geometry-and-trigonometry

[weak shoal]

No. It's just that it requires work with sets. You can't talk about domains and codomains without talking about sets.

[lofty scaffold]

Ik sets

I love sets

I belong to the set of complex humans

[weak shoal]

Yes, hunans

[marble topaz]

What rokabe is talking about is when trig gets fun

[grim halo]

does this type of geometry ever get used except trig?

I have never used it tbh

in like any of my classes

[marble topaz]

Yes

To an incredible degree

[lofty scaffold]

Wait

[grim halo]

is it like way higher level math?

[marble topaz]

It's hella important in tons of fields

[lofty scaffold]

Can you guys check if I properly derived formulas

Brb

[weak shoal]

You'll learn it almost right after you learn about sets & functions in more detail.

[marble topaz]

Higher maths, applied sciences, applications, trig and trig functions show up everywhere

[weak shoal]

Anyways, it's not the geometry that's super important. It's the concept of a function that is more general.

[lofty scaffold]

$\tan\alpha =\frac{\sin\alpha}{\cos\alpha}$

[somber coyote]

PristineWolf:

[grim halo]

well yea trig, but I have yet to use concepts such as triangle similarity

[lofty scaffold]

$\sin\alpha=\cos\alpha\cdot\tan\alpha$

[somber coyote]

PristineWolf:

[weak shoal]

You'll use similarity in calculus

[grim halo]

oh cool

[weak shoal]

Since calculus, as it is taught normally, is mostly geometric

[marble topaz]

Yeah that's valid @lofty scaffold

[lofty scaffold]

$\cos\alpha=\frac{\sin\alpha}{\tan\alpha}$

[marble topaz]

You can play with all the trig identities algebraically like this

[somber coyote]

PristineWolf:

[weak shoal]

Inb4 alpha = 90

[lofty scaffold]

Inb4?

[marble topaz]

Okay in that case it's wrong lol

[grim halo]

yea

sin90/cos90=1/0

[marble topaz]

But assuming theta is just theta its oke

[lofty scaffold]

Ahh

No we won't

[grim halo]

can all trig identities be derived from tangent?

[lofty scaffold]

For this year teacher said only acute angles no 0° no 90°

[marble topaz]

All trig identities can be derived from other identities

[weak shoal]

What's an actute angle?

[marble topaz]

It can get

very hairy

But it's doable

[grim halo]

probably

[lofty scaffold]

So my formulas are right?

[marble topaz]

Yes

[lofty scaffold]

@weak shoal an angle less than 90°

[marble topaz]

There's cooler formulas you'll learn later too

[lofty scaffold]

By definition, I read it in Euclid's Book

[weak shoal]

Oh cool, thanks

[marble topaz]

He's memeing on your spelling

I think

never know with vats

[lofty scaffold]

Ah lmao didn't see it

[grim halo]

why no 0 degrees?

[lofty scaffold]

Vats, I'll meme a surprise limit

[marble topaz]

0 and 90 cause interesting things to happen

[weak shoal]

No u

[marble topaz]

Depending on the trig function you're working with

So the teach is probably avoiding that

[lofty scaffold]

Vats what did it feel like for Rokabe to get rekt by 14yo

[grim halo]

lol my geometry teacher was quite interesting to say the least

[marble topaz]

By interesting I really just mean "it might be undefined"

[lofty scaffold]

Vats I have a new limit

I can express your IQ using infinity

Look

[grim halo]

he taught us radians

it was weird af and no one understood it

[marble topaz]

Radians are very important and they'll never go away

[grim halo]

yea but in geometry its confusing

[lofty scaffold]

Vats IQ$= \lim_{x→∞}\frac {x^\frac{1}{x}}{x} = 0$

[grim halo]

it was a summer class so thats probably why

[weak shoal]

Oh shit rekt

I got pranked

[marble topaz]

Prank

[lofty scaffold]

Wtf

[weak shoal]

I love your latex skills

They're so crappy

Prank

Relax

Memes

Chill

[grim halo]

my teacher got mad at me for not using limits for end behavior statements

[somber coyote]

PristineWolf:

[marble topaz]

That's a new one

[grim halo]

she said "you're an e v o l v i n g math student, no more baby stuff"

[marble topaz]

Well if that's the case did she make you define limits in terms of epsilon-delta

[grim halo]

no

[marble topaz]

IDK what her deal was then lmao

[grim halo]

we're doing a whole unit on graph features

and I already hate it

[marble topaz]

