geometry-and-trigonometry

[sage wren]

so then you have no line, you have a point

just a point to a sphere

[daring cedar]

Nope its a line hello?

[sage wren]

a line in space?

whats the point measuring an angle in space

[daring cedar]

A tangent is a line that touches exactly one point

[sage wren]

you are navigating earth

not a tangent line

[daring sierra]

he is ragebaiting why are you falling?

[daring cedar]

the tangent isnt imaginary, it’s just a reference direction the same way level or horizontal is you dont need a physical line, you just need a direction, instruments like the sextant use gravity to define horizontal, which is exactly that tangent???

[sage wren]

You are not just measuring an angle, you are measuring an elevation angle for navigation. We are navigating earth surface using that angle measurement.
Therefore part of the angle is the earth surface

[daring cedar]

I know hahaha

[sage wren]

not an imaginary line

[daring cedar]

Im so bored

the tangent isnt imaginary, it’s just a reference direction the same way level or horizontal is you dont need a physical line, you just need a direction, instruments like the sextant use gravity to define horizontal, which is exactly that tangent???

[sage wren]

so the lets measure 2 imaginary lines in space the what we do with that angle?

[daring cedar]

Its not in space thats the point

[sage wren]

what if i measure an angle from my kitchen table to the light in the ceiling, can i use that measurement to navigate earth?

[daring cedar]

Lmfao your light isnt the horizon is it

Absolute tard

[spiral relic]

How this maj sense

[sage wren]

horizon is where the sky appears to meet the surface

[daring cedar]

Rearrange, you get y=x-4 and thats what the line is representing

[daring cedar]

So is light showing where the sky meete the surface?

Lol

Thats all i need to see ^

[sage wren]

when you use a sextant to measure the elevatio angle yo a star. You align the horizon lense to the star

[spiral relic]

How this make sense

[sage wren]

you are also calculating the dip angle from eye level to sea level

eye level and sea level has to be paralel in order to calculate a dip

[daring cedar]

Its the exact same line you just rearranged it around, typical line form is y=mx+c where c is the y intercept and m is the gradient

[sage wren]

sea level is the elevation angle baseline

do you understant that we calculate a dip angle from eye level to sea level?

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[sage wren]

eye level and sea level is required to be paralel

[spiral relic]

What is gradient

[daring cedar]

How steep something is

Same as the slope of the line i think

Thats how we call it in england

[spiral relic]

how do i know how steep it is if I need gradient to know how steep it is to do the equation

[daring cedar]

Well you need two points that lie on the line in order to find how steep it is

[spiral relic]

How find two points

[daring cedar]

Idk read them off the graph if you have one

[spiral relic]

What

[daring cedar]

You need the coordinates of each point

[spiral relic]

How know the point I use

[daring cedar]

(x,y)

[daring cedar]

You can use any two points

So long as they lie exactly on the line

[spiral relic]

Ok 0 and 0

What do i do with

[daring cedar]

Someone wanna help him

[pine zinc]

U need coordinates...not just two numbers..

[spiral relic]

Yess

0 and 0

[daring cedar]

I think he saying (0,0)

[pine zinc]

Well 0,0 can be coordinate

[spiral relic]

Ok now what do with that

[daring cedar]

Find another point?

[pine zinc]

Yea great now u want one more coordinate

To find the slope

[spiral relic]

Ok 1 and 0

[pine zinc]

Now apply
Y2 - y1 / x2 - x1

[daring cedar]

Change y over change in x

Search it up

[pine zinc]

Yup

[spiral relic]

0 - 0 / 2 - 0 =

U cant do it

[daring cedar]

0/2

[spiral relic]

u cant divide 0

[pine zinc]

Why not

...

[daring cedar]

You get 0/2

Which is 0

[spiral relic]

Ok what do i do with 0

[pine zinc]

Uhh...that's the slope u wanted..

[spiral relic]

??

[pine zinc]

Gradient

[spiral relic]

how

[pine zinc]

Wot do u mean how

[spiral relic]

How is slope 0

[pine zinc]

That means the line is horizontal

Plot it on desmos or something

Wolfram wotever u use

[spiral relic]

What

[daring cedar]

y=mx+c

M is gradient

[spiral relic]

O

[daring cedar]

C is y intercept

[spiral relic]

C = Y
What u do now

Y =-4

[daring cedar]

Yeah thats the line

[spiral relic]

How it slanted

[daring cedar]

Its not

[pine zinc]

That's the horizontal line

[daring cedar]

y=-4 is not slanted in any way

The gradient is exactly 0

[spiral relic]

so then how is y = x - 4 slant

[sage wren]

the diagram of how a tangent works is they extrapolate the angle from earth center to a tangent plane touching earth surface at a point in order to measure an angle. But the problem is that if you do this you will just have an angle from an imaginary plane thatnis not earth surface. You cannot do anything with that angle, you vannot navigate earth using that measurement. Also nobody went to the center of earth to measure from there.

Earth surface/sea level is part of the angle baseline.

[pine zinc]

For slanted line u need m ≠ 0

[spiral relic]

Why didn't u say

how do i know what m is

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[sage wren]

still failed to adress the issue

you have an issue using an imaginary tangent plane

[spiral relic]

Shut up idot

[pine zinc]

My bad dude

[sage wren]

the you got no measurment of earth that you can use

[spiral relic]

Go talk somewhere else we r discussing something important..

[spiral relic]

What

[daring cedar]

Chewnah

[sage wren]

well how earth is measured is important

[spiral relic]

yes

[daring cedar]

In order for a slanted line m cannot be zero

[spiral relic]

Good thing diogenes did it like 4000 years ago then

Now shut up

[sage wren]

Did what?

[spiral relic]

how do i know m

[spiral relic]

Ur mom

Sybau

Monkey

[daring cedar]

Chewnah do not reply to him

[sage wren]

Any evidence you can aquire an elevation angle measurement from a curved baseline?

[spiral relic]

How find m

[daring cedar]

Change in y over change in x

[spiral relic]

Huh

[daring cedar]

Two sets of coordinates that both lie on the line

[spiral relic]

What line

[daring cedar]

Y2-y1/x2-1

[daring cedar]

Any line

[spiral relic]

??

[sage wren]

so funny you dweebs started randomly spamming to hide the truth you cannot adress

Meanwhile Earth is measured flat without exception

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[spiral relic]

What line I measure

[sage wren]

you failed to provide any measured curvature of earth

[daring cedar]

Any line brother

[spiral relic]

what

[sage wren]

you failed to show how an elevation angle can be aquired from a curved baseline

[daring cedar]

Wdym what line

Find a line to measure??

