geometry-and-trigonometry

[viral tusk]

iM SO smart

man

[old raft]

binomial distribution?

[plush flint]

is that what its called? binomial distribution?

[grave pond]

"Binomial distribution" is something different, belonging to probability. This is just multiplying out (via the distributive law) a product of binomials.

[plush flint]

you guys are genius as fuuck. i want to become more like all of you before i die

troposphere you are like a legend to me

horse pfp and speaking math like a God

yo troposphere, what do i need to master factoring polynomials?

[grave pond]

I don't have any answer other than practice.

[plush flint]

how do you get the equilateral triangle for the 30 60 90 triangle again?

all i keep thinking is about the hypotenuse is 1

[neon iris]

cut it in half

[plush flint]

cut the triangle in half from the hypotenuse of 1?

doesnt look like a half to me

where is the equilateral triangle on a unit circle starting off with a hypotenuse of 1?

lemme think first

a 1,1,1 equilateral triangle with 60 60 60 on a unit circle

cut in half is 30,90,60

had to think about it from the side first lol

harder to think about up there

[plush flint]

you fukkin bot spammers

[marble night]

ez

the unit circle

[plush flint]

i think i get it now

[cinder geode]

Circle

[plush flint]

ladies and gentlemen

what should i learn, or what are the prerequisites before getting into calculus

i want to teach myself calculus

[cinder geode]

IM SELF LEARNING CALCULUS TOO

[minor heron]

me too

[cinder geode]

Where did u started?

I'm reading this calculus book

[minor heron]

khan academy

and stewarts' textbook

[cinder geode]

Idk that one

[cinder geode]

Cooll

R we allowed to talk in this channel?

[minor heron]

there is #calculus if you'd like to talk there about calc

[minor heron]

its a website with videos and course plans and like practice problems, google it

[cinder geode]

I already did

[minor heron]

oh icic

[cinder geode]

Okayy

[minor heron]

heading off for lunch now gotta brain fuel to do more math

[plush flint]

i tried to fuel it with halal food, and respect to the halal cart man but my head is fucked from all the salt and white sauce

[lyric bronze]

Can someone help me understand the unit circle 🙏

[plush flint]

i understand it somewhat but im not qualified enough to teach it

[lyric bronze]

Anything helps lol

Im clueless

[plush flint]

in a unit circle, the radius is always one, and you can impose the 45 45 90 right triangle on it, and logic from the 1,1,1 60 60 60 equilateral triangle on it

[lyric bronze]

I see

How do you solve stuff on it

[plush flint]

i have no idea what the unit circle is for

[lyric bronze]

Ah

[plush flint]

lmao

[lyric bronze]

No worries 🤞

[plush flint]

do you know how to impose logic from the isosceles right triange 45 45 90 , and equilateral triangle 60 60 60, onto the unit circle? @lyric bronze

[minor heron]

idk if im qualified either im js a 9th grader but

Like

There's values where the rays intersect with the circle

While a triangle has 180 deegrees

Limiting how you can solve trig values

A circle has 360

So, you can find trigonometric values you couldn't find otherwise - eg: sin(240 degrees)

The circle repeats values with different signs

And, if you draw a triangle anywhere in it, you'll notice the "hypotenuse" will always be the radius, and in the unit circle, the radius is 1

So, sin is opposite over hypotenuse and cosine is adjacent over hypotenuse...

so with hypotenuse 1, sin = opposite value and cosine = adjacent value

In the unit circle, opposite is the y axis and adjacent is the x axis

in other words, the sin value of an angle is the y value and the cosine value of an angle is the x value

The "reference" angles (quadrant 1) - as I said, coordinates repeat with changing signs - to memorize on the unit circle would be 30 degrees, 45 degrees, and 60 degrees

[lyric bronze]

Wdym

Like I know that cosv is x and sinv is y and shit

[lyric bronze]

Ohh

[plush flint]

9th grade, congratulations, im 26 years old and turning 27 within 30 days lmao

[minor heron]

oop wow xd

you're like double my age im 14 xd

[lyric bronze]

It’s never too late 🥹❤️‍🩹

Alright let me try something

[minor heron]

So like based on where it intersects you can use that to find values

[plush flint]

i dropped outta HS due to family issues.....

[minor heron]

which also becomes useful later on with identities like double angle, sum angle, etc

[lyric bronze]

Happens man, stay strong

[lyric bronze]

Okay I see

Oh I got it now tysm @minor heron

[minor heron]

you're welcome!

[lyric bronze]

Can you help me with a harder question

[minor heron]

sure

ill try xp

[lyric bronze]

The angle V is marked in the figure. Determine cos v precisely

[minor heron]

kk ill draw it on my end and solve

[lyric bronze]

Alr

[minor heron]

so like this

[lyric bronze]

Yes

[minor heron]

So the hypotenuse is sqrt13

[lyric bronze]

Mhm

[minor heron]

based on the pythagorean theorem

[dawn pond]

Notice that V cannot form a right triangle, so ur not dealing with it directly

[dawn pond]

You shouldn't need that

[minor heron]

OH wait

[lyric bronze]

Could you elaborate 😅

How’s it relevant

I suck at these things sorry

[minor heron]

so the v value plus the other angle makes 180

[lyric bronze]

Yes

[dawn pond]

Usually the way to calculate the cos of an angle is by using a trig identity
Cos(V) = the adjacent of some right triangle / the hypotenuse of the same triangle

But V is clearly greater than 90°, so you can't have a right triangle

[lyric bronze]

Oh yea

Makes sense

[dawn pond]

So we're not counting that directly through V

Think of other ways to define V

[lyric bronze]

Should we count the angles of the triangle?

[dawn pond]

One should suffice

[lyric bronze]

True true

It’s a right

[dawn pond]

There's an angle that you can count that is very close to V

You can try using it

[lyric bronze]

By using the cosine rate?

[dawn pond]

Yes

There are other trig properties, are you familiar with the unit circle?