Ohh you hate it now but it'll be a huge boon in higher courses

It's very nice to be able to look at a function and have an idea of what it'll look like without any extra work

[grim halo]

i just hate looking at piecewise graphs

[marble topaz]

Pff

[weak shoal]

Why? You can use them for many interesting things

[grim halo]

and like having to write every little thing down about it

[marble topaz]

Implying I need a piecewise function to make phallic graphs

You underestimate my power

[grim halo]

yea we did a whole unit on piecewises

but like I just hate it cause its mostly review

like finding absolute extrema, or intervals of increasing

[marble topaz]

You'll see those again in calc

Turns out knowing absolute extrema is pretty helpful

[grim halo]

I guess

idk just seems like a lot of things we do in class is kinda useless, but maybe Im just totally ignorant on whats to come

[marble topaz]

I understand that feeling

[grim halo]

we had one extension that felt extremely useless

[marble topaz]

Later on you'll appreciate it, but learning stuff in a vacuum always has this feeling of "why bother??"

[grim halo]

it was like find f(g(f'(g(g'(f(f''(g))))))

[marble topaz]

Are you using 'for inverse or for prime

[grim halo]

inverse

[marble topaz]

Okay

[dark sparrow]

[marble topaz]

I was about to be like "Christ"

[weak shoal]

Welfare, it's just your bread and butter stuff. You gotta do all of that before you get to the cutting edge stuff.

If it makes you feel better, everyone here had to do it lol

[marble topaz]

It's a rite of passage!

🦈💥🔫

[grim halo]

i guess one pro of it is my algebra skills have like improved a lot

[lofty scaffold]

$\sin 30 = \frac 12 \sin 60$

[somber coyote]

PristineWolf:

[lofty scaffold]

That's not valid right?

[dark sparrow]

of course not

unless you somehow insist that sqrt(3)/4 = 1/2

[weary drift]

another thing, if you exclude the degree symbol, i'm reading the left side as sin(30 rad)

[upper karma]

This Rokabe guy..... nerd

[tawdry pivot]

,calc sin(30)-1/2*sin(60)

[somber coyote]

Result:

-0.83562631354175

[weary drift]

who's Rokabe

[deft ingot]

rudy is nerd also

[floral harbor]

I need Proof of pythagorean theorem

[dark sparrow]

there are many

look up "pythagorean theorem" in wikipedia

you'll get like a dozen different proofs

@floral harbor

[tardy junco]

How do I show that this is a hyperbola

(previous img was wrong)

[upper karma]

Hello

Can someone help me

Why does sine work?

Why can we say that the ratio of opposite to hypotenuse is the same for any two congruent angles between 0 and 90 degrees?

[flat spruce]

https://images.app.goo.gl/XxP1ipVL1q3LJeFK7

[dark sparrow]

@upper karma tl;dr similar triangles

[upper karma]

What do you mean

similar triangles

welel sureee

aa works

[upper karma]

@dark sparrow what do you mean by similar trianglee, how doees similar triangle help us prove that any two congrueent angles between 0 and 90 degrees are same

sorry for the tag if you don't like getting tagged

[dark sparrow]

two triangles are similar whenever their angles match

and two triangles being similar means the ratios of their corresponding sides are the same

[upper karma]

right

Ohhh

I see

But

Why can wee say that ratio of oppo and hypo is same with two congruent angle

is it because theeir have the corresponding sides?

[dark sparrow]

...yes

i mean

if your TRIANGLES are CONGRUENT

their corresponding sides match up

so of course the ratios do too

[upper karma]

Right

[blazing basalt]

Which quadrant is -pi/4 (clockwise) located?

[weary drift]

-pi/2 or -2pi/4 is right between quad 3 & 4

[blazing basalt]

okay cool

[rain oracle]

Why cos(π)=-1

[dire rampart]

why not

[rain oracle]

😄

[quiet mason]

cos(pi)=cos(2*pi/2)=1-2sin^2(pi/2)=-1

[mossy shoal]

but why

[wind heart]

Is this 5.4

Is 13) 29.2 and is 14) 34.7?