[spiral relic]

This line is infinite

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[daring cedar]

Yes ok? So is any line

[spiral relic]

How I measure infinite line

[daring cedar]

You pick two points

Two points

[spiral relic]

Ok 1 and 1

[daring cedar]

Doesnt matter if its infinite the gradients stays the same thats the point

[daring cedar]

Bro pick two sets of coordinates

?????

(1,1) is one point yes

[spiral relic]

Ok 1 and 1 and then 2 and 2

[daring cedar]

Okay apply the rule then

[pine zinc]

@spiral relic do u know basic trigonometry?

[daring cedar]

Y2-y1/x2-x1

[spiral relic]

1 - 2 / 1 - 2 = 1

[spiral relic]

yes

[daring cedar]

Okay its 1

[pine zinc]

So u know tangent of angle right?

[daring cedar]

So the gradient of the line is one

[spiral relic]

no it not

[spiral relic]

What

[pine zinc]

This might help

[daring cedar]

Yes it id

Type in y=1x

[spiral relic]

There no line there

[daring cedar]

Bro

[spiral relic]

no calculator

[daring cedar]

Leave the server

[spiral relic]

ok

[tiny acorn]

U dont seem to understand geometry

[daring cedar]

Go back to kindergarten

[daring cedar]

Dont entertain it

Pls

Hes ragebaiting

[tiny acorn]

Ok imma block that guy

[daring cedar]

Yeah block him

Some idiot

[tiny acorn]

Good night and cya

[daring cedar]

Goodnight

[sage wren]

you claimed we use a tangent plane to measure from. A tangent plane is imaginary then you got no measurements of earth

circles of equal altitude intersecting to give you a fix position cannot work on a curve

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

Dont entertain he ragebaits

[sage wren]

You failed to adress the issues and all you can do is mock and block

[tiny acorn]

Theres fridging curves on it, alr im not arguing with a blind person

Look back at the diagram buddy

[upper karma]

https://tenor.com/view/youve-got-no-fans-drunk-no-ground-gif-7807288

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[sage wren]

thats the celestial sphere

[daring cedar]

Keep talking to the brick wall brother

[sage wren]

you cannot aquire an elevation angle measurement from a curved baseline buddy

and if you are claiming a tangent plane is used then you dont have measurements of earth that can be used to navigate it

[tiny acorn]

Yea no blocked him, the diagram blud posted literally has a round earth on it

[sage wren]

thats the celestial sphere

you know what the celestial sphere is?

[tiny acorn]

Counterpoint: get a really tall stick and move far enough from it, now get off b4 i explode

[daring cedar]

Block him asap larp larp

Dont speak

Just post this gif

https://tenor.com/view/dono-wall-gif-24048347

[upper karma]

https://tenor.com/view/watcher-interfere-watcher-will-not-interfere-watcher-what-if-interfere-gif-24268184

[sage wren]

so whats the point?

[tiny acorn]

https://tenor.com/view/dono-wall-gif-24048347

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[tiny acorn]

Ok no spamming gifs

Mods might get us

[daring cedar]

Haha keep talking to the brick wall king

Go on

[tiny acorn]

Just dont say anything anymore

[daring cedar]

Okay

[sage wren]

you are taking the elevation angle measurement from earth surface

in order to navigate earth surface

is not just an angle is an elevation angle

[sharp pilot]

https://tenor.com/view/dono-wall-gif-24048347

[sage wren]

a 45 degree elevation angle measurement form a right angle triangle with Polaris Ground position and observer view at the position from where the angle measurement takes place and the 2 lines of sight to Polaris

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[tiny acorn]

<@&268886789983436800> posting crank theories in math channel and not stopping

[sharp pilot]

Mods forgive us , its fun

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[sage wren]

is not theories im talking about geometry, measuremenrs

a 45 degree elevation angle measurement forms a right angle triangle with Polaris Ground position and observer view at the position from where the angle measurement takes place and the 2 lines of sight to Polaris

does a right angle triangle have a curve baseline?

[daring cedar]

https://tenor.com/view/dono-wall-gif-24048347

[tiny acorn]

Your "geometry" doesnt make any sense yet you keep spamming this bs

Now stop

[coarse saddle]

are you having a stroke or smth?

[daring cedar]

Darq dont get ragebaited

Just observe how this guy waffles all day

[tiny acorn]

Hes a mod bruv

[daring cedar]

Unemployed mfer

https://tenor.com/view/dono-wall-gif-24048347

[coarse saddle]

unfortunately I am a mod

[tiny acorn]

Chill out bruh

[coarse saddle]

so I need to act like an adult

[daring cedar]

Bro king just let it go

[visual dawn]

Please stop spamming this gif

[coarse saddle]

please stop with gif spam

[tiny acorn]

I wish i had pen and paper to debunk this @sage wren guy rn but im too eepy bye

[daring cedar]

Alright darq have a cheeky debate with king here

[coarse saddle]

is there a question here orr... did you just wake up and wanted to talk about antiquated navigation methods?

[daring cedar]

Have fun

Essentially he thinks the earth is flat and gravity doesnt exist

[sage wren]

the latitude system was developed with this method

[coarse saddle]

oh cool lmao

[sage wren]

GPS uses x y z coordinates from latitude longitude elevation

so a cartesian grid system

mapped from measuring elevation angles to Polaris

and other 57 main stars

you cannot aquire an elevation angle measurement from a curved baseline

angles dont curve

[visual dawn]

I can see you're very interested in discussing this, but maybe we could leave this channel to schoolkids who need help with their geometry.

Maybe you could move to #discussion or #serious-discussion?

[coarse saddle]

I'm just gonna ask you to stop ig

[sage wren]

and a tangent plane is imaginary, therefore not an earth measurement to navigate it

[daring cedar]

😂😂😂😂

[tiny acorn]

This shows a lack of understanding of basic geometry

[daring cedar]

Take your theory somewhere else

[coarse saddle]

one more message and you're getting muted

this is your final warning

[daring cedar]

If youre so passionate go get it proved

Come to me when ur done

Ok?

[visual dawn]

Ryze, maybe move on. There's no point in antagonising this person

[daring cedar]

Okok sorry goodbye

[sage wren]

this channel is called geometry and trigonometry, is exactly what im talking about too. elevation angle measurements are part of geometry subject

[coarse saddle]

muted

let's just move on

[daring cedar]

Yeah

Who needs help with geometry or trig?

[blazing thistle]

4 dimesional means a space where there is 4 directions, instead of 3 (like our world). In 3d we have foward/back, up/down, right/left. however 4d would have a completely new direction to travel to (often called ana/kata). 4d space is inherently more spacious than our 3d world, so things can exist in 4d which cant fit in 3d, like the tesseract. (We usually represent 4d objects as a 3d projection, similar to how we can project a 3d apple to a 2d screen).

