geometry-and-trigonometry

[upper karma]

Oh lol

[drifting blade]

uh

[upper karma]

I has question that I need confirmation on::

Do the same trig identities apply for inverse trig functions?

My guess is no

[upper karma]

Absolutely no

Thought so.

My formula is giving me grief over the arccosine present so just wanted to know

Anyway thanks

[acoustic jungle]

@drifting blade the middle shape is probably an octagon by symmtry, from that, use coordinate geometry to determine one side of the octagon then find the area.

if you don't trust the fact it's probably an octagon, use coordinate geometry to find the intersections of all the lines then use shoelace formula.

[light osprey]

sohcahtoa yo

[noble heath]

It’s deceiving but I don’t think it’s a regular octagon — the angle the line y =1/2 x makes with the vertical is irrational, but in a regular octagon you’d expect 67.5 degrees

[upper karma]

How did they make the Sikorsky fly balanced? 360/7 ain’t pretty

Yet the rotors are perfectly balanced

And I mean the super stallion

[haughty birch]

hey guys

so we did some trigonometry is highschool but really basic stuff, now we are getting polar coordiantes and other stuff in linear algebra and they except us to know everything about trigonometry theorems identities etc

anyone can give me a tip how to learn them quick ?

[deep trail]

https://gyazo.com/9be090de873d1836643e583007f57605 what would the proof for this be, corresponding?

[upper karma]

So i subtract X2 by X1 and do the same with Y2 by Y1

Then

I get 7 and 2

Then i have to times them by themselves

I get 49 + 4

= 53

But how do answer the question cuz 53 is a prime number

?

@river forge i @ helpers for help?

[upper karma]

@upper karma do you know the distance formula

I figured it out

Thanks tho bro

Oh lol

[upper karma]

uh
@drifting blade is it Square ?

[astral maple]

why is sin(180-x) = sin(x)

unit circles

[next jackal]

@astral maple wait a min I'll show you the pictures

[astral maple]

ok

[next jackal]

Let me make them

Or you can use geogebra

Geometry

See for yourself

[astral maple]

ok

[dire sand]

Alternatively

Watch some videos on the subject

[astral maple]

Already

...

[dire sand]

I can find you a better video.

As a matter of fact

[astral maple]

In Vietnamese

not English

[dire sand]

and I don't mean this in a mean way

[astral maple]

Language barrier

[dire sand]

oh

that explains a lot lol

[astral maple]

Hm, wait

[astral maple]

sin(180-x) = sin180.cosx + sinx.cos180

lol

proven

[next jackal]

What is sin in triangle(ABD) and AB2E?

[astral maple]

there's no A or B or D @next jackal

I just see B1 B2 B3

Oh I saw D

I don't see A or B tho

[next jackal]

A is the centre

[astral maple]

Saw A

wheres b

[next jackal]

On the top left

B'2

Let's call it B2

[astral maple]

You mean B'?

oh

ok

ABD...

I don't know how to calculate sin,cos in not-square triangles

I haven't learnt

its 11th grade's stuff

[next jackal]

Then how are you learning trig multiplication without learning what sin, cos and tan are?

[astral maple]

idk

ask my education system

[next jackal]

ask my education system
Bruh you said you're self studying

[astral maple]

;-;

[next jackal]

Are you time constrained?

[astral maple]

im self-studying something that i'll learn in less than a month

so kinda

what does constrain mean

[next jackal]

Limit

Time limit

[astral maple]

no

i'm not time-limited

[next jackal]

Then why are you trying to learn it under a month?

[astral maple]

im just learning a bit about it

[next jackal]

@dire sand need a little help here

[astral maple]

im self-studying something that i'll learn at school in less than a month
@astral maple

[next jackal]

@astral maple I'd suggest you start with introduction

[astral maple]

You prob misunderstood me btw

[next jackal]

Okayy

Yeah I misunderstood

Start from beginning

[astral maple]

what's called beginning here is sin cos tan in square triangles

[next jackal]

Yes, and how they're related to unit circles

[astral maple]

idek lmfao

[dire sand]

https://www.youtube.com/watch?v=ILRrqghJzdE

It's english

But I think it may be easier to understand

https://www.youtube.com/watch?v=FRQNRr4BfnI

https://www.youtube.com/watch?v=0JcVsNiyPJ8

[next jackal]

Eddie woo is good

[astral maple]

Hope there's subtile

auto-generated

vote if i should trust google translate

[next jackal]

Probably yes, English transcription is good enough in YouTube

[astral maple]

ok

see ya in 6 mins

[dire sand]

Or just try to listen lol

[astral maple]

I'm back

The teacher - i don't like him

he talks so fast as if he's gonna die in under 10 minutes

[dire sand]

Then slow down the video lol

[astral maple]

@next jackal @dire sand Can you explan me this picture?