Is 17) WZ = 24 and UZ = 19.2

[silent plank]

9 is wrong.
also don't round

didn't check 17 yet

(and its also wrong)

[wind heart]

Oh

Uhhhh

How tho

[silent plank]

show your work

[wind heart]

Ok

[silent plank]

mistake in the very first line

24 and 20 aren't the side lengths of your 2nd triangle

[wind heart]

I’m confused

Is it 4x - 6 = 24

4x - 26*

[silent plank]

wait 1 sec

[wind heart]

I got 12. 5 now

[silent plank]

what you want is something like:

$\frac{4x-6}{(4x - 6) + 24} = \frac{3x-2}{ (3x-2) + 20}$

[somber coyote]

ramonov:

[wind heart]

Ohhhhh were doing that thing

I thought you didn’t need that like

When you have the parallel things

And are only doing the outsides

[silent plank]

you're applying the properties of similar triangles

the side AM = 4x-6 of the smaller triangle corresponds to
the side AB = 4x -6 +24 of the bigger triangle

similar for AN and AC

[wind heart]

I thought like

Since it’s parelel

There’s a short cut

[silent plank]

as for 17, first identify the similar triangles
which allows to conclude something special about triangle WYZ
which then allows you to apply something starting with ||p||

and to reinforce that comment about rounding:
$\frac{104}{3} \neq 34.7$

[somber coyote]

ramonov:

[silent plank]

wait 1 sec, it does work; been a while

fml

sry about that

yeh, mistake was you used 4x - 26 instead of 4x-6

solving:
$$\frac{4x-6}{24} = \frac{3x-2}{20}$$
should be fine

[somber coyote]

ramonov:

[wind heart]

Oh, thanks

Dw it’s all good my teacher himself makes mistakes all the time

For this,

Why would I put 46+n as the numerator?

Like, why does n have to be the bottom

[drowsy walrus]

proportion isn't set up right i don't think

should be 36 over 46.8-n equals 42 over n

[drifting lava]

if i send my hw here can u guys do it for me

im a female

ok bull dinky he is a guy

[mossy shoal]

ahahahaha

ok daddy

[drifting lava]

hiii😉

no but like deadass can some one hel me

[drowsy walrus]

we can help you

but we are not going to do your homework for you

[drifting lava]

but whhhyyyy not

[drowsy walrus]

because that goes against the server rules

[drifting lava]

rules smules

[drowsy walrus]

you are welcome to send your assignment and specify what you need help on

but we can't do the assignment for you as that is your responsibility

[paper mauve]

No paying for hw.

It sucks ik. I’ve tried many times trying to convince otherwise

[umbral snow]

They didn't offer to pay lol

Just "do it because I'm female"

[paper mauve]

Ohhh

Didn’t read it fully I just saw the report

[crisp phoenix]

guys

can someone please solve this for me

[umbral snow]

You'll want to set up a Pythagorean Theorem in each of the two triangles

[crisp phoenix]

ok look i did this

did i do this correctly?

?

[umbral snow]

Ya

[crisp phoenix]

ok

[umbral snow]

The line "144-100 = 44" is strange. I get you're trying to show how you rearranged that equation, but you'll be a bit cleaner if you write the next line as
x² = 144 - 100
instead

Do rearrangements mentally imo

[limpid vector]

can someone help with my homework

plz

its so ahrd

[umbral snow]

Otherwise your work is very clean @crisp phoenix

[crisp phoenix]

ok, i have a lot more questions so be prepared lmao

[umbral snow]

Sounds good!

[drowsy walrus]

@limpid vector just send it

[limpid vector]

Its online homework

i have to get to 90%

im on 20%

I have to like screenshare

[drowsy walrus]

do you think you can take a screenshot?

snipping tool on windows 10 or smthn

[limpid vector]

\

@drowsy walrus

[drowsy walrus]

find the total area of the circle

[limpid vector]

180

right

?

[drowsy walrus]

nope

it should be a value in terms of pi

[limpid vector]

3.14 then
?

i got it wrong

it was 25/2

Idk ho

[drowsy walrus]

what is the formula for finding the area of a circle

[limpid vector]

A= pie r to the 2nd

[drowsy walrus]

yes

and the radius in this problem is 5

so plug in 5 for r

[upper karma]

What effects tension of a cord between 2 masses on an inclined plane? Coefficient, the angle, or the masses?

[spice ridge]

could someone help me with this?

math is the bane of my existence

[crisp phoenix]

guys i need help with one question please

ill be eternally grateful if someone could help me find the answers

[winged zinc]

@crisp phoenix

[crisp phoenix]

ye

[winged zinc]

This is fairly simple

[crisp phoenix]

ok

[winged zinc]

There are a few ways to go about it

[crisp phoenix]

ok

[winged zinc]

But how I would do it is by the following

Do you know about SOHCAHTOA?