The tesseract is a generalization of the 3d cube. If the cube's surface is made of 6 squares which connect at their edges, the tesseract's surface is made of 8 cubes which connects at their faces

[lunar hull]

One thing that I found confusing about 4d space but recently figured out: in 2d, you can make a polygon and each side is a line segment and they meet at a point, so you can imagine the construction of this shape by "bending" a line at points. In other words, in 2d hinges are points.

In 3d, you can take a net, a subset of 2d space. And fold it along lines up into the 3d dimension to make your polyhedron. So 3d hinges are lines.

In 4d, you take your volume net, which is a subset of 3d space, then you fold it along 2d surfaces up into the 4d dimension to make your polychora. So 4d hinges are 2d surfaces.

[blazing thistle]

In 4d there are types of shape called duoprism which have completely unique structure that can only work in 4d. These shape's surface are usually made up of 3d prisms, which connect to form rings, 2 of them to be exact, which are orthogonal in 4d space. (One ring of prism will be alligned in xy plane, and the other zw plane).

there are duotegums, which are related to duoprisms (dual of duoprisms). They are basically 4d shapes made of tetrahedra, which connect on their face similar to a ring, however they do it in 2 different directions at once so the tetrahedra connect like a 2d surface rather than a ring. (Its not easy to explain). The resulting shape is a "double conic-like" shape which amazingly has 2 rings of verticies which stick out the shape.

There are the 4d platonic solids. The pentachora (5-cell), tesseract, hexadecachora, 24-cell, 120-cell, 600-cell. These have names but too long to remember. 4d platonic solids are basically 4d shapes with what i would consider maximum symmytry. Theres a formal definition for platonic solids you can look up though.

And there are way more, way way more

[marsh marlin]

lmao w ref

[marsh marlin]

syfau you insuferable arrogant flat earther

[blazing thistle]

Yeah term for hinges are called ridge. The ridges connect facets of shapes, ridges are like the glue of facets for shapes

[coarse saddle]

I would hate to be a dead horse around this guy

[marsh marlin]

that guy just ignores everyone and just yaps

[blazing thistle]

An example of this, the ridge of a 4d duocylinder is a 2d clifford torus.

[lunar hull]

Are duotegums analogous to antiprisms?

[blazing thistle]

Not quite they analogous to tegums, or the more familiar term bipyramids

Aka duals of prisms

duotegums also contain 3d crosssections which are bipyramids

duoprism and duotegums also have curved shapes they converge to
The duoprisms converges to the duocylinder as you add more sides
And the duotegum converges to the duospindle as you add more sides

[brisk atlas]

😭

I found it entertaining

[humble drum]

UNIT CRICLE I HATE IT I HATE IT I HATE IT

I HATE UNIT CIRCLE GRRRRR

AHHH

MMMM

HRRRRRRR

[upper karma]

What’s cos pi/4

[humble drum]

leave me alone

[upper karma]

🙁

[humble drum]

this is bullyism

youre bullying a child

[upper karma]

I’m crying

[humble drum]

youre bullying a 13 year old child

[upper karma]

Oh no

[humble drum]

YOURE BULLYING A 13 YEAR OLD QUEER FEMINIST OR

WHATEVER

THIS HAS TO BE SOMETHING ISM

[upper karma]

Unit circulism

[humble drum]

https://tenor.com/view/max-verstappen-leomano-le0man0-gif-8203931212861292204

[upper karma]

?

[humble drum]

yes

unit circlism

[upper karma]

I don’t like it either

[humble drum]

why do i do this to my self

[upper karma]

I hate trig identities so much

[humble drum]

i didnt have to be in alg 2

i didnt have to

im in 7th grade i should be in pre algebra

[upper karma]

DAMN

[humble drum]

i couldve had an easy life

why did i have to be an over achiever

grrrr

hrrrr mmmm

https://tenor.com/view/grr-grrr-grrrr-grrrrr-grrrrrr-gif-11468024821216396093

[upper karma]

Wait are you the guy who knew set theory

[humble drum]

uh

no

[upper karma]

Ok, then nvm

But alg II is still very impressive

[humble drum]

i mean i kind of know just a littl ebit

but i dont really know like

in detail

[upper karma]

My ahh took alg 2 last year in 10th🫣

[humble drum]

like i kind of know what it is but

i dont fully understand

[upper karma]

But I’m planning to learn calc 1-3 by graduation

[upper karma]

Me neither, I have no idea what it is

[humble drum]

i know its got like elements and it groups them in to sets

right?

oh curly brackets

i like the curly brackets

[humble drum]

youre a junior?

unc

[upper karma]

☹️

[humble drum]

oh em gosh just let me drop out of school

[humble drum]

unccccc

youre like what

17?

ur grown!!!

[upper karma]

Noooo😭

[humble drum]

yesss

ur uncccc

[minor heron]

oo nice

glgl

[minor heron]

nununu its okay... when i got to that in 7th grade icl... i rage quit ... (until i had to learn it in 8th. rah) just remember, look at one quadrant and see it's really the same all around just with different signs

and, really, from 1 to 0 in quadrant 1, it just cycles through, sqrt4, sqrt3, sqrt2, and sqrt1, sqrt 0, over 2with sqrt4 and 1 being 2 and 1

soon, you might start memorizing common values

i js worked with it a lot in 8th grade (against my will) until i grasped it 🥀

[dawn pond]

It's a beautiful concept

And a great thing about trig is, its uses aren't as abstract as the concept itself

Especially if you're good with circle formula x² + y² = c

Actually no, Pythagorean theorem does the job

[dawn pond]

Also on π/3, it's (√1/2 ; √3/2) prolly a typo

[summer oxide]

same here brother....

[minor heron]

Oh yeah mbmb

[dawn pond]

I'm still not sure how they got that 2 in the denominator tho ngl

[winged plinth]

Unit circle is not bad

[spiral lodge]

Indeed

[hazy harbor]

what a truly RATIONAL distance to walk

[winged oyster]

Is it always though?

[dusk jewel]

https://tenor.com/view/do-not-walk-on-the-grass-don't-walk-on-the-grass-no-walking-on-grass-don't-step-on-the-grass-avoid-the-grass-gif-1051958837418668901

irrational if it's a unit square

||unit because theres a military unit and... i'm not funny||

[hazy harbor]

the joke is that pythagoras thought every number is rational

[winged oyster]

oh

[hazy harbor]

and that it's the most rational distance to walk through

[queen juniper]

nadat fix ur server

[hazy harbor]

double pun

[hazy harbor]

bro shut up

[queen juniper]

fix it

[hazy harbor]

no

[winged oyster]

how do i join MO servet

server

[oblique gull]

Looks like 30° right triangle to me

[queen juniper]

oh uh

i searched up "mo server"

and i got in

[winged plinth]

No the joke is √(2) < 2

It’s a unit square so walking diagonally across would be faster

[edgy moss]

am i allowed to ask general questions abt math and stuff here

not just a specific problem

[exotic yarrow]

This is a discussion channel, so as long as it pertains to geometry or trigonometry, then sure Just don’t do this in the help channels.