[lyric bronze]

Sorta

[dawn pond]

So you can notice that V and the angle next to it form a straight line together

[lyric bronze]

Mhm

[dawn pond]

In other words, 180°

In other words π

[lyric bronze]

Huh

How so

[dawn pond]

So if we call that angle θ
We know that θ + V = 180
Then what is V equal to

[dawn pond]

Ignore that actually let's keep using 180

[dawn pond]

Actually ur right, it's probably a better idea to use that for precise values

[dawn pond]

@lyric bronze In other words, write V in terms of θ

[lyric bronze]

I got 128

[dawn pond]

It's probably a bad idea to calculate the angle

Because they asked for a precise value of the cos

[lyric bronze]

Oh they want cos

💔

[dawn pond]

If you plug cos(128) you won't get an accurate answer

[lyric bronze]

Ahhhhhh

You’re right

[dawn pond]

Ok so if V + θ = 180
Then what is V

In terms of θ

[lyric bronze]

The outer angle??

Or like wdym

[dawn pond]

Just give an expression of v using θ

Like V = something that includes θ

[lyric bronze]

180-0

[dawn pond]

very good!

So cos (V) is just cos(180 - θ)

[lyric bronze]

Yup

[dawn pond]

There's a property of cos(180 -x)

I want you to take a look at the cosine values from the first quadrant, the one on the top right

[lyric bronze]

Yes

[dawn pond]

And compare it to the values of the cosine in the 2nd quadrant the one on top left

Compare the angle that are on the same horizontal line

For example π/6 and 5π/6

[lyric bronze]

X values are just negative orrr?

[dawn pond]

Very good!

So we know that cos(180-x) = - cos(x)

Now apply this to cos(V)

Which we know is cos(180 - θ)

Also when you calculate the values, since we're using ratios, try keeping the fraction

[lyric bronze]

Cos(-180+0) or wdym

[dawn pond]

Cos(180-x) = - cos(x)

[lyric bronze]

Yes

[dawn pond]

Cos(180-θ) would be ...?

[lyric bronze]

-cosx 😭❓

[worn anchor]

whats x then

[lyric bronze]

Im not sure

[worn anchor]

i think x=$\theta$

[somber coyote]

Tangent

[lyric bronze]

Oh yea

[dawn pond]

Cos(180 - a) = - cos(a)
Cos(180 - α) = -cos(α)
Cos (180-π) = - cos(π)

Now try with θ

[lyric bronze]

Alright

-cos(0)

[dawn pond]

Very good

And what is cos (θ)

Using the ratios

[lyric bronze]

Uh

-1?

[dawn pond]

No no

What is the rule of cosine

[lyric bronze]

a^2=b^2+c^2-2bccosA

I think

[dawn pond]

I meant the ratio

What is cos(x) in general

[lyric bronze]

Oh

When u divide the sides?

[dawn pond]

Yes

[lyric bronze]

b/c

[dawn pond]

Very good

And what are b and c

[lyric bronze]

X axis and hypotenuse

[dawn pond]

And what are their values in our example

[lyric bronze]

Uh

180 and 0?

Maybe

Idk

[dawn pond]

So c is the hypotenuse

And b is the adjacent

[lyric bronze]

Yes

[dawn pond]

So what is the value of b

What's its length according to the exercise

[lyric bronze]

Oh

2

I forgot about that

I was looking at the circle

[dawn pond]

It's okay

So we know b = 2

Now what is c

[lyric bronze]

Sqrt13

[dawn pond]

Good

So cos(θ) = b/c

[lyric bronze]

2/sqrt13

[dawn pond]

Now plug those values

And now

Cos(V) = - cos(θ)

Plug the values

[lyric bronze]

-2/sqrt13?

[dawn pond]

Good job

Another thing you can do is multiply the numerator and denominator by sqrt 13

It's preferable to have a rational denominator

[lyric bronze]

Wait I didn’t really understand the point of negative cos

[dawn pond]

So we get that cos(V) is equal to $\frac {-2 \sqrt{13}} {13}$

[lyric bronze]

Was it due to it being in the first quadrant?

[somber coyote]

ScoobySnacks

[minor heron]

Yes, the second quadrant and first quadrant have different signs

(for cosine)

[dawn pond]

It's a general property that cos (180 - x) = - cosx
Regardless of where the x is

[lyric bronze]

So if it was less than 90 then we wouldn’t be doing -cos?

[minor heron]

If it was between 0 and 90, that would be just the quadrant 1 value

[dawn pond]

That's because V = 180 - θ
If V = θ we would've used that directly
If V = 270 - θ we would've been using something completely different
If V = -θ we would've used something else

It's just a property

Think of it like this

x and (180-x) are opposite of each other in the unit circle

[lyric bronze]

Yes

Wait so

[dawn pond]

Which means that they're 2 quadrants apart of each other

[lyric bronze]

What do you do for 270

Or 360

[dawn pond]

Let's not worry about that for now ☺️

[lyric bronze]

😭😭

[dawn pond]

Actually, let's make that a homework for you

I'll help you out with the 270

cos (270 - x) = -sin(x)

Now that's on you to find out why

Oh also, here's a quick summary of what we did

[lyric bronze]

Oh wait

[lyric bronze]

Is that cuz you’re mirroring the y axis

[dawn pond]

I guess that's one way to think about it yes

[lyric bronze]

How would you explain it

[dawn pond]

Try drawing a circle and compare the lengths

[lyric bronze]

Let me cook something up

[dawn pond]

I actually don't have a very good explanation for that

I just accept it geometrically

And it always made perfect sense to me

[lyric bronze]

How would you do 360

[dawn pond]

What is 360 in a circle

[lyric bronze]

A full circle

[dawn pond]

So when you start at an angle, and rotate 360° where will you end up

[lyric bronze]

At the start 😭

[dawn pond]

Nope

[lyric bronze]

Oh

[dawn pond]

Remember, 360 is a cycle

[lyric bronze]

Quadrant below?