It's like, a circle on the lines of numbers or sth with radius of one

and-

idk

;-;

[dire sand]

Aight

So

let's go even more basic

[astral maple]

k

[dire sand]

keep that diagram in the back of your mind

[astral maple]

ok

[dire sand]

Can you define sin(theta), cos(theta) and tan(theta)

Based on the sides of a triangle

So for example, sin(theta) = opposite/hypotenuse

[astral maple]

$sin(theta) = \frac{that - - - line}{\text{the from O to cos(theta),sin(theta) thing}}$

[dire sand]

what

[somber coyote]

Moono:

[dire sand]

no

ok

[astral maple]

Lemme name them

[dire sand]

Use this to define sin(theta), cos(theta) and tan(theta)

[astral maple]

sin theta = AB / OA

[dire sand]

grrrrrrrr

[astral maple]

cos theta = OB / OA

tan theta = AB/OB

[dire sand]

sure

Now

If that's a unit circle

What is the value of the hypotenuse (OA in this case)

[astral maple]

r

[dire sand]

what

[astral maple]

R

radius

[dire sand]

Sure

What's the radius equal to?

[astral maple]

i don't know

[dire sand]

Aight

Remember this

[astral maple]

wait

1

messages not sending

reeee

[dire sand]

The unit circle is defined as the circle of radius 1

[astral maple]

i already said 1

[dire sand]

No.

You said r

then radius

[astral maple]

then 1

[dire sand]

kekw

[astral maple]

okio continue

plsss

sin theta = AB then?

Oh...

I see...

[dire sand]

Yes

And what is cos(theta) =?

[astral maple]

cos theta = OB as well...

[dire sand]

Sure

Now

Remember what you defined tan(theta) as?

[astral maple]

sin/cos

[dire sand]

kek

nice

[astral maple]

lol

[silk patio]

Conceptually it helps to think of cos as the base and sin as the height of the unit triangle

[astral maple]

so tan(theta) = OA/OB?

no?

[dire sand]

bruh

Yes

[silk patio]

No

[astral maple]

ok

[dire sand]

wait

why OA

[astral maple]

wait why oa

i meant ab

AB/OB

[dire sand]

Yeah

[silk patio]

cos = base, sin = height, tan = slope

[astral maple]

hm

so

what is slope

[silk patio]

The gradient of the line OA

[dire sand]

Gradient

[astral maple]

...

Calc? no?

[silk patio]

No basic algebra

[dire sand]

y = mx+c

[silk patio]

Equation of a line?

[dire sand]

m is the gradient

[astral maple]

just one person at oncep ls

ur doubling the confusion

[dire sand]

kekw

I'll leave this one to Euler

[silk patio]

I’m out

[astral maple]

gradient is how you express the line?

[silk patio]

All yours

[astral maple]

why do you name it gradient hto

tho

[dire sand]

I tapped out first.

[astral maple]

gradient is for drawing

reee

[silk patio]

It’s a word dude, it can have multiple meanings

[next jackal]

[astral maple]

ok

[silk patio]

Also I called it slope first if the word gradient doesn’t satisfy thy majesty

[astral maple]

ok

@dire sand come back please

[dire sand]

So what exactly don't you understand about the diagram?

[astral maple]

that joint

that position

[dire sand]

the point?

[dire sand]

Right

So

Let's think of a regular plane

[astral maple]

yay im on plane

[dire sand]

If I say the point is 4 to the left and 3 up

[astral maple]

flying to new york

i understand how the position works

[dire sand]

Right

[astral maple]

just why is it cos theta and sin theta

[dire sand]

So then If I'm cos(theta) to the right

and sin(theta) up

What will be the coordinate of my point?

[astral maple]

Hm

True

got it...

hmm

so that's it?

[silk patio]

The definition of cos(theta) is the base of the unit triangle with angle theta

[astral maple]

chuckles

[silk patio]

It’s coordinates have to be x=cos and y=sin

[astral maple]

I didn't ask

lol

so that's all the basics about trigo?

[dire sand]

beggars can't be choosers.

[astral maple]

ok

[dire sand]

No.

There's graphing trig functions

[astral maple]

hmm

like the plus stuff

double triple

[dire sand]

law of sines and cos rule

[astral maple]

hmmm

[dire sand]

Those two are for solving non-right angled triangles

[astral maple]

sin(a+b) = sina.cosb - sinb.cosa

no?

[dire sand]

nah

[astral maple]

that's the law of sin and cos?

[dire sand]

No.

[astral maple]

HMM

i heard of the law of sin cos thingie

for non-right triangles

a few times

[astral maple]

two years ago

[dire sand]

a/sinA = b/sinB = c/sinC

[astral maple]

hmm

that explains a lot of stuff

[dire sand]

Probably not relevant to you.

[astral maple]

so

[silk patio]

How can you almost remember the addition formula but not know basic trig

[dire sand]

xd

[astral maple]

almost?

👀

[silk patio]

Well you said it wrong

[astral maple]

• not -?

I messed up?

[silk patio]

You messed up

[astral maple]

Ye

messed with cos

[dire sand]

I have the suspicion that they have just "memorized" formulas

[silk patio]

It’s a serious question tho

[astral maple]

i've just learnt it today

yes

lol

a few hours ago

[silk patio]

Incorrectly remembering a formula isn’t the best learning technique

[astral maple]

specifically

[silk patio]

Specially if you don’t understand it in the first place

[astral maple]

remembering incorrectly isn't a learning technique

[silk patio]

Yeah so idk how you can say you learnt it

[dire sand]

Which is what confused me when they realized tan(theta) = sin(theta)/cos(theta) before tan(theta) = AB/OB

[astral maple]

what

i thought you wanted to refer to the sin and cos we wrote above

lol

so i told that first

said*

[dire sand]

so tan(theta) = OA/OB?

well

you meant AB/OB

but still

[astral maple]

i mistaken O being the square point

[dire sand]

my point stands

[astral maple]

because O is usually center and special

[silk patio]

The square point?