[edgy moss]

okay thanks a lot

[exotic yarrow]

[edgy moss]

how can i study for angles, triangles, and prisms im doing it for a unit in math soon and it looks kind of annoying and idrk how to study, any tips?

[vast gust]

angles: learn fundamental theorems/formulas etc
triangles: same as angles
prisms: assuming its algebra only, know your formulas

[plucky crag]

honestly just do practice questions, as many as you can. ask for more practise tests more challenging questions. familiarity with questions helps you understand concepts a lot quicker and helps when introduced to unfamiliar questions

[plush flint]

hello, im trying to learn the unit circle

but i never learned what rationalize the number 1/ √(2) means or why its √(2)/2

in what textbook/subject can i learn this process

[grave pond]

Do you agree that 1/sqrt2 ad sqrt2/2 are in fact the same number, just written differently?

[plush flint]

yes

but why not put a number over 1 as a denomenator

what does it mean to rationalize

[grave pond]

"Rationalize" in this context just means write it such that the denominator is an integer and the less-nice stuff goes on in the numerator instead.

[plush flint]

isnt 1 also an integer

and i probably need to learn what intergers, real numbers, whole numbers and all of that shit is. lol

[grave pond]

Yes, 1 is an integer, but you cannot write sqrt2/2 such that the denominator is 1 (and there are no other fractions hiding somewhere in the expression).

It's not particularly deep, just a practical convention for which of many different forms of the number is "nicest" when there are several to choose among.

[plush flint]

i need to understand what youre saying here better, will probably take some time for it to click

"nicest" is subjective lmao, but maybe im just not understanding something which is probably the case

thats what i tried to do

[dawn pond]

The denominator doesn't have to be 1

[plush flint]

i want to know why

lmao

is there somewhere i can learn this? what subject is it called in math and in which unit

[dawn pond]

It's much easier to deal with numbers that don't contain commas and so because they clutter your formulad

[plush flint]

i know rationalizing that is √(2)/2

[dawn pond]

Also, some numbers cannot be expressed like that

[plush flint]

can i have an example of those some numbers

[dawn pond]

For example, 10/3

That's 0.33333333....

[plush flint]

ok

[dawn pond]

So the form (0.3333...) has 1 in the denominator

But it's not accurate

It's just an approximation

Which we don't want, because we seek precision

Now that's a general rule, keep things compact

That's why we write π instead of 3.1415... or √2 instead of 1.41...

Now another thing is rationalizing denominators

That's just a good practice to have because it's less ambiguous

A good example I gave someone earlier was $\frac {2} {\sqrt2}$

[somber coyote]

ScoobySnacks

[plush flint]

$\frac {2} {\sqrt2}$

[somber coyote]

level1machinist

[plush flint]

i dont know how to read those yet

omg

[dawn pond]

Which admittedly looks funky

[plush flint]

that fraction doesnt look too bad

especially compared to √(2)/2

[dawn pond]

But if you just rationalize the denominator by multiplying both by \sqrt{2} so $\frac { 2\sqrt{2}}{\sqrt{2} . \sqrt{2} }$
It becomes much clearer that this is just \sqrt{2}

[dawn pond]

It just happens to be the case that 0.3333 has a compact form

Try something like √2 tho

[plush flint]

yeah

hard to neatly put over 1 where 1 is the denomenator

[dawn pond]

It's almost impossible to have accurate results with 1 in the denom

[plush flint]

why isnt that acceptable lmao

man i need an algebra textbook or something

[hasty stump]

1/root 2 divided by 1 is just 1/root 2

because anything divided by 1 is the number itself

[plush flint]

yes i know that xD

[grave pond]

It's not that it's "not acceptable".

Its value is the number we're talking about.

It's not a matter of being "correct" here -- there's nothing more to it than there are several ways to write this number which look different, and it's practical to choose one of them to be the form we write it in, such that it's easier to recognize when the same number shows up in a different context.

[plush flint]

ok

[grave pond]

The convention is that, when possible, we choose a form that has just a single fraction bar, and prefer for "complicated" things like square roots to appear in the numerator instead of the denominator.
(One reason to pick this is that it is more convenient in case of adding fractions, because the addition rule for fractions leads to stuff from the denominator infecting several parts of the results, whereas stuff in the numerator stays somewhat contained).

[plush flint]

ok

can i ask another question

1√(2) is 1 and √(2) and not 1 times √(2) right?

[grave pond]

No, $1\sqrt{2}$ means $1\cdot\sqrt{2}$ (which is a bit silly to write because it is the same as $\sqrt{2}$).

[plush flint]

so its 1 and √(2)

[somber coyote]

Troposphere

[plush flint]

omg

[grave pond]

You're being confused by mixed fractions, but mixed fractions are an extremely special convention that only applies when what you see is
$$ digits\frac{digits}{digits}$$

[plush flint]

ok

[grave pond]

As soon as there's anything else than decimal digits in front of the fraction, or above/below the bar, there's no possibility of an "invisible + sign".

[plush flint]

you know what man, ill just learn roots all over again on youtube, ill be back if i need help, thanks for your time anyway lmao

mixed factions? or fractions?

[grave pond]

Fractions, sorry, will edit.

[somber coyote]

Troposphere

[plush flint]

i never heard of a faction before but that means i might need to learn something new

[grave pond]

It sounds like what confuses you the most here is notation rather than the actual underlying computations, which is good. Don't get too dispirited because the accumulated centuries of notation can be a bit hard to navigate at first.

[plush flint]

tysm

notation......

i definitely know my fractions

photo is taking forever to upload

[winged oyster]

bro why not just put 1/sqrt(2)

denominator is useless

[shrewd berry]

Cus rationalize

$sqrt(2)/2$

[somber coyote]

Atri

[slim plinth]

Then you add sin/cos/tan/csc/sec/tan

[cold lava]

can someone explain to me how to solve this

[exotic yarrow]

AT is perpendicular to the radius AP.

[celest fjord]

Yh I think that’s correct

[cold lava]

wait so

uhhhhh

i constructed a segemnt from P to A

idk how to continue from there

[woeful flower]

triangle of 37/2º

[exotic yarrow]

what is the relationship between slopes/gradients of perpendicular segments/lines

That’s basically all you need

[cold lava]

OH theyre reciprocal

[exotic yarrow]

negative*, but yes.