[crisp phoenix]

yeh

sin cos and tan

[winged zinc]

Yep

So since we have two side lengths we can use the inverse trigonometric functions to determine the angles within the triangle

Because we know that the triangle is a right angled triangle.

[crisp phoenix]

ye

ok i can do that

tysm

[winged zinc]

All good

Let me know how you go.

[crisp phoenix]

ok

[winged zinc]

Also, you know that if one of the angles aren't 30, 45 or 60, it belongs to neither triangle because a 180 in a triangle, 90 degrees from the right angle, therefore 90 for the other two angles, so if one angle is 60 degrees, the other has to be 30, but say one is 15, the has to be 75.

If that makes sense.

[crisp phoenix]

not rlly but loo

look

heres what i came up with, is this correct @winged zinc ?

@winged zinc hello?

[sonic perch]

How does Sin work? I know its the opposite side divided by the hypotenuse, but how does the sin button on calculator get that ratio from an angle

[crisp phoenix]

wym

when you solve for an angle you use the inverse of sin (sin-1)

[winged zinc]

Flexify

[crisp phoenix]

yesir

[winged zinc]

Do you know about inverse trig functions?

[crisp phoenix]

yeh

[winged zinc]

So you know that since sin(X)=o/h

[crisp phoenix]

yeah

[winged zinc]

Then X =sin^-1(o/h)

[crisp phoenix]

yeah

u have to switch it

when u put it in the calculator

[winged zinc]

So you know the hypotenuse is 2

[crisp phoenix]

yeg

yeh

[winged zinc]

So you take one of the side lengths, say 1, and do sin^-1(1/2)

[crisp phoenix]

yeah

[winged zinc]

And that is an angle

Is that result either 30, 45 or 60?

[crisp phoenix]

yeha

the angles are given for the triangles

[winged zinc]

What does it evaluate to? Should be 60 degrees.

[crisp phoenix]

i think so, im not sure

[winged zinc]

Do it on your calculator

[crisp phoenix]

ok

i have it set to degrees so

not radian

[sonic perch]

My point is not getting the value of an angle using sides

[crisp phoenix]

its 30 @winged zinc

[sonic perch]

My point is, when you do sin(90) for instance, how does it give you 1

Or sin(56(

How does sin function work

[crisp phoenix]

i understand that each triangle is 180 degrees alltogether

i dont get ur question

[sonic perch]

When you press sin on your calculator and put 56 as the input

What does your calculator do to get the ratio of opposite over hypotenuse

[crisp phoenix]

ohhh

[sonic perch]

Especially since it doesn't know any of the sides

[crisp phoenix]

i just press 2nd

[sonic perch]

I don't mean what you do

I mean what the calculator does to calculate sin(51)

[winged zinc]

@sonic perch

[crisp phoenix]

look

https://nj.testnav.com/client/index.html#login?username=LGN415881023&password=GTCWK5S6 this is the calculator i use

[winged zinc]

I do agree with you learning about what trig functions and ratios are

But I think it is first best to learn about how to simply use them

[crisp phoenix]

i know that In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

[sonic perch]

Mate I'm in Calc AB

I know fully well how to use them

I want to understand them now

[winged zinc]

Ohh wait

I thought you were prompting flexify to learn exactly what they are, no?

[sonic perch]

No

I mean how they worm

Work

You normally find the sin of an angle by taking the ratio of the opposite side of a right triangle over the hypotenuse of said right triangle

But calculators simply have a degree or radian as input

How do they figure out that ratio with that simple information?

Is there a formula or equation that allows you to get the ratio of an angle from just that angle

[languid ingot]

yeah

obv

[sonic perch]

There most definitely is, otherwise calculators would be pulling this scheisse out of its behind

[crisp phoenix]

@sonic perch in retrospect, trig functions just compress basic theorems to do things quicker

they arent very complex

[winged zinc]

Yeah, there is

[sonic perch]

I want to know what that is

[winged zinc]

But it isn't as simple as you think

See, if we draw a circle of radius one

[crisp phoenix]

@sonic perch read away https://en.wikipedia.org/wiki/Trigonometric_functions

[winged zinc]

That

[sonic perch]

Ok we have a unit circle

What now

[winged zinc]

Ok, let me try and explain this now

So we have a unit circle

And if we draw a radius with some angle theta between the positive x axis and the radius going in a counter clock wise direction

The position of where the line touches the circle is the coordinate (cos(theta), sin(theta)) - this is if the circle is centred at (0,0).