[astral maple]

the point that has the 90o

you see the obvious huge huge language barrier here

lol

[dire sand]

the origin?

[astral maple]

idk

[silk patio]

All points in an orthogonal basis have a right angle

Oh, that guy

[astral maple]

So let's say

Basic -> A little less basic

[silk patio]

I’m gonna use square point from now on till it becomes official

[astral maple]

I learnt a Little less basic

and i felt confused

so i came here to ask about basic

does that make sense?

[silk patio]

No

[astral maple]

there's no lesson about basic here

literally no

none in my language

i just search trigo in my language

so it appeared

and i clicked

that simple

[silk patio]

They skip straight to the addition rule yeah?

[dire sand]

lol

[astral maple]

The education system

Ask it

[silk patio]

Which education system should I be consulting

[astral maple]

There's a series of that teacher

teaching about

trigo

the part 1

teaches me addition rule

NO INTROO OR INTRODDUCTION

REEEEEEEEEEEEEEE

[dire sand]

Do you have access to a textbook?

[astral maple]

no

[upper karma]

any one could help me ?@!@

What have you tried so far

all of them bad methods

[dark sparrow]

what?

[silk patio]

These questions have nice symmetry

[upper karma]

hmm yah

What have you tried so far
@upper karma ive got it now

wts now guys ?

wt

[dark sparrow]

yeah i am curious how you did it

can you share the key idea

[upper karma]

i did it ?

not yet

[dark sparrow]

ive got it now

[upper karma]

im tryin to solve it

so...

[junior light]

Do you need hints to get started?

[upper karma]

yh why not

maybe ill use Ceva's Theorem

[junior light]

Okay, so geometry is certainly not my niche. Maybe someone else can give you a better hint.

[upper karma]

oh np

[junior light]

If I were to solve it, I'd drop a perpendicular from the interior point on to the side, solve to get the length of side, then use the formula to calculate area of equilateral triangle. It's inefficient, but bound to work I guess.

[upper karma]

i;ll try that

[dark sparrow]

hold on

i might have an idea

[upper karma]

wt is @!@

...

[silk patio]

The idea is to rotate the picture by 60 degrees to create an equilateral triangle

[dark sparrow]

i'm trying to work it out right now, smile.

[silk patio]

And also a triangle with all 3 sides

[upper karma]

i'm trying to work it out right now, smile.
@dark sparrow hmmmmmm

[dark sparrow]

what

[upper karma]

The idea is to rotate the picture by 60 degrees to create an equilateral triangle
@silk patio okay

[dark sparrow]

why are you "hmmmmm"ing me

[upper karma]

mistake should that qout to euler 2

i'm trying to work it out right now, smile.
@dark sparrow keep goin

[dire sand]

Isn't there a theorem that follows as a consequence of lami's theorem for these exact problems

[dark sparrow]

purple + green + blue = black triangle

the uncolored red triangles can be calculated directly

[silk patio]

There’s a better way to do it

Consider the red hexagon

[dark sparrow]

yeah what about it

[silk patio]

It’s area is twice the equilateral triangle

[dark sparrow]

yes that was my point

[silk patio]

Ahh, then we’re both big brain

[upper karma]

yes that was my point
@dark sparrow i did not get it @!@

[silk patio]

So then it’s just an application of Heron’s formula. Also what’s sexy about this is you can get it into a symmetric form

[dark sparrow]

this is not the entire solution

[upper karma]

ik

[silk patio]

Where a,b,c and L are all on equal footing

[dark sparrow]

just a diagram

[silk patio]

Something like 3(a^4+b^4+c^4+L^4)=(a^2+b^2+c^2+L^2)^2

[upper karma]

@dark sparrow @silk patio i did it xd

[dark sparrow]

congrats

[upper karma]

area = (35/4)sqrt3+3sqrt14

ezzzzzz

[silk patio]

If you guys got any more nice geometry problems ping them to me, this one was really nice

[upper karma]

@dark sparrow

@silk patio

[silk patio]

The pretty solution was to use Heron’s formula instead of trig

[upper karma]

law of cosines

i'll try to solve it by elementary method @@

wtihout trig method

thats the general case , have fun

@silk patio

@dark sparrow

[silk patio]

It’s nicer than that, try and show
(x^2+y^2+z^2+w^2)^2=
3(x^4+y^4+z^4+w^4)
Where w is the side length of the big triangle

[upper karma]

well okay

but idont have that side

w

[silk patio]

Label it w, prove it satisfies that equation

[upper karma]

i'll try it

[silk patio]

Using Ann’s method with the hexagon

[upper karma]

wt is Ann’s method

?

[upper karma]

try it , and have fun

@silk patio

[hot wind]

could someone help with this 🥺

number 1

[deep trail]

Can anyone send me a video explaining all the proofs to solve for angles or triangle congruencys or something. I wasn't really paying attention in class and missed out..

[hot wind]

my teacher has a website

he has videos explaining what he does

and teaching the whole class

uh do u have geometry?

