape into triangles then did 360/s for the angle at I guess the top of each triangle
Then I divided it in half to make it a right triangle
I then put it in pi(degrees/180) for the opposite side which happens to also be part of a side in the shape
I taht whole thing in sin
I multiplied it by 2 to get the full side length then by s to get the perimeter
S = amount of sides

Hold on I forgot a step

I fixed ut

So it turns into

(sin(pi/((360/2s)/180)))2s

It works I guess but it probably could be simplified

[obsidian hornet]

Agreed, nice problem, any faster solutions?

[bleak blade]

3 months is diabolical

all you do i complete square

[maiden brook]

one of the other calc teachers in my school said it took him “ten years” to understand delta epsilon proofs.
That would be disappointing

[upper karma]

yo can someone pls help me w this dam question i have no fckin idea how to solve it🙏 😭

[neat wigeon]

ya ngl i don't even know what completing the square means

[full quest]

can someone help me with this

[neat wigeon]

too much to read

[full quest]

its for my personal finance class and i think its 11 but idk

just need the one thing thats wrong please lol

skim it

[neat wigeon]

idk

[full quest]

ok thx anyways

[bleak blade]

then how do you understnad the quadratic formula

[maiden brook]

??

[maiden brook]

geometrically for some reason

[neat wigeon]

ya geometrically

[maiden brook]

But the thing is the quadratic formula always works no matter if the roots are real or not so it’s not perfect to think just geometrically for multiple reasons

[neat wigeon]

true

[ivory rain]

I figured it wasn't directed at me

[neat wigeon]

interesting

they never taught this to me in school

i wonder why

[maiden brook]

rlly?

what grade r u in

[neat wigeon]

10th

algebra 2 honors

currently

tbf i had a really bad algebra 1 teacher

[maiden brook]

what r u doing rn?

[neat wigeon]

rational root theorem

[bitter roost]

Does anyone have any resources to learn geometry? Some thing like a review packet or practice final since im pretty comfortable w math

[tulip ether]

@ruby walrus

[chrome token]

i velieve i did the same thing but instead of the length cgase at the end, i did a inversion, but i guess those are equivalent

[obsidian hornet]

Yeah, I noticed inversion later, but anyway thanks for the information

[mellow merlin]

i thought the triangle was inside the unit circle

[graceful talon]

the red one is

[hybrid belfry]

1. How would you wanna define what "straight" mean?

2. How would you wanna define a line?

[split tide]

1. points are collinear
2. shortest distance between 2 points

[hybrid belfry]

1. I thought collinear and straight are just synonyms?

2. That's a straight line, not any line.

[split tide]

Lines are straight

Well collinear points form straight line

But you can construct curved lines by joining points in any way you want

[crisp quail]

@wicked lark

[wicked lark]

thanks

[tame oriole]

guys should i learn all the sum to product and product to sum identities by heart or not

[wise zodiac]

depends on what u want to do with t

always better to understand why it's the case

but if your exam/course just requires you to directly apply it then sure i guess...

it's your choice

[tame oriole]

aight

[grave forge]

Prove that the angle bisecotor of an angle and the perpendicular bisector of the side opposite to that angle meet at the circumcircle of the triangle which we're talking about.
I contemplated the following:
DE = EB since AF is the perpendicular bisector of BD and the centre of the circle is A.
angle DAE = angle BAE
angle DCB = 2θ (let)
angle DCF = angle FCB = θ (since CF is the angle bisector of angle C)
angle DAB = 2 * 2θ = 4θ
angle DAE = 2θ
angle DBC = x (let)
angle ACB = x + 2θ - 90
angle FCA = θ - (x + 2θ - 90) = 90 - x - θ
angle CAF = 2θ + 2x
angle CFA = 180 - (2θ + 2x + 90 - x - θ) = 90 - θ - x = angle FCA
This implies AC = AF = radius = R
But the circle is the locus of every point at a fixed distance from a given point, which is here the central point A.
So F must lie on the circumcircle to satisfy that AF = AC = radius.
Done.
Is this proof of mine correct?