@sonic perch

[sonic perch]

Yeah I know that much already

And because of the right triangle formed by angle theta with the hypotenuse being the radius

Then cos^2+sin^2 = 1

As it should as the circle has the equation x^2 + y^2 = 1, and every point on its graph should be 1 away from center

Ok what next

[upper karma]

Can someone give me the answer to this please ????A spring is attached to the ceiling and pulled 20 cm down from equilibrium and released. The amplitude decreases by 5% each second. The spring oscillates 9 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t.?

[winged zinc]

@sonic perch There is no simple formula you can use

There is an infinite series that converges to the correct value.

@upper karma

Are you saying the spring's amplitude of oscillation reduces exponentially or linearly?

[sonic perch]

Thank you

[winged zinc]

There is one for cosine and tangent - along with other things like e^x

Have a look at taylor series.

[winged zinc]

Hmm

Doesn't say

Because it could say be an amp of 20 at t=0

Then amp of 19 at t=1, and then at t=2 have an amp of 19*0.95

Or it could be 20, 19, 18, ...

But anyway, the position of the end of the spring is going to be modelled by either a cosine or sine curve

Let us use a cosine because it has a max at 0 when there is no horizontal translation

Now we know that it will be in the form of Acos(bx)+c

Calculating b is simple enough

T=2pi/b

where T is the period

Period is the time divided by the number of oscillations

As for c

We are going to make it such that y=0 is when the spring is in the equilibrium position

And so we don't need to worry about the c value

As for A

It is difficult

It could either be an exponential or as a linear function

@upper karma

[upper karma]

i think its linear because the next question asks exponential

[winged zinc]

Ok

So we some function of time that describes the sequence, (20, 19, 18, ...)

What do you think that is?

[upper karma]

is it just -1

[winged zinc]

Expression please

[upper karma]

-20cos(pi/4)

idek💀

[winged zinc]

Haha

[upper karma]

im so bad at this 💀

[winged zinc]

All good

My bad, we were given a different problem

6, 4.8, 3.6,...

[upper karma]

and its due in 12 minutes 😫

[winged zinc]

Is the amplitude at t=0, t=1, ...

And that is described by the equation 6(1-0.2t)

So our final equation is 6(1-0.2t)cos(n2pit)

Where n is the number of oscillations a second

and we were told 8

So D=6(1-0.2t)cos(2nt*pi)

Should be the equation you are looking for.

[upper karma]

This is what its saying

says a variable issue

[winged zinc]

Ohh, whoops

Was meant to sub in n=8

[upper karma]

oh okay

[winged zinc]

D=6(1-0.2t)cos(16t*pi)

Should be correct

Hopefully

[upper karma]

says it was wrong

[winged zinc]

Well then I'm not sure sorry

[upper karma]

its okay

i appreciate the help tho ☺️

[winged zinc]

Can the spring go 'above' the equilibrium?

[upper karma]

it says below

[winged zinc]

Yeah, but spring typically exhibit harmonic motion. so they go below then above, then below and so fourth

[upper karma]

what would it be if it was above

[winged zinc]

It should be described by that equation

Are you meant to answer only with sine or something? Anything about how answers should be expressed?

That equation should describe the harmonic motion of a spring

[upper karma]

it just says find an equation

its okay tho the due date time just passed

[winged zinc]

Ohh rip

[upper karma]

yeahh 😭

oh well

[winged zinc]

Did it matter much?

[upper karma]

not really its just hw

[winged zinc]

Graded?

[upper karma]

yeah

[winged zinc]

Summative?

[upper karma]

yeah

i have good quiz scores and did good in my mid term so i should be fine

i appreciate the time you gave to help me tho

@winged zinc

[winged zinc]

All good

Just in the future, try to ask for help a while before you have things due

[upper karma]

yeah i know 😅

[winged zinc]

That way people can explain it and let you get there - we don't love simply giving people answers

[upper karma]

i just totally forgot about it

[winged zinc]

All good

That is what I found online

Phi is simply a phase shift

But if we wanted to write the answer in terms of cos

we just need to change the phase shift

So I'm still unsure as to why it was wrong

[upper karma]

yeah idk

[winged zinc]

Unless it was exponential

[upper karma]

it wasn't specific tho on it being linear or exponential

but another problem it was

[winged zinc]

Yep

You in uni?

[upper karma]

yeah

[winged zinc]

Nice, doing what degree?