[dawn pond]

If you're in a roundabout

And you rotate a full circle around it

Where do you end up

[lyric bronze]

Where you started??

[dawn pond]

Correct

[lyric bronze]

Am I tripping

Oh

[dawn pond]

So if you have an angle x, and you rotate 360 degrees, where do you end up?

[lyric bronze]

Where you started

[dawn pond]

And where did u start

What's the angle

[lyric bronze]

X

[dawn pond]

Correct

So what is cos(360 +x) ?

[lyric bronze]

Cos(x)?

[dawn pond]

Correct!

And that's why we say cos(x) is cyclic/repetitive

Because every 360° you get the same value

So cos(x + 720) is also cosx because 720 = 360*2 aka two cycles

In general, we say that cos(360k + x) = cos(x) for any integer k

This applies to sinx as well

[lyric bronze]

Wait so just to make sure I got everything right

Can you explain why sin(v+90)=cosv

[dawn pond]

I actually do not know

But that is correct

[dawn pond]

Perhaps @minor heron knows the answer 👀

[minor heron]

oops i was editing um

[lyric bronze]

Fingers crossed

[minor heron]

i mean like

you could prove it

with a sum identity

we did that as an example in class like five days ago

but like idt you know the sum identity

but if u did it would expand out to 0sinv+cosv=cosv cosv=cosv which is true, but like, hmm im not sure how to prove without sum identity

[minor heron]

errrr

like

so when u add 90

the rule is

(x,y)-->(-y,x)

So, the y value, sin(v+90) becomes the x value aka cos(v)

I think..

....... @dawn pond does that sound right

[dawn pond]

Good point actually

You could prove that using complex numbers

[minor heron]

gulps

Let's stick to the sum identity to prove it

if i can prove it simply then fack complex numbers!

[queen juniper]

wait do we use exponential def of sine

if we wanted to prove it that way

wait that works

[dawn pond]

Let z1 be such that

z1 = cos(θ) + i sin(θ)
To have the effect of a 90 degree rotation that's the same as multiplying by i
And thus we get z × i, which should give another complex number with an angle (90+θ) therefore
z×i = cos(90+θ) + i sin(90+θ)
Algebraically we get
z × i = cos(θ)×i + i² sin(θ)
z × i = - sin(θ) + i cos(θ)

[minor heron]

... yes i understand what that means ack

[queen juniper]

orz

[dawn pond]

So we got from

1. cos(θ+90) to -sin(θ)
2. sin(90+θ) to cos(90+θ)

It's pretty much saying that i×z is a complex number with angle 90+θ and then comparing that to the algebraic result of multiplying z by i

And since they're equal, their Real part is equal and their Imaginary part is equal

[queen juniper]

wait i see ur active now

[dawn pond]

I'm sure you do mhm mhm

[minor heron]

yesyesyes (google google google agh complex numbers are weird)

[dawn pond]

Did you study those?

Because that kinda just uses the definition of z1 = z2
And that multiplying by i is rotating a 90°

[minor heron]

wait

how does multiplying by i like

rotate

[dawn pond]

3blue1brown has a GREAT video about that

[minor heron]

oh

ill go google that

[minor heron]

n-no..

my classes at school barely taught about complex numbers

and stuff

so

[dawn pond]

But you know about the complex plane, right?

[minor heron]

yeah

[dawn pond]

That there's a real numbers axis and an imaginary one

So take the number 1

[minor heron]

with a+bi, a is x and b is y

[dawn pond]

Multiply that 1, by i

Where does that get you

[queen juniper]

i(a+bi)=-b+ia

u can probably see where that would take the point

[noble quiver]

need help w trigonometry

[minor heron]

uhhh from the x axis to y axis

[minor heron]

elaborate pls

OH

i get it now

[dawn pond]

Wouldn't that just be a 90° rotation? ^^

You know, a great mind-blower for me was to discover that multiplying two complex numbers has two effects:

1. Changing the angle (the effect of the imaginary part of the number)
2. Changing the length/radius (the effect of the real part)

[noble quiver]

Can you explain how did that first marked line went from this to that
Thanks for helping ( i know this is just a multiplication but for some reason my brain denies this idea)

[dawn pond]

So if you multiply a complex number z by a real number that just increase the radius, but the angle is preserved
And if you multiply it by just the imaginary part (which is just b×i), the radius is preserved and the angle changes

[dawn pond]

You have an expression (a-b)²

Multiplied by 8

8(1-cos²(θ))²

[noble quiver]

OH GOD YOU ARE RIGHT

[dawn pond]

Expand it and multiply by 8

[noble quiver]

I cant be wasting my time over this

this is embarassing

how did i not know this lmao?

[dawn pond]

All good, it sometimes feels weird xd

Especially when dealing with trigonometry because some operations might seem obscure

[noble quiver]

yeah its after overthinkin alot of maths made me forget the simple methods

nahh i cant get over this
I am boutta hate myself all nigh for this

[queen juniper]

dw

[dawn pond]

That sounds like a waste

[queen juniper]

brain farts happen

[dawn pond]

So you wanna waste even more time crying about it? Dammit dude

Lock in smh

[noble quiver]

needa lock in

[dawn pond]

You got this dude let's go 🔥

[noble quiver]

can i ask for another help if you are free?

oh its just a formula

thanks for helping

[dawn pond]

Yeah I was gonna say that might be an identity

[plucky marsh]

can anyone help with polar graphing

[indigo obsidian]

i can try what do u need

[plucky marsh]

how do i graph like 5, pi/4

[indigo obsidian]

find angle

which is 45 degree i believ

e

then count distance

from pole ofc

5th concentric circle

make sense @plucky marsh?

i guess yes

[plucky marsh]

yea

okay

[indigo obsidian]

👍

[sonic ermine]

isnt sin for [0,2pi] buit arc sin is [-pi/2,pi/2[

or am i mixing thigns up

!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.