[deep trail]

i hate videos teachers make beacuse they are always terrible and boring

[hot wind]

but this one makes everything kinda easy

[deep trail]

ok

[stray flax]

might sound dumb but -

i have to find x

[paper vale]

you didnt show the whole question bruh

[stray flax]

the question is find x

lol

[paper vale]

it seems like M is midpoint

[stray flax]

yes

it’s a line segment

[paper vale]

well u need to say that next time

[stray flax]

i did

i said i need to find x

[paper vale]

but anyway just equate them it's easy

[stray flax]

it says no exams, this is just a quiz

[paper vale]

i did
@stray flax no u didnt

[stray flax]

how do i equate them?

[paper vale]

=

[stray flax]

sorry i’m just a sophmore lol

[paper vale]

a sophomore??

[stray flax]

yea

[paper vale]

and u cant just put down a = ?

[stray flax]

wdym

i have to find the value of x

numerical

[paper vale]

well LM=MN

[stray flax]

right

i don’t know the distance of either

there’s no values given

[paper vale]

yes there is bruh

[stray flax]

other than 9x-11 and 3x+43

[paper vale]

😐

[stray flax]

dude i’m slow

[paper vale]

just equate them

[stray flax]

i literally have no idea what that means man

[paper vale]

do u know what equals means

[stray flax]

do i not have to find x to find LM?

OHHHH WAIT

your saying i should just say LM = 9x-11

[upper karma]

kane

[paper vale]

if u equate them, u can discern x and then infer the desired segment

[stray flax]

ok i get it

thank you, sorry i’m slow

[paper vale]

[stray flax]

bruh

[upper karma]

synergy, is this a quiz

[stray flax]

nearpod assignment

i’ve just spent 2 hours trying to find x when i didn’t have to i’m actually stupid

sorry

[upper karma]

first they say it's a quiz and now a assignment??....

yeah

[paper vale]

i’ve just spent 2 hours trying to find x when i didn’t have to i’m actually stupid

[upper karma]

<@&268886789983436800> https://discordapp.com/channels/268882317391429632/326138757474680852/751508687721463869 it says "quiz" on the pic

it looks very suspicious

@stray flax plz don't ask for help for exams

[paper vale]

so in that 2 hours did u really not think to just equate them

i think it is just called "nearpod assignment"

[stray flax]

i beg mercy

[paper vale]

not necessarily meaning that it is actually a test

[stray flax]

what kane said

[upper karma]

if it's false he's gonna say it; doesn't seem to be the case

[paper vale]

what did u do in those 2 hours

[stray flax]

watched every khan academy video on geometry probably

[upper karma]

and there's a DUE there...

^

[stray flax]

yes all assignments have due dates

[upper karma]

May you not help him kane?

it's against the rules

[stray flax]

nah don’t blame kane i’m sorry guys i’ll leave the server

peace out

[upper karma]

I'm not blaming him

[stray flax]

thanks kane

[paper vale]

yea it is usually a good idea to think about the question a bit before just watching yt or something

[upper karma]

thanks for your comprehension

thanks Scientifica for coming

thank you as well for reporting that

hope you get cured from the flu 😉

yes i did i have to remove that lmao.

[hot wind]

anyone wanna help me with geometry 🥺

[upper karma]

Sure

[hot wind]

oh yay

i need to find out the conjecture

[unborn bison]

do they mean the numbers like 2,4,6 or the sums like 2,6,12

[hot wind]

2 6 12 i believe

[unborn bison]

but this one used those odd numbers 1,3,5,7 @hot wind

[hot wind]

i’m confused

[unborn bison]

lol

i think youre right

since in this one they all would be even anyways

[hot wind]

i have no idea what ur saying 👁👄👁

[upper karma]

Which question is giving you problems?

[unborn bison]

The first one I posted

[hot wind]

8

OH

[unborn bison]

i just posted the second image to show the trend of this book

to use those numbers on the left, not the sums

[hot wind]

cloud , u need help too ?

[unborn bison]

yes

[hot wind]

ohhhhh

[upper karma]

Cloud please wait

[unborn bison]

oh ok

sorry I didn't know you were talking to him/her/other genders

[hot wind]

so um

help 🥺

[upper karma]

How does the question work

[hot wind]

what do u mean :/

like what’s the pattern ?

cuz that’s what i’m tryna figure out 🤧

[unborn bison]

is it the amount of letters between them

i think i know

[paper vale]

i cant read your question it is too blurry

[hot wind]

do u want me to take another pic B

[upper karma]

Just try all the possible answers

[hot wind]

?*

[unborn bison]

A, B, C, D, E , _F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z.

the ones highlighted would be the ones in congecture

[upper karma]

8

[hot wind]

still so confused

[paper vale]

ok what is actually going on here

cloud and shwishi are u still asking your questions

[hot wind]

i am

[unborn bison]

i'm trying to help skwishi

the letter thing I posted is his math

[hot wind]

i’m sending a better pic of it

[unborn bison]

thanks

i couldn't see it either

i'm 99% sure i figured out mine

[hot wind]

my assignments are do in an hour 🥺

[paper vale]

your what?

[hot wind]

work

[unborn bison]

you shouldn't wait until the deadline like tht

give yourself a few hours at minimum

[hot wind]

i did

i started working at

9:45

[paper vale]

lol i found a pattern

[hot wind]

rly ?!?