[cold lava]

oh right

thx

[exotic yarrow]

[celest fjord]

Guys if I have to graph log 10x how wld it be

[exotic yarrow]

tbf you can just do log rules here

$$\log (10x)=\log(10)+\log(x)$$

[somber coyote]

Civil Service Pigeon

[celest fjord]

Oh Yh

Thx

[exotic yarrow]

[marsh marlin]

bros pfp is that one pascal contest question

https://klipy.com/gifs/lebron-elite

[limber dagger]

can somebody help with this?

[hasty stump]

Hmm what is the sum of angles on a straight line?

[limber dagger]

wdym

180?

[hasty stump]

Yeah

Maybe you could try finding TUA

[heavy quarry]

I'll try to answer it

I already solve it

[vocal sentinel]

PRU is subtending arc UP, right?

If an angle at the centre, says A, subtending an arc. Also, if there is another angle on the circle (not inside circle), also subtending same arc, let this angle be B. then B = A/2

Looks like you already got UAP = 40, then URP>

[heavy quarry]

The answer I got it's (310°)

[limber dagger]

uhh

im afraid i dont really understand

[vocal sentinel]

this

[heavy quarry]

@limber dagger Look my message to you

This is I got

[silent plank]

you mixed up angles TAU and UAP in your long equation (answer is wrong)

also you can get m_arcPRU directly from UAP and angle in a revolution/full circle

@heavy quarry

[heavy quarry]

Yes? sorry

[heavy quarry]

Oh, okay sorry, I was just enjoying solving, that’s why I did that.

[silent plank]

ok. But you still need to fix what I mentioned

[heavy quarry]

I just follow the question

[heavy quarry]

It says that PR and QT are diameters of circle A. Find mPRU. So I focused on finding mPRU.

[silent plank]

that's supposed to be <TAU
you ended up with <UAP = 50° when thats 40° in the diagram

determining every angle is a valid approach, but you made a mistake in setting up your equation

[heavy quarry]

Ow, okay I get it

Thank You!🤗

[echo egret]

Where should I start when learning geometry

[loud geyser]

depends on what you want/need

Is it for school maybe a test? or just for fun

idk who in their right mind would learn geo for fun tho

~~ That's right, I'm talking to you Carbonite~~

[orchid brook]

I would

I would love it

But I am too dumb to understand it, will try harder though.

[loud geyser]

I would suggest you study combinatorics instead

[slim plinth]

Set <UAP as x

And make it x=360-(40+40+50+90+90)=50

[orchid brook]

Good idea

[slim plinth]

Who thought of sum of the angles of the circle is 360 degrees

[echo egret]

A test

[loud geyser]

What you would want to do is find all the materials, if possible, from your school website or your teacher. there are many types of geometry, but they are the same, you can always find video of them on youtube, I would advice you to watch this youtube channel. After that, do problems, a lot of them

I can't tell you anything specific cuz idk what's your test about

[echo egret]

Similarity
Triangles
Pythagoras’ Theorem
Cartesian coordinates
Polygons and circles
Solid figures
Volume of curved-sided solid figures
Geometric transformations
Congruence.
Geometry and measurement, my bad

And some word problems included

I don’t think there’s enough time to get through it all; what do you think is the most important part of it?

[loud geyser]

yk what, that's pretty close to what the playlist I sent you have

[loud geyser]

You can just watch anything you need, order from top to bottom is suggested

[plush flint]

the unit circle is something you memorize?

[fallen comet]

You didn't have to do all of this ... The question asked about the angle subtended by PRU which is just 360° - 40° = 320°

[sudden talon]

Why is tan sin/cos?

[grave pond]

It's a definition.

[sudden talon]

ok well why does it work out to be that?

Im not really talking about the function itself but why the distance that is labelled tan happens to be sin/cos

like can that triangle OEF there explain why its that

[snow karma]

do u mean OPF

OEF isnt rlly a triangle

[sudden talon]

sorry OPF yeah

[snow karma]

well the line (PF) is tangent to the trigonometric circle

at point P

so OP and PF are perpendicular this OPF is a right triangle

[sudden talon]

alr

[snow karma]

in that triangle itself, try expressing tanθ in terms of the sides of that triangle

since its a right triangle

[sudden talon]

uh ok

$\tan^2 = \overline{OF}^2 - 1^2$

[somber coyote]

Quinn

[snow karma]

noo like

adjacent

and opposite, hypotenuse

not pythagorean theorem

[sudden talon]

oh

in terms of angle POE?

[snow karma]

ya

no wait

OPF

[sudden talon]

thats the right angle

it doesnt have an adjacent or opposite

[snow karma]

in OPF, theta isnt the right angle

[sudden talon]

but the tangent segment PF is perpendicular to the radius of the circle OP

[snow karma]

yes

so angle OPF is 90 degres

not theta

[sudden talon]

I said that

[snow karma]

theta is angle POF

[sudden talon]

Yes.

[snow karma]

then

[sudden talon]

.

[snow karma]

it has adjacent and opposite

oh i didnt see it edited

[sudden talon]

Its congruent to POF alr lets not be pedantic

[snow karma]

i thought of triangle sorry

[sudden talon]

anyway the opposite is the tangent and adjacent is the radius I.E 1

[snow karma]

yeah so tanθ = PF/PO = PF/1 = PF

so PF is tanθ

wasnt that ur question

[sudden talon]

uhhh no you misunderstood it a bit

[snow karma]

o

[sudden talon]

i was asking as to why that line segment which is the tangent

happens to be sin/cos

[snow karma]

the tangent happens to be sin/cos?

[sudden talon]

yeah

thats the definition of tan()

[snow karma]

well if its the definition

u cant argue with it

[sudden talon]

bro im not

aghhh

[snow karma]

u cant question it either lol

[sudden talon]

like that segment is always sin/cos

why is it

like there must be a explanation for that consistency right

[snow karma]

i dont understand what u mean by that line being sin/cos

a line is something

and sin/cos is smt else

[sudden talon]

no it is

it is sin/cos

the sine of the angle theta over the cosine of the angle theta

its always gonna be that tangent length

i want to know why

[snow karma]

oh ur talking the length

not the line itself

[sudden talon]

sine is the y coordinate of a point on the circumference of the unit circle

cosine is the x

[snow karma]

yes

[sudden talon]

and those values divided

give you that tangent length

[snow karma]

so the distance PF u mean?