[upper karma]

this was for math 112

bachelors

[winged zinc]

Nice

[upper karma]

yeah im majoring in computer science

[upbeat fog]

I don't really understand the logic behind calculating the area of a hexagon.. anybody mind explaining

why is this not true man 😂

[dark sparrow]

the blue height isn't 4 and even if it were the area would not be 4 + (2*4)*4

[upbeat fog]

oh I see

oh i get it now, thank you

[blazing basalt]

where would -pi/4 clockwise be?

[dark sparrow]

what

[blazing basalt]

Well it's a linear algebra question. I'll just post the quesiton in linear algebra

[vale nimbus]

i dont know if this belongs here because in my country we dont use these terms but can someone explain this to me?

this was what i tried (sorry for bad camera quality) but this is not what sin(3a) equals to

(task is to prove the equality)

[devout harbor]

You need to do some more work, I think it would've been easier if you started with sin(2a + a) then expand

then expand 2a into a + a

[vale nimbus]

sorry for the inconvenience, i looked into it some more and found out that tripple angle formulas exist

and the thing i have in my last line is one of them for sin(3a)

[devout harbor]

yeah they do

[vale nimbus]

so my proof is correct

sorry to bother

[devout harbor]

np you didnt say if you were allowed to use triple angle identities

[vale nimbus]

we havent learned them yet sadly

@devout harbor hm i dont see how i could do it with the method you suggested, i tried it out but didnt work

i cant seem to get the pi/3 into the equation

[dire rampart]

are you just asked to prove that identity?

[vale nimbus]

yea

[dire rampart]

what have u covered in class?

so u havent done angle sum formula?

[vale nimbus]

well

we've seen double angle formulas

not tripple

[dire rampart]

i mean

youve done general angle sum right

[vale nimbus]

and also the sum n stuff

yea

[dire rampart]

like u can expand sin(a+b)?

[vale nimbus]

yup

[dire rampart]

ok thats all u need tbh

[vale nimbus]

yea

[dire rampart]

expand the sines on the rhs

[vale nimbus]

yeah thats what i went with

just expanded those and then solved the stuff i got

but now i need to prove that sin(3a) = what i made the RHS equal to

and that isnt working out for some odd reason

[dire rampart]

you should get 3sinx-4sin^3(x) eventually

[vale nimbus]

got it

ty

wait no @dire rampart im supposed to get 3cos²(a)sin(a)-sin³(a)

i simplified the rhs down to the top one

but i cant get sin(3a) to equal it aswell

so dumb

[dire rampart]

cos^2=1-sin^2

[upper karma]

Can y’all help me on this? Maybe give me a private session?

[visual mist]

find the coordinates of the point that divides the segment joining (-2,0) and (3,4) into the ratio of 1:2. Ratio is to be considered from left to right.

[nocturne grove]

anyone have like a song or anything to help memorize the, sum to product and product to sum trig things?

[desert vortex]

yeah I’m not even in geometry anymore but how do you do this again lmao

[nocturne grove]

sin73 = 6.3/x

cause sin of that angle is equal to opposite (6.3) over hypotenuse (x)

[desert vortex]

okur just making sure

bruh what is it not 9.3

@nocturne grove

I’m TRIPPING hard

[nocturne grove]

make sure your calculator is in degrees not radians

[desert vortex]

I hate calculators

[nocturne grove]

rip lol

[desert vortex]

ok I just got like 5 wrong in a row because of that I actually feel bad for my friends

;rotate

what’s the command to rotate

you’re telling me

That is not 1..7

11.7

,rotate 270

[nocturne grove]

i got 11.6 dunno

[desert vortex]

Yeah I’m gonna have an aneurism why would you actually use 0.600860619 be 0.6

[visual mist]

find the coordinates of the point that divides the segment joining (-2,0) and (3,4) into the ratio of 1:2. Ratio is to be considered from left to right. can someone help me?

[desert vortex]

uh graph it?

[visual mist]

but still how do i find the coordinates

[rich wolf]

@visual mist think about it this way

What is the vertical and horizontal distance between those points

[visual mist]

vertical is 4 and horizontal is 5

[dusky thorn]

<@&286206848099549185> can someone pls help me with this math problem

https://cdn.discordapp.com/attachments/638058993104977931/683341400502566952/unknown.png

[gritty flare]

If I were to guess Id say A

Cause it should be Regular hexagon area minus the all unnecessary parts

[dusky thorn]

why do u say that?

i want to understand it

[gritty flare]

and area of the hexagon is 6sqrt(3)