[paper vale]

so far all letters without a curl work

which means K would be next

[hot wind]

omg thank you

[unborn bison]

you are far from my timezone

it's only 16:01 her

here

[hot wind]

oh wow

also

[paper vale]

wait was that actually the answer they were looking for

[hot wind]

well i don’t know

That’s the first reasonable answer

but maybe not...

[paper vale]

these questions can have multiple interpretations, but this is one is definetely consistent

[hot wind]

mhm

what abt number 9

the one below it

[unborn bison]

that's what makes geometry interesting

😄

[paper vale]

oh i got it

sum of first n squares

so next one is 91

[hot wind]

omg i think you got that right

[unborn bison]

@paper vale is like having a supercomputer at your fingertips

[hot wind]

that was one of the answer choices

thank you sm

[unborn bison]

like a brand new CPU

[hot wind]

HONESTLYYYT

[paper vale]

lol

[unborn bison]

it's like Ryzen vs Intel

he just blows Intel away

[hot wind]

ONG 😍✨

BUT TY FOR THE HELP I RLY NEEDED IT ALSKJSC

[unborn bison]

back in the day the internet wasn't a thing

it's fun to be able to talk to people possibly around the world and hear from really intellegient people like @paper vale

lol

[paper vale]

[unborn bison]

asking to find a pattern here

guessing it would just be M,V,E,M,V,E

it just seems too obvious

[acoustic jungle]

V

[upper karma]

hey guys
if f(x) = 10
and then g(x) = f(x+10)
how would I write g(x) in an equation

could anybody help me with this?

[paper vale]

g(x)=10 also

[unborn bison]

how would i go about solving this

do i just do a line of fit and kinda estimate where it would be next?

[void moat]

@unborn bison so ur going to use correlations

it depends what u want to do

u can do the median median line

or meyer line

line of best fit would work, but it is very tedious

the best is the median median line because instead of taking the mean, u take the median so ur answer will be more accurate

for median line ur gonna need three groups

three groups for x, three groups for y

the 1st and 3rd group need to have the same amount of values

if u still need help just @ me

[placid moat]

someone can help me ?

[maiden vapor]

interesting

[paper vale]

ok i proved it @placid moat

ill send a pic from geogebra to make things clearer(we dont need the red or purple line here)

so first let HCF=x, so HGS=90-x/2 (due to isoscles triangle CGF)

then note that HAE=180-x (due to AEF =CFE=90, and quadrilateral CAEF sums to 360)

similary we have GHE=x/2 (again by isosceles AEH), therefore GHS=90 (as triangle GHS sums to 180)

[upper karma]

Hey broskis, anyone help me
In a regular hexagon ABCDEF, let M be a point on AC and N a point on CE such that angle ABM + angle AMN = 180°. Let AC have length 1, and suppose AM/AC=CN/CE=r. Find r

have you started drawing it?

Yeah

[midnight swan]

may i ask a question or do u still need help @upper karma

[upper karma]

Erm I am still stuck but I guess you can ask yours

[midnight swan]

i dont know how to help you sorry

[upper karma]

No prob dude, I'll sleep and dream about the solution 😔

[midnight swan]

gn 🙂

[mossy narwhal]

I don’t understand

[dark sparrow]

what don't you understand

[mossy narwhal]

Everything

[upper karma]

Erm

From the looks of the scribble, you got the idea

[mossy narwhal]

I actually got the “2” and “pi/2” from graphic calculator

[upper karma]

Oh

[dark sparrow]

bruh

[mossy narwhal]

But whats the equation u use to find the area

[dark sparrow]

this is a TRIANGLE

[upper karma]

Area of triangle..

[mossy narwhal]

From the looks of the scribble, you got the idea
@upper karma not my scribles

[dark sparrow]

there are many ways to find the area of a triangle

[mossy narwhal]

Oh yeah

[dark sparrow]

half base times height

[mossy narwhal]

0.5bh

[dark sparrow]

is the one that ended up being used here

...

bruh

[mossy narwhal]

Bruh I hate myself 😂

I swear idk

[dark sparrow]

why do you insist on like

desecrating the beautiful fraction 1/2

by writing it as the ugly 5/10

[mossy narwhal]

0.5 is 1/2 tho

When it comes to typing i like the decimal version

[midnight swan]

fractions > decimals

[dark sparrow]

i am not claiming 0.5 and 1/2 to be unequal

i am saying that writing 1/2 as 0.5 is just ugly

[mossy narwhal]

Thats to u😂

They are equal anyways so it doesnt matter

[upper karma]

Anyways for a graph that is in the form of f(x)=a sin bx,
Amplitude is a and period is 2π/b

[mossy narwhal]

You know I get more and more embarrassed as I ask

[dark sparrow]

if i wanted to give you half of a muffin, would you rather i cut it in two pieces and give you one
or would you rather i cut it in ten tiny pieces and then count off five of them for you?