[sudden talon]

atleast the distance between the tangent's point of intersection with the circle and the x axis

[sudden talon]

bingo

do ya know why

[snow karma]

uh

didnt we js give u a bit of an insight of tanθ being PF

tanθ= PF

[sudden talon]

wait maybe i read your justification wrong

[sudden talon]

no see look you are using the tangent function to define it

like

ya cant do that

i'll ask math discus

[snow karma]

if we will talk abt tanθ we ought to have a definition for it

whats ur definition for it

[sudden talon]

well we know the definition for it

[snow karma]

which is the distance PF?

[sudden talon]

yeah

but im not talking about the definition

im talking about like the geometric explanation as to why the length of the sine divided by the length of the cosine always give that segment from the point of intersection to the x axis

like there must be a geometric explanation for that

[snow karma]

perhaps u mean triangle similarity

[sudden talon]

maybe?

[snow karma]

OPE and OPF are similar triangles

sooo sin/cos = tan/1

[sudden talon]

https://cdn.discordapp.com/attachments/326138757474680852/1486804401153638521/trigonometry_0043.png?ex=69c6d600&is=69c58480&hm=e01618752bddc0606d3e17326d9b23d34ead9bb3442ec807c9df8c7008d7de5f&

[sudden talon]

Oh damn yeah

you're right

See that's intuitive!

Thanks don

[snow karma]

np but

its a definition

dont get too philosophical w it

[sudden talon]

again im not talking about that

i just want to know like why its consistent

i want a better grasp on the function

[snow karma]

okayy

[sudden talon]

and why that geometric object has consistent length

[marsh marlin]

flat earther is still muted

[neon iris]

I wish I could afford a flat piece of earth but the granite table I want costs 6 figures.

Seriously though thank fuck I wasn't around to read all that.

[marsh marlin]

lmao

[gusty geyser]

wait til that boy learns himself some differential geometry

[marsh marlin]

i aint waiting for shit

That

Idiot

All he needs to do is read proof of gravity

[neon iris]

bro's definitely homeschooled

[marsh marlin]

https://klipy.com/gifs/what-65660

[plush flint]

i dont know who youre talking about but im definitely homeschooled

i had to dropout at 8th grade due to family issues lmao

[neon iris]

oh I meant this in that homeschooling has no quality control, you can have a pretty good teacher if you're homeschooled but quite often very shitty parents use homeschooling to be shitty teachers to their kids (ie not teach evolution/etc because it's contradictory to the parents' beliefs)

[plush flint]

oh yeah those are a problem too

my parents are just straight up uneducated vietnamese/cambodian immigrants

[neon iris]

they should not have homeschooled you then

[plush flint]

my dad failed at everything his whole life, couldnt get a job or a wife, my dad sucessfully immigrated to america, and my grandma bought him a house and got a wife because she wanted a greencard

my dad projected his insecurities at me and yelled at me intensely until i blacked out, so i dropped out before 9th grade

i thought i was going to kill someone lmao, didnt want to project my issues onto others

[neon iris]

this is depressing ngl, I'm in the math server because math for me is an okay antidepressant

can we talk about math?

[plush flint]

i should delete my shit lmao

[neon iris]

nah

[plush flint]

and yes

im trying to figure out the unit circle

i have a very shallow understanding of it

[neon iris]

ok so the unit circle is as follows
you make a circle with a radius of 1

[plush flint]

yes

2(pi)r is 360degrees

pi is 180 degrees

pi/2 is 90 degrees

pi/6 is 30 degrees

radians

[neon iris]

if the latter numbers are in degrees I don't see the problem

[plush flint]

yes

[neon iris]

radians work in that going 1 radian around the unit circle is the same as travelling 1 unit in a straight line

[plush flint]

i dont get what that means

unless youre saying that if you unroll the circumfrence into a straight line

its the same distance?

[neon iris]

yes

[plush flint]

ok

[neon iris]

so you know the circumference of a circle is 2pi*r, that's why 2pi is 360 deg

[plush flint]

yes

[neon iris]

is there anything else you would like help understanding?

[plush flint]

there still is more to the unit circle

if you draw a radius to 45 degrees, the hypotenuse is always 1 with a unit circle, but the x,y values are root2/2

the a + b legs are the same with the 45 degrees radius when you draw them out on the cartesian coordinate system

[neon iris]

a^2+b^2=c^2
a=b
c=1
2a^2=1
a^2=1/2
a=(1/2)^(1/2)

therefore x and y is root(1/2)

root(1/2)*root(1/2) is 1/2
multiply both numerator and denominator to get root(1/2)/2

[plush flint]

yeah i was missing that a bit

2a^2=1

i get it easily

is there an easy formula for root3/2 and 1/2 for 30degrees

[neon iris]

and for pi/6 or pi/3, one of the two sides is 1/2
both angles are related to the equilateral triangle, where all sides are 1
cut the triangle in half, then try to substitute a and c using this info

what do you reckon

[plush flint]

all sides are 1?

oh

ok

[neon iris]

of the equilateral triangle, all sides are one

but you cut it in half from one of the angles to the middle of one of the sides

[plush flint]

you cut the equilateral triangle to get a 90degree triangle

[neon iris]

yes

[plush flint]

two

so not just "a"

dang i got no idea where to go from here though

[neon iris]

use one of the two resulting triangles, don't use them both, because you just want information for the angle you're looking at

[marsh marlin]

.

[neon iris]

what are the known lengths of the sides of that right triangle?

[plush flint]

30 60 90

angles not length

rip

ok lengths

1/2

root3/2

[neon iris]

you didn't derive that one

we're doing things from scratch to reach that answer

[plush flint]

ok

yeah youre right

i dont understand it enough here

the known lengths are just 1,1,1

when you cut it in half, the bottom is 1/2th

the hypotenuse on the outsides are still 1

[neon iris]

yes, now how does this fit into the pythagorean theorem?

[plush flint]

so its a^2+b^2=c^2

where a = 0.5^2

and c= 1^2

solve for the missing leg

[neon iris]

I'll have to catch you a quick sec

a =/= 0.5 ^ 2, a = 0.5

you then put it into the formula so you get 0.5^2+b^2=...

you should be vigilant about the small stuff like this because you can end up making mistakes and be unable to track them later if you don't

[plush flint]

ok

[neon iris]

you'll get good at it with practice though, so don't be discouraged

so how does the formula look now?

[plush flint]

i was pretty good at math in 8th grade

i hope ill get this

good

and youre right to be more specific

1-0.5^2=b^2

1-0.75=.25

.25=b^2

b= sq root of .25

[neon iris]

no

what is 1/2 * 1/2?

[plush flint]

1/4

[neon iris]

and 1/4 is?

[plush flint]

.25

[neon iris]

so why did you say 0.5^2 = 0.75?