[spare ibex]

Can somebody help me make a square?

https://www.desmos.com/calculator/j4hvmrluci

I made it with a diamond

But I want actual square

[rugged vault]

you are correct for sine that it is [0,2pi], this is when you graph it, if we are looking for values of theta, it will have the values of [-pi/2 , pi/2]

[dire ember]

I believe because cos wave is shifted by 90 deg

[limber dagger]

Can somebody help me here?

[vocal sentinel]

what do you think?

have you learned angles subtend arcs theorem?

[limber dagger]

uhh no

[vocal sentinel]

You want to see N, then which angle also cover arc PL>

[limber dagger]

im confused

[limber dagger]

wdym

[vocal sentinel]

If two angle subtending same arc, they are equal.

If you got these kinds of exercises, better revise fundamental theorems!

https://thirdspacelearning.com/gcse-maths/geometry-and-measure/subtended/ read this please

[static mason]

I understand why it’s 45 degrees because of the formula, but the diagram on the left with the red and blue triangles is a bit confusing. I understand the lengths and stuff because it’s a linear transformation and it’s i and j unit vectors but how do i know what angle i need to find to know the rotation

[exotic yarrow]

Look at what happens to (1,0) ig? The diagram just seems to confirm/check that the same happens to (1,0). Then idrk what you’re asking.

[plucky marsh]

4pi/3 isn’t in the domain of arc sine that’s why your answer doesn’t work

[silk totem]

use this instead:
outline of a square:
max(|x|, |y|) = 2
filled square:
max(|x|, |y|) ≤ 2
that makes a square centered at (0,0) with sides from -2 to 2.

[gilded acorn]

If the sum of |xi - yi| is the city block distance between two points and the square root of the sum of (xi - yi)^2 is the euclidean distance, is the third root of the sum of (xi - yi)^3 anything special?

[silk totem]

I think Your idea is a natural extension of the pattern, and the proper version (with absolute values and p=3) is a valid but unnamed member of the Minkowski family of distances. It doesn't have a catchy "real-world" analogy like city blocks or straight-line flight.

[silk totem]

The measure of angle N is 17°

[gentle jewel]

Hi can someone help me understand on y I have to do sin60 to find the side length cause I stilll don’t understand. Ty

[dawn pond]

See, trig functions are just ratios between two sides of a right triangle

Sin(x) is the ratio between the hypotenuse and the side that's opposite of your angle

Which means, if you have one of your length, you can divide or multiply by that ratio (which is sin(x)) to get the other length you want

[queen juniper]

cuz sin(60) gives h/(hypotenuse), and h/(h/(hypotenuse))=hypotenuse, which is a side of the equilateral triangle

[gentle jewel]

Ohhh

And the oppposite is h

Ohhhh

Tyty guys

[dawn pond]

We can see that h is the length of the side opposite to your 60° angle
We get that sin(60) = h/ hypotenuse
Thus h = hypotenuse*sin60

[gentle jewel]

Ohhh ok ty scooby

I get it now

[dawn creek]

great prblem

[upper harbor]

yeah the substitution needs to be clean

[dawn creek]

yep

[plush flint]

wait, so for the unit circle, you can only use it for 17 measures?

wtf is euclidean geometry

[tiny acorn]

Geometry invented by euclid

[plush flint]

ok

wow we got a genius in here

[neat sedge]

ACTUALLY

[plush flint]

now i wanna know who he is and i want to know what antquity is

[tiny acorn]

,w euclid

[somber coyote]

Results provided by WolframAlpha

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

Requested by hexagon69_

[plush flint]

i barely know who rene descartes is,

rene descartes, the i think therefore i am guy

guys, how do i know that i understand the unit circle?

i understand how its derived now from a 45 45 90 triangle, and a 1-1-1 60 60 60 triangle cut in half

but where can i test my depth of understanding?

[exotic yarrow]

this is not rlly hard, but it's cute(-ish)

[plush flint]

oh shit

i hate that i can AI this but i wont

what is a vertex again?

i dont even remember the names of all the triangles

[minor heron]

vertices is like the points

that make up like

the triangle

like the 3 points

[minor heron]

and like isoceles would be like

2 sides are the same

[dawn pond]

The sharp pointy things

[minor heron]

and one is different

[plush flint]

3 points on a triangle is very intuitive, on a circle wtf

[dawn pond]

Basically where two lines connect

[minor heron]

if thats what u mean by names of the trirangles

[plush flint]

but okay

oh

3 points on a circle ok

two sides are the same

so im imagining right now

[dawn pond]

∆

This is isosceles

[plush flint]

beginning with a 60 60 60 triangle, but you can squeeze the two bottom ends

to the sides

or inner

[dawn pond]

Basically that but u can move that top vertex up and down

[plush flint]

yeah that too

cos 40 sin 40

arent they both just 40 degrees? but cos represents an x and sin represents a y leg

this question is cooking me holy shit

[spare ibex]

Ty

[plush flint]

yeah, see i dont know this shit enough. what a sad day to be me

when i think of cos and sin 40 all i think about is

cos40= adj/hyp and sin40=opp/hyp

[grave pond]

The first thing to think of here is that (cos(40°), sin(40°)) and (cos(60°),sin(60°) and (cos(t°),sin(t°)) are all points on the unit circle.
So the question is essentially asking you to find points on the unit circle where such-and-such is the case .... and then you can stop thinking about trigonometry in particular.

[plush flint]

the unit circle

0,30,45,60,90,120,135,150,180,210,225,240,270,300,315,330,360

[grave pond]

No, but that's an easy misconclusion to draw from those common diagrams.

[plush flint]

tell me how im wrong

omg troposphere the legend

this is a truly a special moment in my life

[grave pond]

Every angle is the direction to a point on the unit circle whose coordinates is the cosine and sine on that angle. There may only be a few angles where those coordinates have "nice" expressions in terms of square roots that are worth memorizing, but no matter which angle, you always end up on that circle. And that is the more important point.