[mossy narwhal]

Even tho i rarely ask

Usually they are stupid questions xD

if i wanted to give you half of a muffin, would you rather i cut it in two pieces and give you one
or would you rather i cut it in ten tiny pieces and then count off five of them for you?
@dark sparrow first

[dark sparrow]

yeah see

i think my point has been made

[mossy narwhal]

It does

Btw

From the previous question

He guessed correctly the height is 2 before using graphic calculator

[upper karma]

Anyways for a graph that is in the form of f(x)=a sin bx,
Amplitude is a and period is 2π/b

[dark sparrow]

the equation of the curve is y = 2sin(2x)

maybe you gotta know a thing or two about the sine function

such as

[upper karma]

Maximum value of sin2x is 1, so 2(1)=2

[mossy narwhal]

Oh the amplitude is height

[dark sparrow]

...yes

[mossy narwhal]

Ok thanks

[midnight swan]

i think i have got the radius, diameter and co ords for the centre of the circle but am stuck on how to get the equation for the line OA

hopefully my handwriting is readable

(not sure if its right)

<@&286206848099549185>

[idle bloom]

@midnight swan I don't feel like checking the work so let's assume that point is correct

How many points do you need for a line

How many points do you need for a line

[midnight swan]

2

[idle bloom]

Cool

You have one

Read the question again, it talks about another point

[midnight swan]

ah the origin

[idle bloom]

There ya go

[midnight swan]

so gradient is -4

then from there i can sub in values right to get the form y = mx +c

but i dont get the form ax +by = 0

[idle bloom]

Get the form in y = mx + b

And then rearrange it until you get ax + by = 0

Also

The slope is not -4

Change in y / change in x = slope

[midnight swan]

oh yeah my bad

-1/4

[idle bloom]

There ya go

So get into y = mx + b form

And then rearrange

[midnight swan]

oh yeah c = 0

x+4y = 0

correct. ty :))

[idle bloom]

👍

[midnight swan]

i got so close and just didnt see the obvious final part about the origin

😔

[rotund parrot]

138.230076758 is what to the nearest hundredth?

[upper karma]

What is your guess?

[rotund parrot]

138.20

[upper karma]

Correct

[rotund parrot]

Hm, I guess my math is wrong somewhere

I'm doing angular speed

[upper karma]

What for

[upper karma]

Wait

There's a missing 3

138.23

[rotund parrot]

I used all my attempts on that problem so let me come back to it

Can I see your work for that one?

[upper karma]

138.230076758 is what to the nearest hundredth?

138.23

You just forgot a 3

[rotund parrot]

Crap

Alright well that at least gives me confidence I'm doing the math correctly

Just need to pay attention to the rounding

[rotund parrot]

How do you get 22,340 in this example?

Nvm

[rose tulip]

What do the lines on the triangles signify?

I was thinking since we know each measurement. That that's what there there for.

[upper karma]

Equal lines on different sides mean congruent sides

[rose tulip]

and that too

So FE and CA are congruent?

[upper karma]

Yes

[normal heart]

hi, i want to know the shortest distance to travel when you have a point in 2d plane and a 2dline. How much should you move in (X,Y) so that the point get in line? (making it for game, programing c#)

[rose tulip]

If we know the measurements for every angles. Why don't we know that F=C

https://youtu.be/OIRZd5mDu_o

1:50

[paper vale]

if u know only AAA then it is simlar but you dont know the ratio of the lengths

[rose tulip]

So C can be anywhere on the outline of the circle?

I got confused when he started drawing the circle.

[paper vale]

do u know the definition of a circle

[rose tulip]

Nvm I got it

It could be at F or on the other curve

and Yes I know what the def of a circle is.

[supple wedge]

The lines $x=2$ and $y=3$ are tangents to a circle $C_1$.Given that that the centre of circle $C_1$ lies on the positive $x$ axis, find the equation of $C_1$.

ive got a feeling the x coordinate is 1

idk

[somber coyote]

Hmm:

[supple wedge]

ima try a big brain move brb

ok it didnt work

ima just wait

[tired terrace]

would anyone be down to vc and walk me thru this trig review that i do not remember at all

[dark sparrow]

if you're ok waiting like ten to fifteen minutes for me to get all set up for vc

then yeah i can

[supple wedge]

noo what about me

[dark sparrow]

@supple wedge the center of C_1 is of the form (x_1, 0) with x_1 > 0

the distance from (x_1, 0) to the line y=3 is always 3 therefore the radius of the circle is 3 therefore with the other tangent line you get |x_1 - 2| = 3 therefore x_1 = 5

therefore your circle has center (5,0) and radius 3

[supple wedge]

fuck thats big brain i tried to use some distance formula bs

[dark sparrow]

@tired terrace still here?

meet you in the 256kbps voice channel & #mathematics-voice

[tired terrace]

yes i am

[surreal vector]

Hello, I'm trying to find the min and max points on this function:
y=4x-tan(x)
I found that theres min and max points at (60,y) and (-60,y)

I put -60 and 60 in the original equation and get (60,238) (-60,-238)
when I convert it to radians (dividing by 180 and multiplying by pi) I get (π/3, 1.322π),(-π/3,-1.322π)

but in the answers it should be (π/3, 2.456), (-π/3,-2.456)

[silent plank]

using degrees in calculus is a very bad idea

you end up mixing radians with degrees in your calculations

[surreal vector]

im not learning calculus tho

But thats why I converted it to radians at the end

[silent plank]

you should be using radians throughout

in this case subbing in x = 60**°** into the equation gets you:

[surreal vector]

if I put n/3 instead of 60 in the original equation, I get 4.170

[silent plank]

you really need to check your units

tan(pi/3) and tan(60°) have the same numerical value and that is sqrt(3)

subbing x = 60° into the equation would get you
y = 240° - sqrt(3)
(the sqrt(3) isn't in degrees, those two terms don't have the same unit and you can't combine them directly)

[surreal vector]

I see

[silent plank]

im not learning calculus tho
this sounds like something that should be in a calculus course

[surreal vector]

Im just really not comfortable with radians

[silent plank]

it is quite questionable that you're getting this type of question

[surreal vector]

I'm doing a pre uni math course, we're studying trigonometric functions

[wild storm]

can someone tell me how to find the angle between the hour hand and the minute hand using two angles, the angle from the 12 mark to the hour hand, and the hour from the 12 mark to the minutes hand?