[plush flint]

lmao oh crud

leave the mistake there, its good to know where i made my mistakes

1-.25=.75 or 3/4

b^2=.75 or 3/4th

b= sq root of 3/4

[neon iris]

do you know the distributive property? wrong principle whoops

[plush flint]

yes

(a+b)(a+b)= a^2+ab+ba+b^2 = a^2+2ab+b^2 and you can use that knowledge in reverse to factor polynomials

im not tooooo confident with it yet though

i really want to get into calculus

so i should be

a(b+c) = ab+ac

ab+ac= a(b+c)

[neon iris]

I set you down the wrong track

[neon iris]

return here

[plush flint]

root3/ root4

rationalize is root3 / root4 is a perfect square of 2

root3/2

[neon iris]

that property yes

so that's why we have that

[plush flint]

i want to understand more about rationalizing roots though

i have a lot of question marks in my head but i know how to do it

my understanding of it is there, but it isnt solid

i used to have a question

why cant the denominator be 1

and i know its because anything with a denominator of 1 is just the number on top lol

im super confused on what rational , real , numbers are

integers

[neon iris]

nth roots are 1/n exponents, and can be distributed as exponents are

and square roots are 2nd roots

[plush flint]

i need to learn the last one lol

[winged oyster]

is the easiest way to learn the unit circle just to find the 15 degree and 30 and 45 and 60 and 75 and 90 and then set the results to negative

[neon iris]

rational numbers are quotients of two integers, the denominator of a rational number can be 1 therefore all integers are rational numbers

real numbers are scalar, in that they have no "imaginary" component, where "imaginary" numbers are generally defined as (-1)^0.5
another definition for real numbers is that they are one-dimensional, they exist on only one dimension

[plush flint]

set the results to negative depending on the quadrant

[winged oyster]

ye

ok

still dont know the 15 and 75 degree stuff tho

or any way to derive them 😭

[neon iris]

you need to learn cos/sin laws

[plush flint]

isnt that just soh cah toa?

what are cos sin laws

[neon iris]

there's a specific rule I remember but can't name that defines what sin2x is and cos2x

[winged oyster]

do you mean law of sines and cosines or soh cah toa

[plush flint]

law of sines, i want to understand what the fuck that is

how do people calculate 99degrees or 103 degrees and solve for the missing length? not with the unit circle right?

do they all just use the calcuator for that

[neon iris]

https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Multiple-angle_and_half-angle_formulas

if you want 15 or 75 degrees this is where to look

[plush flint]

i see 45

ok

[neon iris]

use these identities to turn one of the other angles you know about into one you don't

[plush flint]

i dont really know how to read that yet

lmao

what is the first one saying

sin(2theta)= 2sin(theta)cos(theta)

is it just saying the full length of the bottom of the triangle + the length upwards?

[minor heron]

the sine and cosine are function returning a value that takes theta, an angle, as input

so like

sin(2times a certain angle) = 2 sin(that certain angle) cos(that certain angle)

might be a bit advanced for u idk

[plush flint]

is there a good video on it

df

[minor heron]

umm idk

ill try googling double angle formulas on yt

[minor heron]

organic chem tutor pr good https://youtu.be/SE5SBTgrwH8

also see videos proving it if you want that as well

[plush flint]

i like him

ok

[viral tusk]

wht is ths

how tf r u still typr

yala

say it cuz

[sage wren]

Any evidence you can aquire an elevation angle measurement from a curved baseline to a star and measure the angle and use the measurements to navigate earth? Any evidence you can aquire 3 circles of equal altitude with the elevation angle measurements of 3 different stars to give you a fix location Latitude and Longitude from a curved baseline?

been a while, yet nobody was able to prove that an angle curves

Let me guess? an imaginary mathematical concept of a tangent extrapolated from the center of a presuposed sphere earth that was measured with elevation angles in the first place to be constructed?

You are not navigating a tangent plane here, you are not on your mathematical notebook in real life, we are navigating earth

baseline of the elevation angle is the earth surface itself

At least even you globies understant that you need a flat baseline to measure angles. But this is an "Elevation" angle measurement in celestial navigation. Elevation from sea level, Angle measurment.
2 straight lines meeting at a vertex

this measurment also forms a right angle triangle with the opposite side of the 90 degrees that can be used to calculate distances using the degrees measured

[alpine garnet]

flat earther

[sage wren]

Thats how its measured

Im not the one who came up with this, this is how latitude system was measured and how Cel Nav works

[orchid brook]

Bro

Yousef

Why are you here

that's cool ig

[viral tusk]

cause i am

tf u even learn here

[sly urchin]

Let $ABC$ be an acute scalene triangle with altitudes $AD, BE, CF$. From $A$, drop perpendiculars to the lines $EF, FD, DE$, and denote the feet by $X, Y, Z$, respectively. Let the line $BZ$ intersect the circumcircle $(BDY)$ again at $P$, and let the line $CY$ intersect the circumcircle $(CDZ)$ again at $Q$. Prove that the point $X$ has equal power with respect to the two circles $(YFP)$ and $(ZEQ)$.

[somber coyote]

Nerdyasianguy

[sly urchin]

I'm denoting the intersection of EF with (YFP) and (ZEQ) as M,N and trying to prove XE/XF=XM/XN, idk if that's the right approach

https://www.geogebra.org/geometry

Here's the GeoGebra link if anyone would like to see for themselves, some points are kind of close to each other

[slim plinth]

Is this bearing

[sly urchin]

Uhm... Wdym

[sturdy remnant]

any efficient ways to help me learn the laws of sine/cosine? how come there is no law of tangent?

[celest fjord]

@dry jungle

@dry jungle

can u help me

with my hw

[marsh marlin]

Be civilized and ping once

[celest fjord]

hes my friend irl

[marsh marlin]

So then go dms?

https://klipy.com/gifs/jgmm-monkey-think

[celest fjord]

he doesnt respond to dms

[dry jungle]

Hi

[celest fjord]

look

oof

[sly urchin]

You can totally derive the law of tangent (you can probably look it up online too), but it's not easily applicable so no need for that

[viral tusk]

@orchid brook

is ths ur fav server

[orchid brook]

Yes.

[orchid brook]

You will not understand.

[deep kiln]

heyy

[viral tusk]

ok solid liquid and gas

s

[fallow palm]

ooh vietnam tst

[scenic cove]

How does one get better at geometry

Particularly spatial reasoning and deducing?

[fallow palm]

do more

[silent plank]

wdym by spatial reasoning and deducing
can you give specific examples of the type of questions you want to improveon?