[spice current]

https://www.desmos.com/calculator/guir75gvha

Made the Witch of Agnesi graph in Desmos

Also shows the area under the curve (without the circle).

[ruby fulcrum]

does someone know the defintion of a inscribed. like exact.

[spice current]

Usually just the largest something that can fit in another something without crossing any lines.

[ruby fulcrum]

ok ty

[spice current]

👍

[hybrid belfry]

I mean if collinear and straight are just synonyms then it's not a definition, it's like saying a straight line is a bunch of points that connected into a straight line.
Kind of a circular definition.

And you need to draw a straight line or a curve to connect 2 points,
how can you join 2 points without any straight line or curve?

[split tide]

you cant join 2 points without any straight line or curve

you have to use something to join and it is always gonna be either straight or curved

[obsidian harness]

it really depends on your definition and conventions

[hybrid belfry]

What kind of connection is that? 😅

When you join something together,
you need to connect them using something.

2 points can be connected using an infinite number of points or no point at?
Then... the points touch each other or something?

It's really messy when you make a cross-over between the dimensions like a point and a line,
infinity is not something that we can do anything with 🤔

[obsidian harness]

in physics or chem you can say that a line is curved, if you want to specify you need to say straight line

[graceful talon]

what do you mean by connect

you don't have to answer me

[split tide]

hmmm, there can be infinite points between two points but those infinite points form a line

[hybrid belfry]

I wanna ask your definition of a line no matter if it's straight or curved and
your definition of a straight line.

Define them in any order you like

[graceful talon]

what is a line

,w define line

[somber coyote]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[graceful talon]

same here

[hybrid belfry]

Yea, because it's infinity,
so it's very difficult to calculate or do anything with it since we can't do anything with infinity.

[graceful talon]

limits

[hybrid belfry]

That's what i'm asking

[graceful talon]

yeah i didn't see

[graceful talon]

is this the original question

[hybrid belfry]

I wanna know how clear definitions OR descriptions
about the foundational stuff can be 😄

[graceful talon]

what is foundational stuff

[split tide]

straight lines are 1 dimensional but curves are 2 dimensional

[graceful talon]

there's a #foundations channel but i barely know what's it about. I guess it's about like the really fundamentals of the fundamentals

[split tide]

both are mode up of 1 array of points

[graceful talon]

what do you mean by dimensional

[split tide]

their representation

straight lines can be represented in 1 dimension like in 1 axis but curves cannot be represented on 1 axis, it has to have 2 axes or above

[graceful talon]

so you're saying like the least dimension they can exist in?

what if the dimension itself is curved? if that even makes sense

[split tide]

yep

[split tide]

yes

the surface it is on can be curved but it will still be considered straight as the surface is bending but not itself

[graceful talon]

what if there's a curved 1 dimension

[split tide]

if you bend the surface monogons and diagons are a thing

[graceful talon]

ah

[graceful talon]

idk these

[split tide]

monogons and diagons are shapes with 1 sides and 2 sides respectively

[graceful talon]

I'm guessing they're polygons with 1 and-

[split tide]

yep

[graceful talon]

ok

[split tide]

if you walk towards one direction straight you will end up in the same position because earth is round

that position is a vertex

and the path you travelled is a side

therefore you have a monogon

[graceful talon]

is a sphere a monogon?

[split tide]

even though you went straight you curved bcz of earth but you didnt curve yourself so the line in itself did not curve

[split tide]

sphere isnt, it's circumference is

[graceful talon]

a circle?

[split tide]

yep

the largest circle

[graceful talon]

or an ellipse

idk if u can produce an ellipse if u slice a sphere

[split tide]

no you cant

[graceful talon]

ok

[split tide]

you can get an ellipse if you slice a cone

[graceful talon]

,w paraboloid

[somber coyote]

Results provided by WolframAlpha

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Requested by lkjsfkjsiu

[graceful talon]

could you get an ellipse by slicing a paraboloid?

[split tide]

it is irregular so maybe yeah

[hybrid belfry]

Can we somehow prove that the shortest path to move from a point to another point is a straight line segment?