[upper karma]

Can you show the drawing?

[wild storm]

something sort of like this, find the hour between h and m using the angles from 12 and hours and 12 and minutes, I'm thinking you subtract the angle from 12 and hours and 12 and minutes and find the absolute value for the answer. but that does not work when you get numbers that get the bigger angles from 12 and hours and 12 and minutes. Like with the example s and p.

[paper vale]

it is really unclear what u are saying; is is that u are given the angle from 12 to both the hour hand and minute hand?

in which case all u do is just minus them

[wild storm]

I figured it out nvm thanks for offering to help

I need help with this new problem though: so given a diameter, I was able to find the formula for the area of a slice of a circle. Now given a new larger diameter, I have to figure out a formula that would solve the new angle between hour hand and the minute hand given this new larger diameter so that the area of the slice of the circle remains the same

[upper karma]

How do i find the value for d (phase shift)?

[paper vale]

the proper term is sector btw. just use (theta/360)pi*r^2

[wild storm]

thanks

[paper vale]

do u know about that?

[wild storm]

no I don't

[paper vale]

so pr^2 is of course the area of the full circle, and the theta is the angle between the two radii which make the sector

and theta/360 is a ratio of the sector's area to the full circle

[wild storm]

ok got it so to find the new angle you have to use the old angle from the old diameter

[paper vale]

well you need to work out the area of the old one, then set that expression with the new radius equal to that area

then u can solve for theta

[wild storm]

ok so set the expression of the old sector, with the new radius. is this another seperate formula to find theta first?

[paper vale]

so do u already know the area of the sector

[wild storm]

yes

[paper vale]

then the old circle is redundent

[wild storm]

with the old radius

[paper vale]

yea so the old circle doesnt matter any more, all that matters is the area

[wild storm]

alright

[paper vale]

just equate that area to the formula i told u about

solve for theta

[wild storm]

so treat the area as theta?

[paper vale]

no that is not what i said

we are solving for theta, i.e the angle between the two radii of the sector

[wild storm]

ohh ok

so treat the old angle as theta

so to solve for the new theta: plug in the old theta into the formula

from the old radius

[wild storm]

thanks for giving me the formula @paper vale

[wild storm]

So what is the value of theta in the formula to find the new theta with the larger radius? Sorry If I’m starting to get annoying Im just a bit confused

[acoustic jungle]

what is question

[normal heart]

Hi, im sorry if this is stupid question, have been a while since I studied math.
I want the direction of the vector CB where C is perpendicular to point B.
I know the length and derection of AC and AB and angel bettween AC-AB
I also know the cordinate of A(x,y) and C(x,y)

[upper karma]

Can you post the statement of the problem?

[normal heart]

there is no statement, i dont even know if there is a solution with the given information

[wild storm]

I need help with this new problem though: so given a diameter, I was able to find the formula for the area of a slice of a circle. Now given a new larger diameter, I have to figure out a formula that would solve the new angle between hour hand and the minute hand given this new larger diameter so that the area of the slice of the circle remains the same @acoustic jungle

[acoustic jungle]

well set the area of the slices equal to each other to find the other angle

and note that each minute is 6 degrees

and each hour tick is 12 minutes

12 minutes is 6 degrees for the hour hand, or 1/2 degree per minute for hour hand

so the minute hand is moving at 5.5 degrees per minute relative to hour hand

[tropic tide]

How do you find OR

[silent plank]

consider the radii of sector OPQ

[tropic tide]

O

Damn ok thanks

[unborn bison]

@void moat or you can plot line of best fit on a calculator

thanks for the explanation

[lapis knoll]

How to find the length of x?

[silent plank]

secant-secant theorem

[lapis knoll]

Thanks

[lapis knoll]

AB = BC = CD
Find angleACD
Can’t solve...

[upper karma]

A lot of isosceles triangles

For example triangles EBC and EAB

@lapis knoll

Consider triangles EBC then DBC

👻

[upper karma]

Bruh :(

[lapis knoll]

@upper karma Wow haha thanks got it

Again find x

[paper vale]

x=70

first because BCA=110, as any angle subtended by its arc=140/2, and opposite angles in cyclic quad sum to 180

also BDA=40 by same reason

and obviously ACD=70, triangle CAD sums to 180 and now u can get x

[lapis knoll]

Sorry but I can’t understand...

How you got BDA?