[scenic cove]

Reducing tunnel vision n training critical thinking

[silent plank]

in general, experiment
apply what you know
see for yourself what works / doesn't work in certain situations
if ur still stuck, then seek assistance as you may have a knowledge gap or missed a certain approach

can add more to that without a specific question and details on how you approached/would approach it

[marsh marlin]

https://klipy.com/gifs/blackbeard-blackbeard-writing

[regal drift]

So i am really bad at geometry and the next year’s math competition has a lot of trig

And that type of stuff

How should i re-learn everything from the start

[marsh marlin]

what math comp

[marsh marlin]

relearning is pointess

pointless

just practice weak areas

[orchid brook]

This is not a Physics server, bro. dk what you're talking about.

[marsh marlin]

I mean noone rlly cares

[orchid brook]

I know

But I know this guy

He is a friend of mine

He joined this serv to annoy me or js make fun of me, I hope that is not true.

[marsh marlin]

Why would he make fun of you

[spring drift]

Guys
Should I assume that two trig functions next to each other are nested? like tanxcosx - should i interpret it as tan(x)cos(x) or tan(xcos(x))?

[minor heron]

tan(x)cos(x)

[spring drift]

Thanks (have to redo a worksheet at this point)

[minor heron]

oop

yeah you can just imagine it like seeing f(x)g(x), they just multiply

[spring drift]

Sure thing!

[daring cedar]

yeah it should be tan(x)cos(x)

[tiny acorn]

why?

cant have shi moving on the same axis anymore

[strong owl]

Please someone help

Me

[silent plank]

what are you being asked to do with that

[strong owl]

finding line PQ

[silent plank]

what have you tried?

[karmic olive]

sorry if i cant explain it properly, but i think the simplest explanation is:
In triangle OO'H
OH = OQ+QH

QH=OP (OPQH IS A RECTANGLE)

OH = 9 + 6
OH = 15 UNITS
USING PYTHAGORAS THEORUM,

OO'^2 = OH^2 + O'H^2

400 = OH^2 + 225

OH^2 = 175

OH= 5 ROOT 7 UNITS,
OH = PQ (RECTANGLE)

PQ = 5 ROOT 7 UNITS

[strong owl]

tyyyyy

[rustic turtle]

Hey everyone, I'm a 12th grade student (Biology) who derived a set of geographic formulas completely from scratch — covering distance between coordinates, time difference between places, and an equirectangular approximation for straight-line distance. Starting point was just the fact that Earth rotates 360° in 24 hours. Sharing my handwritten notebook — curious what you think, what I missed, or how it compares to standard methods.

[warm salmon]

help me i thought the angle of depression will be like this diagram but idk why it isnt working tan18*x40 is wrong

[silent plank]

angles of depression/elevation are angles made with the line of sight and the horizontal (not vertical)

[silent plank]

^

[dawn creek]

great problem

[grave pond]

<@&268886789983436800> mrbeast spam

[somber pendant]

angle of depression will be like this (angle DAC) it's the angle between line of sight and horizontal

[orchid brook]

Because he does, sometimes. But it is a joke (mostly), so yeah.

[edgy jacinth]

Can someone give me a Equation for 8th grade.

[somber coyote]

Civil Service Pigeon

[exotic yarrow]

[edgy jacinth]

#teXit is that for me??

[minor heron]

(I see you were already supplied an equation, but also btw, this is the geometry channel, this would be better in #prealg-and-algebra )

[regal drift]

Yeah but i mean im really terrible at geometry

Like dont know anything terrible

[marsh marlin]

Hm

Like are u shit at like analytical geometry or just geometry in general

[quaint chasm]

is it possible to parametrize the implicit approximation for a gyroid in terms of, say, z?
i.e the implicit form of it is sin(x)*cos(y) + sin(y)*cos(z) + sin(z)*cos(x) = 0

i've tried rearranging it, taking the arcsine or arccosine, but ive only managed to extract one z term - i imagine it would go about the same for the other axes as well

z = -arcsin((sin(x)/cos(x)*cos(y)) + (sin(y)/cos(x)*cos(z))) is about as good as i've gotten

i thought of taking the arcsin and then just canceling out the sin terms but you can't do that since arcsin(sin(x)) != x

[minor heron]

ah... this is kinda complex

is this calc?

[queen juniper]

ye

[minor heron]

oh

[minor heron]

maybe move to #calculus or other early uni channels

[queen juniper]

and i think it's possible

but i'm genuinely too lazy to try rn

[quaint chasm]

i dont think its calculus

maybe it requires it but i figured it would be able to be done without it

[minor heron]

oop i js realized i read it wrong lmao

idk cus i think this channel is like more hs geo

hmm

[queen juniper]

hmmm

[winged oyster]

not even geometry

[graceful moon]

any good resources to self trig i am kinda lost in my trig unit of precalc

[tiny acorn]

Khan academy

[summer lion]

the answer is probably not infinity

[tiny acorn]

How do i prove the volume of a pyramid is V = Sh/3

[loud geyser]

Using calc ?

[tiny acorn]

Havent learned that yet

[plush flint]

guys how do people calculate missing side length of a triangle when a side is like 78 degrees? do they all use a calculator?

[silent plank]

whether this is even possible depends on what other info you're given

[plush flint]

in a right triangle

the angles are 78 90 and 180-both

and there is like 1 length given for the length of abc

[silent plank]

ok, it's a right triangle
you'll need a calc for a decimal approximation

there's no other nice exact value representation

[plush flint]

so you need soh cah toa sin cos tan?

there is no easy way to manually do it on paper?

[silent plank]

it'd be very tedious

[grave pond]

Since 78° is a multiple of 3°, in principle there would be a way to write the answer exactly by combining a few dozen square roots with basic arithmetic. But sensible people just use a calculator (or a trig table) already. You'd want a calculator for those square roots anyway ...

(Though, thinking more about it, you won't need even one dozen square roots, as 78° = 90° + 60° - 72°, and those three angles are simple to construct. Still, use a calculator instead).

[plush flint]

i wonder what that looks like on paper

[grave pond]

You have

cos(90°) = 0, sin(90°) = 1 (duh!)
cos(60°) = 1/2, sin(60°) = sqrt(3)/2
cos(72°) = (sqrt(5)-1)/4, sin(72°) = sqrt(1-cos²(72°))
Then apply angle addition/subtraction formulas to 78° = 90° + 60° - 72°.

As you see, this is not a uniform procedure that one can go on to apply to arbitrary angles.
What I had in mind first was to derive sine and cosine of 3° first (by bisecting 12° = 72°-60°­ twice, though in hindsight using 3° = 45° + 30° - 72° would be easier­) and then work my way up from there using addition formulas. Somewhat more general, also more work, and still only applies to multiples of 3°.

[viral tusk]

(x+3) (x+7) is x squared plus 10x plus 21