[plush flint]

the bigbang and abiogenesis happened so troposphere can bestow upon me some wisdom

yes

[grave pond]

Okay, I'll shut up, sorry for bothering you.

[plush flint]

alll the angles

no youre not bothering me at all

i love your words, no jokes

please tell me more troposphere 😭

[plush flint]

i genuinely dont understand the point, i know 17 angles and i know you always end up on the circle

for any angle like 77.78 degrees, 3 degrees, 99 degrees

but what of those angles that arent easily remembered?

i know the angle makes a line on the circumference, and the line that extends onto the circle can be read with x and y coordinates , sine and cosine

i dont know a damn thing past that

(okay this is sad, troposphere interpreted my words sarcastically or aggresively ;()

[tough vapor]

True, you can treat sin as y value, and cos as x value of the circle point,

[plush flint]

where do you even find these questions

i want a workbook with these kinds of questions so i can practice and be aware of what im ignorant of

ive never seen a question like that in my life

[exotic yarrow]

The first screening test in the United States - scroll to the bottom and you should be able to rabbit hole your way to the past questions from many many years ago.

[plush flint]

ok

[silk totem]

Your welcome

[plush flint]

troposphere , if you are here, i just want to say im amazed by your confidence in math, its very inspiring. you are absolutely not a bother, im just enamored that a hoorse profile pic is teaching me math

[tall pasture]

Guys what is sin cos and tan for trig

[spiral lodge]

Functions

[celest fjord]

so

[queen hemlock]

Sin is o/h, cosine is a/h and tangent is o/a. cos/sin=tan

They are ratios between side of a 90deg triangle relative to one angl

[tall pasture]

Ok thank u

[azure blaze]

ye and additionaly to remember that u can memo SOH CAH TOA

[warm tendon]

If ur solving a trig equation with some ratio and then 2x as the angle does what does the new domain become , for regular question with just x we use 0<=x<=2pi

[queen hemlock]

Trig never clicked for me until I actually applied it in a classroom even though I knew sohcahtoa

[faint sentinel]

you mean tan = sin/cos?

[queen hemlock]

Yeah my bad

[faint sentinel]

are we allowed to post math memes? im new here

[celest fjord]

do it in disc 2 prob

[broken geode]

airball

[wise heart]

when should I do ad/bc for composite fractions instead of a/bcd (fraction is a/b/c/d)

I have a test tmr and composite fractions keep tripping me

I've been using ad/bc for my calc work but one of the problems involved 1/a/b and provided a reciprocal and the more I look into it the more confused I get (about when to use what I can understand a reciprcal)

[leaden lantern]

I can explain?

[wise heart]

okay

[leaden lantern]

Okey

@wise heart

[wise heart]

ty do you also know when it'll be a/bcd and how to tell if its a/bcd or ad/bc?

[leaden lantern]

Hmm

[leaden lantern]

There can be alot of cases but

Usually we cant see a/bcd

If you know how to arrange it you can solve any question

[wise heart]

hmm what do you suppose by the arrangements

[leaden lantern]

Its all basic maths

[leaden lantern]

What is your occupations

Like student?

[wise heart]

yes student

I'm bad with composite fractions

seeing the multiplication rather than just translating positions did help though

[leaden lantern]

See

I gtg

See ya

[wise heart]

okay thank you cya anmol

[leaden lantern]

If you wanna understand geometry and trigonometry you can ask me

[tall vector]

This may be a but of an ask... but, would it be possible for you to teach me all of Algebra2 and PreCalc in 30-200 days?

[long wing]

Full time job

[mellow moth]

The whole course

[leaden lantern]

I am learning calculus too

[winged oyster]

self study it atp

use uh

3b1b

[nocturne breach]

Khan academy is free and is super good for both of those… try that I doubt anyone would have the time to teach u individually

[wild portal]

This is where I learned calc from https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx, but I would recommend watching 3b1b’s calc series

Sorry, I read the question wrong, but the link I sent has a algebra section and 3b1b has videos on both I think

[wise heart]

Okay

[wise heart]

pauls notes is a great website I use it to study

[tall vector]

👍👍👍👍

[leaden tartan]

that website is so good

[distant monolith]

ad/bc

[young pewter]

guys can anyone explain the basics of trigonometry

im having a little trouble

[foggy heron]

what part?

[young pewter]

Basics from the start

[young pewter]

Yeaaaa

[grave pond]

You'll need to be more specific than that. Right now you're basically saying "please write me a textbook" without giving them anything to go on -- not even what you find lacking about the textbooks that other people have already written and which you have presumably tried some of before you concluded your best bet was to ask for help from randos on the internet.
Even if you find someone willing to take you up on that request, chances are they won't be particularly good at writing textbooks, and the book they choose to write won't match what you need.
You have a much better chance of getting useful help if you ask much more concrete questions about something you don't understand.

[foggy heron]

yeah, from what I consider basic, just know that what you know as degrees can equal to radians. radians is basically degrees, but in terms of the circumference of x circle.

you can change radians to degrees and vice versa.

to do that, have, for instance, the degrees.

90 degrees x pi/180 degrees = pi/2

therefore, 90 degrees, in radians, would be pi/2. also, radians don’t have a unit. so when you see a measure without degrees(in trig) it means that it’s a radian.

pi/2 x 180 degrees/pi =90 degrees

also, you should know what’s standard position. this is the positive x-axis. from there, if you move counterclockwise, you have positive degrees/radians. however, if you move clockwise, the degrees/radians will be negative

[upbeat lava]

I thought the basics were sohcahtoa

[foggy heron]

i mean, the algebra and trig books start with what i said. however, you have a point because in geometry books, they start with sohcahtoa

[minor heron]

depends, precalc or more advanced courses that assume foundations will start with unit circle

while simpler courses, maybe designed for.. 9th or below graders? maybe, will start with sohcahtoa type stuff

so if a course assumes no prior trig work then sohcahtoa, if a course assumes prior foundations then unit circle intro

[foggy heron]

yeah, what she said

[leaden lantern]

https://tenor.com/view/cat-trigonometry-table-cat-trigonometry-table-math-gif-25973656

[foggy heron]

lowk, i never learned that

i just did it on the exam

the teacher looked at me bad for some reason

[leaden lantern]

Tan30 is 1/root3

[leaden lantern]

I also never learned that

I know how to make those

[foggy heron]

wait, what are your pronouns?

you have everything

[leaden lantern]

I am male and a student

And i have brain with neurons

[foggy heron]

lol

[leaden lantern]

Basic trigonometry is like ratios

https://tenor.com/view/hypotenuse-a2b2-square-geometry-trigonometry-gif-18715277

[minor heron]

isn't pythag theorem like 8th grade stuff...