This requires the answer for the questions
what is a line and what is straight,
that's why i asked 😄

[faint pasture]

i mean any other way (even a curve) could essentially be considered to be made of a number of line segments

nvm doesnt really work

[split tide]

There isn't any shorter path so a line is the shortest. Although it is very obvious I am not sure how to prove it mathematically

[graceful talon]

so is it basically straight line vs any other type of line, example a curve?

it should be a straight line (segment)

vs a curved line

in euclidean geometry

idk how non euclidean geometry works

[undone quest]

Helo guys

[graceful talon]

,,x^2+h^2=0

[somber coyote]

0_א

[graceful talon]

\begin{align*}
x^2+h^2&=0 \\
 x^2&=-h^2 \\
 \sqrt{x^2}&=\sqrt{-h^2} \\
 x&=\pm h\sqrt{-1} \\
 x&=\pm hi
\end{align*}

[somber coyote]

0_א

[low shore]

so is the sin(-90) = -sin(90) = - (1)? or - is there because sin is negative in 3rd q

[ruby fulcrum]

proofwiki defines a polygon as a closed figure with points and lines that come in pairs. So is a circle a polygon?

[maiden brook]

No and u know that

[cunning lion]

a circle contains no line segments

[ruby fulcrum]

but people say a circle has infinte sides

[proud vine]

Need help real bad

I want to understand points and distance on the plane( geometry) here’s a lil exercise so y’all have an idea of what I’m talking bout

[sweet spoke]

would this problem be geometry:

1. Draw a loop that ends and begins at A. This loop can intersect itself at 90-degree (or approximately 90-degree) angles
2. Write the number 1 once on either side of the line at point A.
3. At each crossing, alternate between the numbers 0 and 1 in each corner of the intersection, for example(attatched image)
   Prove that no matter how the region is drawn, at least 1 region’s numbers sum to an odd integer(a region is an enclosed space in the loop)

[forest hemlock]

@blazing raft this is where ill be active if i come here

[weak plaza]

could I get some help here

[blazing raft]

Breathes fire

Ty Ty snowie

[obsidian harness]

well, you know that an arc length of 2pi * 10 = 20pi would subtend the whole circle, 360 degrees

use the unitary method now

an arc length of 1 would subtend how many degrees?

(divide both sides by the same thing)

then you can just multiply both sides by 5

[weak plaza]

oh boy lets see if I remember
wouldnt it be 1/2 for radians
and I always forget how to get the degrees

like I learned this yesterday but procceeded to forget 😭

[obsidian harness]

yep!

a radian is actually defined as the angle where arc length = radius

1 radian on a circle with radius 1 has an arc length of 1
make the circle 10 times bigger, and the radius and arc length are both 10, yet you didn't change the angle so it's still 1 radian

so the angle is 5/10 = 1/2 radians, correct

[obsidian harness]

yep, so another unitary method might help then

if pi radians = 180 degrees
1 radian = ?? degrees
1/2 radian = ?? degrees

[weak plaza]

57.3?

and 28.65

[obsidian harness]

yep, I think they want the answer in exact form though

so (180/pi)/2 = 90/pi

[chrome token]

Qn)
Show that given a tetrahedron, in which all opposite sides sum to the same value, opposite dihedral angles sum to the same value

i have showed all the edges of the tetrahedron are tangent to a sphere

can anyone hint?

[hybrid belfry]

Can we somehow prove that?

[split tide]

there is one way we can define a straight line

if we graph a straight line like y = x

it just means that the rate of change of that graph is the same at every point

however that is not the case for a curved line because the rate of change changes

[hybrid belfry]

We need the definition of a straight line BEFORE we can draw any kind of graph 😄

We need to draw at least 2 straight line segments to locate a point and the Ox, Oy before that.

[split tide]

we are just defining points and those points make a line due to their behaviour

y = x doesnt say that it is a line, it says that for every x coordinate the y coordinate is the same

that is what forms a straight line

[hybrid belfry]

Yea, i've encountered this question a few times and i still can't decide how to define or even just describe what
connect/connection or path/line (straight or curved)
is.