Regular Hexagon area formula = 3a^2√(3)/2

[dusky thorn]

what is a in that formula

[gritty flare]

the answer A

[dusky thorn]

and also how do i find the "unnecessay parts"

[gritty flare]

Ye I said "If I were to guess" im tryinf to figute out how to get them

[dusky thorn]

oh ok

[wise pawn]

can't be A cause 6sqrt(3) is the hexagon, 3pi is the area of the 6 half circles of radius 1

but there's an overlap

https://prnt.sc/r9kmoy

check out this parallelogram, with that corner of 60 degrees

there are 6 grey copies, and you have a simple circle sector to take out of that parallelogram to compute the area

[dusky thorn]

so

i get what u are saying but what do we do from there

[dense sky]

Is anyone familiar with how to do these kind of problems

[gritty flare]

@dense sky radius is perpendicular to tangent

[dense sky]

Can you help me

[gritty flare]

which problem

[dense sky]

Like.. all :/

Sorry

[gritty flare]

Btw is this an exam?

school test which is important

[dense sky]

It’s like a retake form

[gritty flare]

wats dat

[dense sky]

Cuz I messed up on a test

[gritty flare]

@zenith ember is this allowed?

[vale nimbus]

just had a very quick look at the last one and that looks like sin/cos formulas galore

sk is this graded?

[dense sky]

It’s not a test

It doesn’t have any grade value

[vale nimbus]

oki

[gritty flare]

Okay then ig ill help you?

[vale nimbus]

id try helping but not home atm sadly

@gritty flare can u use sin and cos formulas for this? yeh right

[gritty flare]

After samantha confirms i can help

[zenith ember]

[gritty flare]

You dont need sin/cos

[vale nimbus]

thats how id solve it

[zenith ember]

We can't be certain. Helping is a reasonable action.

[gritty flare]

Okay

@dense sky

Okay lets get started with the n1

[dense sky]

Alright

[gritty flare]

A central angle is __ its intercepted arc (degrees)

Do you know this

Its a rule that we cant give you answer directly

so sorry

[dense sky]

I don’t really know

I’m really bad at math

Is it possible we can move to number 5

[vale nimbus]

i wanna know nr 1 now

[gritty flare]

No. if you dont know this lets just do this

Okay I will draw you to things hold on

[vale nimbus]

i dont understand the question cuz not native tho xdd

[gritty flare]

Okay so we have the central angle Alpha

ans the intercepted arc AC

[vale nimbus]

OH THIS

lmao

[dense sky]

Dude

[gritty flare]

Now what is said that:
Central angle is always equal to the arc measure it is intercepting

[dense sky]

Please the number 5..

[gritty flare]

okay...

quq

[vale nimbus]

i wanna know

[gritty flare]

Ill give you a hint

and you tell me

[dense sky]

Is it Pythagorean’s theorem

[gritty flare]

Radius is perpendicular to Tangent line at the point of touching

so ye it si Pythagorean theorem

What is OV then

[dense sky]

One sec

[gritty flare]

👀

[dense sky]

Gotta grab my calculator

[gritty flare]

Some pythagorean triples which are really helpful to know:
Side-Side-Hypotenuse
3-4-5
6-8-10 (multiplied by 2 3-4-5)
5-12-13

^remember these

definitely

[dense sky]

Is OV 5?

[gritty flare]

yes

By pythagorean triple

5-12-13

OV is 5

[dense sky]

Sweet

Is number 6 the same thing

[gritty flare]

yes

different values doe

[dense sky]

Is it 9?

[gritty flare]

Mm yes

[dense sky]

Ok on to number 7

[gritty flare]

41^2-40^2 =(41-40)(41+40)=81

yep it is 9

okay next

[dense sky]

How do I do this

[gritty flare]

Okay another property

If the radius is perpendicular to a chord it splits the chord into half

Now you should be able to do this

[dense sky]

I can’t remember the parts

[gritty flare]

There is again a pythagorean theorem there

owo

[vale nimbus]

can i put my answer in spoil things

[gritty flare]

No

[vale nimbus]

bruh

[gritty flare]

Some people are impatient and click

[vale nimbus]

yeah fair

[dense sky]

What’s the formula .-.

[vale nimbus]

for pythagorem?

[dense sky]

No for number 7

[gritty flare]

There is no formula

[dense sky]

Am I cutting 17 in half then doing the theorem?

[gritty flare]

its just pythagorean theorem

No no

[vale nimbus]

no

[gritty flare]

Dont cut 17.

Lemme draw it better for you

hold on

[vale nimbus]

can i say what he cuts in half or should i sh?