[paper vale]

well u know that arc BA subtends same angle everywhere, and it is half that of angle subtended from it to the centre which is 140

BOAD is a cyclic quadrilateral

and opposite sum to 180

[lapis knoll]

Oh I get it, didn’t notice thanks

[valid holly]

how do u know O is centre tho?

i mean obv O is usually used for centre

but it doesn’t say

[paper vale]

well O is used for the centre

[lapis knoll]

It’s got state

[upper karma]

Are the 2's exponents here ?

No

They used double angle formula

[upper karma]

jeez

semester is not off to a good start

lol

[frail tapir]

anyone here good at factoring polynomial equations?

[cosmic pebble]

From

#❓how-to-get-help

Rule 1

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

[upper karma]

@frail tapir

I really don'tt get what's happening here

sin(A+B) = sinAcosB + sinBcosA

cos(A+B) = cosAcosB-sinAsinB

Does each cos become sinAcosB + sinBcosA and same for sin ?

[dark sparrow]

no, they are literally just expanding the square

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

[somber coyote]

Ann:

[upper karma]

Ah lol

Thank you

What about the i ?

It becomes -1 ?

[dark sparrow]

what do you mean

you're overthinking it again

$(\cos(\theta) + i \sin(\theta))^2 = [\cos(\theta)]^2 + [i \sin(\theta)]^2 + 2[\cos(\theta)][i \sin(\theta)]$

[somber coyote]

Ann:

[upper karma]

Right, so in [i * sin(theta)]^2

The i has exponent 2, so it becomes -1 * sin(theta)

[dark sparrow]

what a complicated way of saying i^2 = -1 lol

[upper karma]

fair lol thanks

[upper karma]

I'm dumb but I don't get this part still

What happens to the cos^2 and sin^2

[paper vale]

do u know the double angle formulas

[fresh pike]

can someone explain to me what's the differnet between DEDUCTIVE reasoning and INDUCTIVE reasoning in lamen's terms? im kinda dumb so

[upper karma]

deductive reasoning means "founded on logic" while inductive usually means, it sounds like it will be true based on these examples so we will say it's true

here is an example
proposition: the sum of any 2 odd numbers is even
inductive reasoning "proof": I have tested it on 20 different odd number combinations and it held for all of them, so it's gotta be true
deductive reasoning proof: Suppose we have two odd numbers, call them a and b. Then by the definition of odd, we can put a=2m+1 and b=2n+1 for some integers m and n. Then their sum, a+b, equals 2m+2n+2. Then we can factor out a 2 and write a+b=2(m+n+1). Since m+n+1 is an integer, we have expressed a+b as 2 times some integer, which means a+b is even. Hence we have shown the result is true for any odd numbers.

inductive reasoning is not really a thing in math

[earnest echo]

Adding to what Botnuke said,
In Inductive reasoning we start from a special case and then generalise it
In deductive reasoning we use general case to prove the special case, in other words deduce(hence the name)

[upper karma]

also I might add, inductive reasoning is not to be confused with mathematical induction, which is a valid deductive method that you might stumble upon if you look into this stuff more

[earnest echo]

That was a very important disclaimer

[upper karma]

does this all make sense @fresh pike

the wiki pages look pretty good too https://en.wikipedia.org/wiki/Inductive_reasoning https://en.wikipedia.org/wiki/Deductive_reasoning

[upper karma]

Can someone help me solve this? Basically the area of the red part is equal to pi*a cm^2 and i need to write the side of the square in function of the a

Have you tried anything?

Yes, i did

But couldn t get the answer i was supposed to get, if u want i can send it here

Yeah do so

,rccw

[upper karma]

R is equal to 1/2 of the square side

Also the "supposed answer" if you can post it, do so

R is equal to 1/2 of the square side
Is that the book's ans? Or what?

Its 2* square root of a

But yeah it says that the square is inside the circle

So the diameter of the circle is equal to the side of the square

I'm deeply confused by what you are saying, are you giving out your thoughts?

Its 2* square root of a
@upper karma also is that the book's answer?

Yes it is the answer of the book

Yes to what

Oh okay

And, that is what is written in the question

"But yeah it says that the square is inside the circle,So the diameter of the circle is equal to the side of the square"

Wait did the question have that info you didn't gave initially

"But yeah it says that the square is inside the circle,So the diameter of the circle is equal to the side of the square"

Yes it does have the info i just forgot to mention it as i though it was easy to understand from the picture it self

Yeah

Okay wait

[acoustic jungle]

the area of white circle has radius s/2

radius of big circle has radius s*sqrt2/2

then subtract.

where s is the length of square

[upper karma]

Wait, but how did u get the sqrt of 2?

[acoustic jungle]

pythagorous theorem

[upper karma]

I mean, with ur method what we re trynna find is the value of a right?

Or am i just being dumb

,rccw

[upper karma]

s=2*sqrt a, i think this is maybe what i needed to do?

[upper karma]

@upper karma okay ig i'll go with my method

You there?

Yeah

Okay my method starts with:
Let r be the radius of the big circle
Let l be the length of the square

And a little bit of knowledge of areas $\ A_{\text{red thing}}=A_{\text{total area of the big circle}}-A_{\text{area of the small white circle}}$

[somber coyote]

Al𝟛dium:

[upper karma]

So far so good? @upper karma

Yeah

Okay

$aπ=πr²-π(\frac{l}{2})²$

[somber coyote]

Al𝟛dium:

[upper karma]

Know why?