[hasty stump]

yeah

[minor heron]

ah

[leaden lantern]

I didn't find a trigonometry meme

https://tenor.com/view/trigonometry-math-formula-cursed-math-trigonometry-formulas-gif-16297076018223031490

What can be a bigger flex then remembering them all ( there are more)

[marsh marlin]

memorize all identities

[minor heron]

Ah ic xd

[sharp void]

know how to prove them

[long wing]

I just got PTSD from that

I remember doing flashcards

And drilling all of that into my memory

[radiant hill]

Isn't it better to learn how to derive them?

[long wing]

Well my exams were more prove bigger identities using those formulas rather than derive them

[radiant hill]

For understanding I think it's better

[long wing]

Yeah sure

But my exams don't really reward that

Strict time constraints

[radiant hill]

Does it need to be all about the exam?

[long wing]

In the short term yes

[radiant hill]

What about the long term

[long wing]

When there's not much time left before the exam comes

You have a point

But it wasn't practical back then

I had exams in like 4 days back when this happened

[radiant hill]

What is your use for mathematics? Is it to pass an exam or for any future thing?

[long wing]

Lmao 😭

U win

I agree

[radiant hill]

No I wasn't here to win I just wanted to understand why you needed to memorise them all

[long wing]

E X A M

😭🙏

[radiant hill]

Yeah no I get that now

[long wing]

Bruh on second thought I just realised I can derive them from scratch

[long wing]

🧠🧠

[drowsy abyss]

Any trigonometry questions

Must be hard?

[spiral lodge]

Wdym?

[upbeat lava]

This

[leaden lantern]

We can derive them

[ruby ruin]

I can have one for you, can I recontact you like in a couple of days ?

Or when I have 15min for pose it

[drowsy abyss]

Va sure

[ruby ruin]

Thanks !

[slim plinth]

I only know deriving quadratic formula

[upbeat lava]

I don’t even know about that haha

[slim plinth]

I can

[upbeat lava]

My friend sent me that, I don’t take further maths

[upbeat lava]

How?

[slim plinth]

Think about using completing the square

and use (b/2)^2

[upbeat lava]

Kk

[slim plinth]

You want to me to do it step by step?

[minor heron]

i had to take notes on a long ahh video on it

🥀

[upbeat lava]

I’ll try and derive it tmrw when I have some time

[slim plinth]

Okay

[upbeat lava]

Do you take ap math/further?

[minor heron]

ahh yeah AP

[slim plinth]

If you want I’ll teach you

Just get a paper

And take down my steps

[slim plinth]

^

[minor heron]

im in US so idt we have further maths, but im in ap precalc atm

[slim plinth]

Me too I’m also in US

[upbeat lava]

They’re basically the same as far as I’m aware

[minor heron]

ah

icic

[slim plinth]

ButI’m taking normal pre-calc class

[minor heron]

prolly js diff education systems then

ah

[upbeat lava]

I don’t take further so it’s not covered

[slim plinth]

If u want my units what im taking go to #precalculus

[minor heron]

ah ic

[minor heron]

like the quadratic formula stuffs?

[upbeat lava]

We use it but we haven’t had to derive it

Maybe it’ll change though because I’m pre calc

[minor heron]

ahh

idk

i learned it before pre calc

the course where i had to take notes on it was in integrated 3 (like alg2 level ish)

[slim plinth]

Me too

[minor heron]

and they didn't have "enhanced" (honors) for online classes for it so it was js a regular class

[slim plinth]

I did it myself

[upbeat lava]

We don’t have ‘algebra 2’

[slim plinth]

I do

[upbeat lava]

What’s covered in that?

[slim plinth]

In my 4 years of HS

I took Algebra 1, Geometry, Algebra 2, and Pre-Calc

[upbeat lava]

So I assume y’all are American?

[slim plinth]

There is Algebra 3

But I think I’m too smart that my Algebra 2 teacher recommend me to Pre-Calc

And skipped algebra 3

[minor heron]

yeah im from US (born elsewhere)

[slim plinth]

Yes

[minor heron]

oh wow ive never heard of alg3

[slim plinth]

I heard there is matrix

[upbeat lava]

I was failing math until this year 😅

[slim plinth]

Fun fact

[upbeat lava]

It’s actually so fun though

[slim plinth]

I only learned Cramer rules with 2x2

[upbeat lava]

What algebra number is linear algebra?

[slim plinth]

Algebra 1

[queen juniper]

hmmm

[slim plinth]

Like 2x2 matrix

[minor heron]

ah

[minor heron]

ouh, i see haha

[slim plinth]

I feel bad

[minor heron]

linear algebra as a full course would typically be in uni

[upbeat lava]

You do that in highschool?