I've considered using movement to define/describe path/connection,
but different matters have different ways to move/go from a location/point to another,
so i'm still trying to find a way to define or at least describe what a path/connection is, so then i can define what a straight line segment is
🤔...

[split tide]

a connection between two points makes them kind of dependent on each other. A change in one will lead to a change in the other

picture this:

[graceful talon]

"Synthetic geometry - Wikipedia" https://en.m.wikipedia.org/wiki/Synthetic_geometry

[split tide]

you can walk intependently but if you tied a rope between you and someone else, the other person has to move before you could move farther than the length of the rope. That is a connection

[hybrid belfry]

What if the connection is not a rope but a ray of light or a stream of water?

It's still a connection between 2 things, but those 2 things don't depend on each other 🤔

[split tide]

It will not be considered a connection because movement or a change in one doesnt affect the other

you can think connection as a constraint too

[hybrid belfry]

But the shapes are obviously connected.
Visibly connected.

[split tide]

exactly

they seem connected but they arent

[hybrid belfry]

Like if you poke 2 holes on dirt and then draw a line
(is there a better word in English to describe a line that doesn't matter if it's straight or curved?)
that leads from this hole to the other,
are those 2 holes now connected?
It's just like connecting 2 dots on paper.

If according to your definition they are not connected,
then i don't think people (including me) wanna use this definition 😅😅

[graceful talon]

what if you're blind

maybe the only way to tell by yourself is to touch/feel it

if it's even physical in the first place

[hybrid belfry]

I said "visibly connected" just to emphasize that they're clearly connected,
i didn't mean their visual characteristics are the most important 😂

[hybrid belfry]

---

Is there any way for LITERALLY ANYTHING to move without space?

[graceful talon]

did you edit your chat. it didn't look like this before lol

[graceful talon]

define space

[hybrid belfry]

Yea, a few times, i don't even remember what i editted 😂

[hybrid belfry]

Let's say i can just accept that space can not be defined.

Or you can define space if you can, i can't 😂

[graceful talon]

ok i think any kind of space would make sense

and define move

ig you'd define it as

to change one's position

a chess board can be a space for chess pieces

imagine you only have a knight and it has to move around the chess board the way it moves

[hybrid belfry]

if i agree with any definition that i ever thought of,
the definition of movement won't even exist without space.

So i want someone else's perspective, definitions 😄

[graceful talon]

so movement implies a space (to move around)

ok

what if the movement is the simplest movement you can think of

maybe not the simplest but

let's say you're just able to move to two "places" in a given space

that is, the space has only two positions (you can move at)

this feels like going to sets

like the more abstract you go

yeah

so is space a set

and everything goes down to sets?

what even was the original problem

shortest distance between two points?

maybe sets can answer it

if you have an abstract space which is a continuous set of points, how would you define the "distance" between two points in that space

[obtuse stag]

Geometry and trigonometry is unironically the hardest thing on my syllabus, it don t even compare to calculus or statistics and probability

Calc is ez plz compared to trig

Fucking hate geometry

[graceful talon]

why is it hard

u don't have to answer

[obtuse stag]

Because there is so much complicated bullshit that you have to remember

[worldly wigeon]

Does anyone here knows about transformations?

[obtuse stag]

You mean geometric transformations?

If you gonna study that, it’s best you learn matrices, and transformations with functions

[marsh fractal]

does anybody have notes on property of equalities / simple proof (reasoning & proofs)

ex. reflexive, symmetric, transitive, etc.

or if anybody can dumb it down for me

would be very much appreciated

[split river]

hi guys

if i get tan(θ) = 1.5

what do i do next

tan(1.5) ?

[restive oasis]

what are you solving for ?

the angle ?

[split river]

yup

or am i supposed to do the tan-1(1.5)?

idk how to make it look like that

[restive oasis]

yup tan-1

[split river]

tbh i never really understood the "why" behind it

[restive oasis]

the tangent is the length of the opposite side on the length of the adjacent side

so you have the value of the tangent

thus you use the inverse function arctan/tan-1

[restive oasis]

in a right angled triangle

[split river]

hmm

i think i was in the toilet when they explained this

[restive oasis]

you know SOHCAHTOA ?

[obsidian harness]

well $\tan^{-1}$ is what we call the function that undoes $\tan$

[somber coyote]

south

[obsidian harness]

$\tan^{-1} (\tan \theta)) = \theta$

[somber coyote]

south

[obsidian harness]

in algebra we apply the same operation to both sides

so your right hand side ends up being $\tan^{-1} (1.5)}$

[somber coyote]

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

[obsidian harness]

,w tan^(-1) (1.5) in degrees

[somber coyote]

Results provided by WolframAlpha

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

Requested by sooouth.

[obsidian harness]

and at this point just trust your calculator

or you can use the bot

[split river]

yuh

still got it mixed up sometimes

[obsidian harness]

it's okay, your question isn't directly related

[split river]

i don't even think the teacher explained why it is why it is

she just gave the formula

[obsidian harness]

your question is actually about inverse functions, how to solve for x if you know f(x) = 1.5

the function f could be anything

[restive oasis]

Comes from the unit circle if im not mistaken

[obsidian harness]

it just happens to be tan here

[split river]

😭

what are these words

i have to lock in

[restive oasis]

i mean for sohcahtoa if it's still that you meant

[obsidian harness]

make a Quizlet for maths if you need it

the words function and inverse are very very important

[split river]

mann

what is a function anyway

[obsidian harness]

it's just a machine actually!

it takes in some input, does something to that input

spits out an output

[split river]

so like if i put 1 it outputs 2?

[obsidian harness]

eh

[split river]

so like 1 of x gets me 2 of y?

[obsidian harness]

that could be the function multiply input by 2

that could be the function add 1 to the input

input = x, output = y

[split river]

south where did you learn math

[obsidian harness]

and f() is the machine

[split river]

if i may ask

[obsidian harness]

can't remember exactly, but Khan Academy and Paul's Math Notes

also school most definitely

my tutor, I had tutoring for AP Calc BC

for high school maths it's not necessary to read any maths books outside ones in your class

[split river]

oh man school's a no go for me

the teacher sucks

[obsidian harness]

oh I really recommend org chem tutor on YT

they're good at maths and explain well

they're also good at organic chemistry in college, hence the name

[split river]

prealgebra?

[obsidian harness]

yeah

doesn't hurt to watch a few videos

to see what you do and don't know

[split river]

i honestly think i lack so much prior knowledge

[obsidian harness]

exactly

[split river]

i didn't pay attention in maths for uhh 3 grades

[obsidian harness]

I think it doesn't hurt to finally understand the things in maths

that haven't made sense for so long

[split river]

just been existing and getting 3s on the myp

[obsidian harness]

ah MYP? that's incredible

I did MYP and DP

[split river]

well i just now have realised what an idiotic thing it was for younger me to slack off in math

cuz i wanna b an economist and they do a lot of calculus

and algebra

[obsidian harness]

it's okay don't be too harsh on yourself

and this is very very true, what you said about studying econ at uni

so it's good you're trying now, hey

so that from this point onwards, especially during DP, you can give yourself good options to study what you like and to have an easier time studying

[split river]

yea

ok i guess i'm going to go back to my assignment

thank you for the insights 🙏

[obsidian harness]

no worries! good luck with your assignment

[stoic raft]

hey so imma be real, im so confused idek how to explain it. ive looked at the example and tried watching some yt videos and am still just completely lost

[graceful talon]

cotangent is the reciprocal of tangent

-π/8 and 7π/8 would have the same angle

-π/8 is π/8 from the x-axis at the 4th quadrant

7π/8 is π/8 from the x-axis at the 2nd quadrant

tan=sin/cos

tan in 2nd and 4th quadrant are negative since sin and cos have different signs

so yea it's just 1/(1-√2)

just always use the unit circle

[median plaza]

how the frickity frackle can i always find the opposite for trig

[graceful talon]

opposite of what

[obsidian harness]

the opposite side to an angle depends on the angle..