😭

[slim plinth]

Let us know we can help you improve

[minor heron]

linear algebra may be covered in small amounts at a basic level in high school

eg: basic matrix work

[slim plinth]

I had took Algebra 1, and Geometry, and Algebra 2

I’ll help you

[upbeat lava]

I’m just grinding math as much as I can. I went from F’s to now B’s

[slim plinth]

Good job

[upbeat lava]

That’s crazy because we don’t cover it at all

[slim plinth]

Let us know we can make u from Bs to As

[minor heron]

nice nice, improvement is improvement

me can try to help 2, im js a 9th grader

[slim plinth]

I agree

[slim plinth]

I’m 12th grader

And I’m taking pre-calc

[upbeat lava]

I’m in my final year of highschool

[minor heron]

ah

so like 12th ish

[upbeat lava]

In uk, highschool ends in 10th grade

Then we have sixth form and then uni

[slim plinth]

Me too in American

[slim plinth]

What’s that mean

[upbeat lava]

Just college basically

[slim plinth]

Good for u

But good luck

Tell me what college do u want to go

[upbeat lava]

I mean if you’re willing, I could add you and dm if I really don’t understand smth

[slim plinth]

Okay

Added

[upbeat lava]

You wouldn’t know them haha

[slim plinth]

Like how do u apply colleges in UK

[minor heron]

ohh interesting

[upbeat lava]

You need ucas points

[slim plinth]

I can tell u I use Commitapp

[upbeat lava]

Which are equivalent of credit I think

[upbeat lava]

What’s that?

[slim plinth]

It’s a portal where u apply colleges

U will also need essays

[minor heron]

is it like

[slim plinth]

And SAT/ACT scores

[minor heron]

the common app?

[slim plinth]

Yes

[minor heron]

or something?

Ah

[upbeat lava]

I’ve heard of sat but not act

[minor heron]

act is like

theres optional science

with the required reading and math

and its out of 36

i think

its basically just another standardized test

ACT tests speed more and SAT tests harder questions... I've heard, anyway

[upbeat lava]

Y’all are so lucky you take sat

[minor heron]

wait how is it like 4u

[upbeat lava]

You literally get to take all multiple choice for every subject 😭

[minor heron]

what exams do you take?

oh

[upbeat lava]

I’m taking gcse

[minor heron]

ouh icic

[upbeat lava]

I feel like multiple choice would be so free

Someone could theoretically get 100% without knowing any content

[minor heron]

Igs

[minor heron]

There’s some sat math questions that go like so x=(blank box to type number)

I mean if they guessed the number right lol

But

[upbeat lava]

Must you show working?

[slim plinth]

I take SAT

It’s a digital test with only math and English

On math section it’s just multiple choice and student produce response

Or it’s a box where you put ur ans

[upbeat lava]

Is that not super easy?

Every question we have requires you to show working with almost zero multiple choice

[minor heron]

no, its digital

[minor heron]

damn e.e

[upbeat lava]

Is English multiple choice? 😅

[minor heron]

yeah taking the sat is lucky ur right

[minor heron]

yeah..

[upbeat lava]

😭

Do you not have essays in America?

[queen juniper]

i believe there used to be an essay section on the sat

but it was removed cuz grading an essay isn't that easy i think

[minor heron]

yeah

[upbeat lava]

So you removed the only valuable metric in favor of efficiency 😭

[minor heron]

I mean igs state testing has essays

[queen juniper]

uhh search it up

i think there might be other reasons

[upbeat lava]

Maybe fake ones but that’s still ridiculous

[queen juniper]

hmmm

ye ig

[upbeat lava]

How do they test literature?

Like what would they ask you in a question about a book you studied?

[minor heron]

uhh

[queen juniper]

umm

[minor heron]

theres no books

like

[upbeat lava]

😭

[minor heron]

standardized books to test u on

[queen juniper]

the reading section is split into 2 sections

[minor heron]

the sat reading is like “heres two paragraphs” analyze and pick a b c or d

[queen juniper]

vocab and the reading & questions part

[minor heron]

and like grammar ones

[upbeat lava]

So you don’t need to memorise quotes for a given book

[minor heron]

yeah grammar/vocab and like analyzing and stuff

[upbeat lava]

You just have to be literate?

[queen juniper]

ye

wait what use is memorizing quotes tbh

[upbeat lava]

I mean to write essays to develop understanding of literature

But you’re in part right

[queen juniper]

u could use techniques from the writing ye

[upbeat lava]

Y’all definitely need to reform your education system though

[queen juniper]

hmm

[minor heron]

meh

[upbeat lava]

Yeah but you learn any given subject by applying

[minor heron]

I mean they look at grades and u have to write essays in english class

[upbeat lava]

But why when they don’t even test you on it?

Also what percent (roughly) is an A*

[minor heron]

90% and above

oh a* is like a+ right?

like…

97%+

[queen juniper]

a+ is 95+ i think?

[upbeat lava]

Yeah

[queen juniper]

maybe it differs

[upbeat lava]

So you have very high grade boundaries?

[minor heron]

i mean the sat doesnt twst u

like ap exams do

[upbeat lava]

So what’s it for then?

[minor heron]

like we habe an ap exam where u write 3 essays in random topics in 2 hours

[upbeat lava]

In conjunction with your normal classes?

[minor heron]

Likeee

instead of honors or regular

u can choose ap

[upbeat lava]

As in you have to take ap English with regular english?

[upbeat lava]

So you have a triple tier system?

[minor heron]

it replaces regular english if u take AP

[queen juniper]

aps are classes that are usually administered in college

[minor heron]

honors regular and AP at my school

[upbeat lava]

So you take calc in highschool?

[minor heron]

but u cant take the ap level of some courses till like 11th

[minor heron]

can… deoending on oathway

[queen juniper]

honors, g/t, reg, and ap i think for hs

[upbeat lava]

Also, is it true you can get held back a grade?

[minor heron]

yes

depending if u fail too much

like theres summer school but u can only make up so many classes

[upbeat lava]

So you can have 30 year old men stuck in the 6th grade?

[queen juniper]

uhh

[minor heron]

er

wellll

[queen juniper]

ig

[minor heron]

after ur 18 like

[queen juniper]

but why

[slim plinth]

But anyway

[minor heron]

u can js drop out

[slim plinth]

Taking SAT is like ABCD

[queen juniper]

i suck at sat reading 😭

[slim plinth]

Multiple choice

[slim plinth]

I got 400

[queen juniper]

ehh i have a lot of time

[upbeat lava]

I would love to take sat instead of gcse, icl

[minor heron]

Same..