[mellow merlin]

radians are so confusing

i didnt understand a single thing on how to convert radians to degrees

why does the pi cancel out

[obsidian harness]

not only does the pi cancel out, but the radians cancel out too

maybe it's easier if you use the unitary method

start with pi radians = 180 degrees

divide both sides by 3, so pi/3 radians = 60 degrees

[obsidian harness]

okay now if we start again

multiply both sides by -1/2 and you get -pi/2 radians = -90 degrees

[mellow merlin]

degrees to radians r easy radians to degrees is a little more harder to grasp

[mellow merlin]

this is a nice method

[graceful talon]

also it's just multiplication. maybe what ur not understanding is why do u have to multiply them?

[obsidian harness]

that's interesting

[mellow merlin]

i get the process but its more difficult to understand

for degrees to radians its easier to visualize since youre dividing a semi-circle by 180 degrees (π/180) and multiplying it by whatever degrees to get the radian

[obsidian harness]

might it make more sense if I say

you're replacing (pi radians) with (180 degrees), because they're the same thing?

so (pi radians)/3 = (180 degrees)/3 = 60 degrees

[graceful talon]

what's the formula for circumference of a circle

[obsidian harness]

for this reason I find degrees to radians harder, haha

because you have to visualise the degrees as a fraction of 180 degrees first

[mellow merlin]

maybe the cancelling part confuses me when converting from radians to degrees

its hard to visualize it

[obsidian harness]

yeah if that doesn't help you understand

don't think of it like that

[obsidian harness]

something like this method might be more helpful to you

[graceful talon]

How many degrees are there in π/3 radians?
For every π radians there are 180°. 180° per π radians. 180°/(π radians).
So in a third of π radians, there are a third of 180°.

ok maybe it didn't fit the reason for cancellation

maybe the cancellation is just the result of notation and it's hard to explain it intuitively

in other words, you don't need to visualize the cancellation

you could visualize the statement

it happens a lot in conversions

for example maybe you wanna convert 60 feet to inches

conversion factors are 12in/ft and 1ft/12in

[mellow merlin]

this is great

its easier to convert radians to degrees this way

[graceful talon]

,,60 \cancel{\mathrm{ft}}\cdot\frac{12\mathrm{in}}{\cancel{\mathrm{ft}}}=720\mathrm{in}

[somber coyote]

0_א

[graceful talon]

it should've been 60in to ft

,,60,\cancel{\mathrm{in}}\cdot\frac{1,\mathrm{ft}}{12,\cancel{\mathrm{in}}}=5,\mathrm{ft}

[somber coyote]

0_א

[solid pilot]

Any good resources on rotation transformations in french ? I study in a francophone country

And I can barely find any detailed English resources on it

[median plaza]

we learning like sin, cos, and tangent right

so

lets say i have to find the sinuse for a triangle and make a ratio for it with the formula

i can never find the opposite

[unique nacelle]

guys

what is a rational equation I don't understand!

[steel tide]

hey guys, im stuck on this problem, mainly with the setup. any help is appreciated

[obsidian harness]

have you tried drawing the problem out?

your diagram should look like this

then you should make two equations given the angles 29 and 29 + 1.5

solve for the base length in both equations, then set the equations equal to each other

[steel tide]

thank you!

[obsidian harness]

no worries!

[nova jungle]

what is the area of this shape , i keep getting 65 . but its not an option on the question

[obsidian harness]

what are those Arabic numbers

[nova jungle]

oh mb i forgot

the long sides are 5

the tiny cuts are all 2s

[shut bronze]

so there's a 5x5 square in the middle and four 5x2 rectangles

5x5 + 4 * 5x2 is 65

it definitely is 65

[mellow merlin]

why does a fraction in a denominator equal multiplying by its reciprocal

[hallow burrow]

Is just rhat they skipped the middle step

[obsidian harness]

try multiplying by 2/sqrt(3) on top and bottom

or -2/sqrt(3), same thing

[shut bronze]

why does x/(a/b) equal x * b/a?

because x/(a/b) = (x * b)/(a) = x * b/a

multiply top and bottom by b

[frosty kraken]

Prove we can cut a rectangle R1 in such a way that the pieces can be put together to form a rectangle R2 with same area as R1

Is there an elegant proof for this?

[mellow merlin]

Im learning pythagorean trig identity (sin^2 + cos^2 = 1) and the things im learning feel isolated rn

i get it but i have a hard time connecting it to other ideas

[frosty kraken]

What's the other ideas?

[mellow merlin]

the ratios kinda confuse me

maybe i just need to give it some time

[mellow merlin]

For example this, like i get that sin = (x/hypothenuse)and cos = (y/hypothenuse) and ik that cos has a hypothenuse of 8, but like i feel like there is a missing bridge

I know how to do it

but like its just difficult rn to connect it all together

[flint marlin]

Make a triangle, get the side using pythogaros theorem and done

Or else just use cos²x + sin²x = 1

[upper karma]

Division is just a convenient notation for

$a \div b = a \cdot \frac{1}{b}$

Why?

What number do we need $x$ to be, to get 1?:

$a \cdot x = 1$

Answer: $x = \frac{1}{a} = 1 \div a$, since $a \cdot \frac{1}{a} = 1$

$\frac{1}{a}$ is the (multiplicative) inverse of a.

$\frac{1}{b}$ is the (multiplicative) inverse of b.

We can rewrite any integer as a fraction:

$3 = \frac{3}{1}$

We can rewrite any division with multiplication:

$3 \div 1 = 3 \cdot \frac{1}{1}$

$42 \div 2 = 42 \cdot \frac{1}{2}$

You surely are aware of other inverses, such as the additive inverse: $a + (-a) = a - a = 0$.
We just assume that an additive inverse $(-a)$ exists for each number.
Similarly, we just assume a multiplicative inverse exists for any number except 0.

$0 \cdot x = 0$

Can you solve that? I have no idea what $x = 0 \div 0$ is…

Frankly, there is no need for “subtraction” and “division” as you can do all with addition and multiplication alone.

Also, there is this notation for inverses:

$a^{-1} = \frac{1}{a}$

Anyway, if I get your question right, you would like to know why we swap the numerator and denominator when we divide fractions:

$\frac{a}{b} \div \frac{c}{d}$

What is the multiplicative inverse of $\frac{c}{d}$?

$\frac{c}{d} \cdot x = 1$

Multiply both sides by $d$:

$\frac{c}{1} \cdot x = d$

$c \cdot x = d$

Divide by $c$, but remember, we can also multiply by the multiplicative inverse of $c$, so we multiply by $c^{-1} = \frac{1}{c}$:

$x = \frac{d}{c}$

So, since we write $a^{-1}$ as $\frac{1}{a}$, we can also rewrite $\left(\frac{c}{d}\right)^{-1}$ as $\frac{1}{\left(\frac{c}{d}\right)}$, so:

$x = \frac{d}{c} = \frac{1}{\left(\frac{c}{d}\right)}$

If you see a division symbol, you know you can just use another notation for it:

$\frac{a}{b} \cdot \frac{1}{\frac{c}{d}}$

So we rewrite the bottom part (denominator) as:

$\frac{a}{b} \cdot \frac{d}{c}$

All I did was use notation and recursively apply the definition of the “multiplicative inverse”. Even if we have fractional numbers, we can just rewrite it like any other number.

Hope it helps.

[somber coyote]

Lab Mechanic

Lab Mechanic

[upper karma]

This is just horrible to read from.
If this is not helpful, feel free to either delete or repost my message with the proper formatting.
Discord seems to complicate multipart messages (message limit).
Can I just leave text off, from MathJax?

@mellow merlin

The key insight of a/b : c/d is:

c/d * x = 1
x = d / c

Rewritten:

x = 1 / (c / d), since we have this notation of multiplicative inverses, i.e., a * (1 / a).

You need to get the multiplicative inverse of c/d like you do with other numbers, which is 1 / (c/d) = d / c.