[upbeat lava]

Is summer school like purgatory?

For failing?

[minor heron]

lmao u should fly to america take it then go back and apply

[upbeat lava]

Lmao

[minor heron]

u can take summer school like if u wanna get some required courses done with … or you may be forced into it if you fail

[upbeat lava]

I actually would as well 😭

[queen juniper]

i believe u can also take courses through summer to jump to a higher level in the next yr

[minor heron]

oh yeah like math

[upbeat lava]

I would lowkey do that for math

[minor heron]

bridge pathways and shi

[queen juniper]

i want to

[upbeat lava]

Recently, I’ve become obsessed

[minor heron]

my district has those

[queen juniper]

but my counselor keeps dodging my questions

[upbeat lava]

I be dreaming about math 😭

[minor heron]

my advice

[queen juniper]

math is fun

[minor heron]

is to find a diff counselor thats not assigned ti u

and beg them

[queen juniper]

hmmm

[minor heron]

to help you

(im serious btw ts is what i do cus my counselor is buns)

[queen juniper]

actually i might do that

[upbeat lava]

What’s a counsellor?

[queen juniper]

uhh

[minor heron]

uhhh its like a person at your school thats supposed to guide you and help u pick classes and help with mental helth and stuff

[queen juniper]

idk how to explain this

[upbeat lava]

You get therapists assigned to you by your school? 😭

[queen juniper]

usually there's only like 1 or 2

[minor heron]

errr kinda

[queen juniper]

but u can go talk to them if ur having mental health issues and such

[upbeat lava]

I’m actually fascinated

[minor heron]

my school has like 14 cus big school

[queen juniper]

hmmm

[minor heron]

my counselor mamages students from puente (profram) and koo-mah last name (quite specific)

[upbeat lava]

Do you have those Disney movie high school bullies?

[queen juniper]

[minor heron]

Idk i mean not really

[upbeat lava]

I swear I’m serious

😭

[queen juniper]

there are bullies

but not disney bullies

[minor heron]

but two minths ago in bio they made us sit thru a presentation on bullying and harrasement

but idk i never been bullied tho seen fights and stuff

[queen juniper]

they say hanging up posters is gonna make them stop smhw

[upbeat lava]

Do you get shoved into lockers if you’re getting bullied?

[queen juniper]

uhhh

no

[upbeat lava]

As in, is that something that’s ever happened?

[queen juniper]

friends might do that for fun ig

[minor heron]

not like seriously bullied, most bullyong is online/just fighting

we dont habe like wall to floor lockers anyway

only ones for backpacks

that u request

[upbeat lava]

Oh okay 👌

[slim plinth]

Do u know that we are also in a Spanish server

[upbeat lava]

ye

[slim plinth]

Let’s talk in tgere

[upbeat lava]

kk

[slim plinth]

Done

[cinder dagger]

Is geometry explaining why a square is a square

What do people even do in geometry?

[minor heron]

there's more to it than... proofs

also like

working with angles

volume

surface area

i think

my school doesn't have geo but im pretty sure its that stuff

[cinder dagger]

I have to prove why a square is a square?

That is like the dumbest thing ever

A square has FOUR sides

Bam thats a square

[fallow palm]

wdym explaining why a square is a square

[exotic yarrow]

A Mathematician's Lament enters the chat

[cinder dagger]

Idk

You have to literally explain why a square is a square

Thats a waste of time...

If you have two eyes you can clearly see its a square

Its sides meet each other a specific way

And they must be equal longness

[fallow palm]

yeah but there are non-square things with 4 sides

[cinder dagger]

Like what

[exotic yarrow]

I'm assuming you're American, in which case many people agree the two-column proof format is a bit overkill at times and also the claims that one is asked to prove with them are kinda boring (you can dig #math-pedagogy for examples of such discussions). Old things die hard ig. Things like Morley's trisector theorem are pretty cool tho.

[cinder dagger]

Holy wall of text

[marsh marlin]

What is the point of telling him this

He literally doesnt even know how to properly define a square yet

Showing him this merely causes more confusion

I get it you wanna flex ur knowledge but like..

[cinder dagger]

A square has equal langths and they must meet each other going straight directly

Thats like what a square is

[marsh marlin]

True

But theres so much more to a simple square

[cinder dagger]

Am i missing any unknown einstein explanation

[fallow palm]

oh look a thing with 4 sides, it must be a square

[fallow palm]

yes

[cinder dagger]

The sides have to be equal longness

[marsh marlin]

He said going through straightly aka ninety degrees

[cinder dagger]

And they must touch each other in a specific way

[fallow palm]

no

ok good you know geometry

yay

[cinder dagger]

Yay

[fallow palm]

what’s so difficult

[cinder dagger]

You know what i can skip geometry right now

[marsh marlin]

dude

[fallow palm]

why would you skip something you already know

[cinder dagger]

Because there is no point learning it now

[marsh marlin]

I learned walking

I still walk

Its good practice for my muscles

[cinder dagger]

Ok thats good smartness

[marsh marlin]

The analogy was ass

I just said the first thing that came to mind

[cinder dagger]

Who

[marsh marlin]

mine

[cinder dagger]

Whats analogy

[marsh marlin]

comparison between two different things in a way that highlights their similarity

[fallow palm]

@marsh marlin ooh you have MO tag

hi fellow MO tag person

[marsh marlin]

yah

Hii

[hybrid kestrel]

7.05 Quadrilaterals built from triangles | Level 8 Maths | Victorian Curriculum Year 8 - 2020 Edition | Mathspace
https://mathspace.co/textbooks/syllabuses/Syllabus-999/topics/Topic-19895/subtopics/Subtopic-263700/?activeTab=theory&activeLessonTab=content