So

(a/b) * (d/c)

The problem might have been, that you “alienated” fractions and did not treat them just like any other "regular number".
If I can do 1 : a = 1 / a, so can I do 1 : (b / c) = c / b.

[weak plaza]

Can someone explain step by step how to find the length of an arc that subtends a central angle of 4° in a circle of radius 18 km.

I keep getting confused how it works

[cunning lion]

think about:
a) what the circumference of the whole circle is
b) what fraction of the whole circle a 4° arc represents

[median plaza]

i need trig help

like quickly

10 packets and a test due tommorow

[median plaza]

how do i solve this

[cunning lion]

pythagorean theorem

[tepid oyster]

i was taking a nap when this was explained and i have a test tomorrow plz help

[valid crow]

What do u Know about sin and cos bc u can use it here

[viral cliff]

bro he has to use tan

[viral cliff]

here you go it is approx 560ft can convert to other units if asked

[valid crow]

let him do

[split river]

yo guys

what's cosecant, secant and cotangent?

[shut bronze]

the reciprocals of the normal trig functions

1/sin, 1/cos, and 1/tan respectively

[split river]

so like

i switch the fraction?

[shut bronze]

yeah

[obsidian harness]

to check your understanding, cot = 1/tan = adj/opp

[tepid oyster]

tysm i got up to tan and when i put tan inverse into the calc it said syntax error ?? prolly smth wrong w my settings… i got it on my phone calc

[toxic radish]

I'm learning vectors for game dev and I was wondering why he didn't use this formula to calculate the P instead he added the x's and y's together and didn't use a square root

[trail tendon]

P is the addition of many vectors, whereas C is the magnitude of one vector

[toxic radish]

so that's like a law if it's on vector I use the c formula if it's many vectors I use the p formula right?

[trail tendon]

if you want the length of a vector, you use the pythagorean theorem
if you want to add vectors, you add them like they do in the first picture

not really a "P formula", its just adding vectors

[toxic radish]

I know but I want you know what I mean by my question p is for point and the c is for the side of that traingle

I there any book you recommend me to start with mathematics

I'm really bad

Like i'm not even good with arithmetic

I have IGSCE mathematics and extended prealgebra by willey custom which one should I start with

Or there a better book

[ruby fulcrum]

A polygon is defined as a closed bounded figure made up for line segments. What confuses me is why can't a circle count as a polygon. I have been takking calculus and could you not inscribe and circumscribe a cricle with 2 different polygons and repeadealy add more sides, with the middle of the 2 being a circle? I just don't get what makes a circle so special that it gets excluded from every other shape.

[neat wigeon]

is a circle even a possible shape

[ruby fulcrum]

wdym

[shut bronze]

a circle isn't made of line segments

[neat wigeon]

well first of all, I'm not smart enough to answer ur question
but idk if circles are even possible to actually make irl cuz wouldn't they just have like a million sides and we couldn't tell

[shut bronze]

how is that relevant this is math

[neat wigeon]

geometry

[sturdy sand]

would AC||BD in this scenario

assuming the distance between AC and BD is infinitly small

[quartz wind]

if the distance between two lines≠0 l_AC and l_BD could be parallel
Otherwise, if A,B,C ,D all in the same line ,i think l_AC couldn't parallel l_BD, because in this circumstance l_AC=l_BD

[sturdy sand]

Thanks!

[ivory rain]

Does cos x = x have a known closed form

[cunning lion]

it's called the https://en.wikipedia.org/wiki/Dottie_number

[ivory rain]

Ooh thank you

[split river]

yes yes

[split river]

hey guys

so i got 3.37

or 3.4

cuz i used cos(68) x 9

is that correct? or am i missing something

[rapid valley]

I got 4.76174417508

The statement ab=ac means that both sides are equal

So both of ab=9 and ac=9

And c=68

[split river]

this is my calculations man

[rapid valley]

Thats supposed to be an uppercase A=22

[split river]

my god...

what are you doing

that is madness

[rapid valley]

Law of cosines

Wait

[split river]

i think you may be overcomplicating it

[rapid valley]

Thats how you solve it lol