[dense sky]

Am I doing 8^2+b=17?

[vale nimbus]

thats a good start but keep in mind its b²

[dense sky]

DO I CUT 8

[vale nimbus]

and 17²

[gritty flare]

Okay now

OK is 8 (Distance from centre O to midpoint of chord K)

OA is 17 (Radius of the circle)

By the problem text itself

[dense sky]

Ok so..

[gritty flare]

OKA is right angle

so

AOK is a right triangle

and you can apply which theorem?

[dense sky]

p y t h a g o r e a n ?

[gritty flare]

yes

lol

[vale nimbus]

[dense sky]

[gritty flare]

So by pythagorean you can find which Length?

by my drawing

use the point letters

[dense sky]

I don’t know what it finds but

[gritty flare]

Can you write out the pythagorean theorem for right triangle pls?

[dense sky]

It’s 15?

[gritty flare]

using letters

[vale nimbus]

no almost

[gritty flare]

I want you to write it out to understand what youre finding

[dense sky]

What do you mean almost?

[vale nimbus]

[gritty flare]

ignore him he is just making mt job harder

[vale nimbus]

now write out the formula

ey sorry man

i also wanna help

taking notes

[dense sky]

a^2+b^2=c^2?

[gritty flare]

That is not what I want

[dense sky]

What do YOU WANT

[gritty flare]

Look at the triangle AOK

IN MY FUCKING PICTURE

[vale nimbus]

use his letters

[dense sky]

[gritty flare]

[dense sky]

Ok I see it

[vale nimbus]

agressive math session

why am i being policed

[dense sky]

help

[vale nimbus]

write the formula using his letters

[dense sky]

AOK WHAT DOES IT EQUAL

[vale nimbus]

pythagorem

with his letters

side opposite of a point(angle) = lowercase of that points letter

[dense sky]

18

[vale nimbus]

what

[dense sky]

I don’t know

[vale nimbus]

dont guess :(

write pythagorem with his letters and then itll be noice to solve the problem

[dense sky]

OK + OA?

[vale nimbus]

wait lemme draw u smth aswell

[gritty flare]

@dense sky look at the drawing I sent

THEN look at the TRIANGLE AKO/AOK/OKA WHO GIVES A SHIT

then write out the pythagorean theorem for the SIDES

USING THE LETTERS FOR THE SIDES

[dense sky]

...

[gritty flare]

Like if we have a line with one end having point A and second end having point B then that line is AB

Ill send my picture again

Focus on the triangle AOK

The one which is created by the lines AO:OK:AK

[dense sky]

AO+OK= AK? ._.

[gritty flare]

Wat?

I said write pythagorean theorem

Close

[dense sky]

I’m sorry

I have

math deficiency

[gritty flare]

It needs practice nothing else

[vale nimbus]

^

[gritty flare]

Okay look

Pythagorean theorem: The sum of the squares of the sides of a right triangle is equal to square of the hypotenuse

AK²+OK²=AO²

Now we know OK =8 ans AO=17

[dense sky]

OH

[gritty flare]

AK²+8²=17²

so which side are we finding?

[dense sky]

AK

[vale nimbus]

8

[gritty flare]

yes

[dense sky]

OH

[gritty flare]

So what is AK

find it now

[dense sky]

15?....

.-.

[gritty flare]

yes

Okay

What line does the problem want us to find btw

Can you tell me that

[dense sky]

Yes

The H

[gritty flare]

wat

[dense sky]

Wait

The line above 17

[gritty flare]

Uh

Read the problem

[dense sky]

AK

[gritty flare]

chord

What is the chord in my drawing

[dense sky]

HOW LONG IS IT

IS IT 15?

[gritty flare]

AK is 15

vut thats not the answer

Chord what is the chord in my drawing

[dense sky]

AB

[gritty flare]

using the letters again

YES

okay if K is the midpoint of AB

wat does that mean

[dense sky]

It’s 34

[gritty flare]

wat

[dense sky]

Wait nvm

[gritty flare]

Answer on my question first

What does it mean to be midpoint of AB

mid-point

[dense sky]

Half

Of AB

[gritty flare]

So If AK is 15 what is KB

[dense sky]

Or in the middle

7.5

[gritty flare]

no

AK!

[dense sky]

Oh

[gritty flare]

If AK is 15 what is KB

[dense sky]

15

[gritty flare]

K is rhe midpoimt of AB

ye

then wat is AB

[dense sky]

[gritty flare]

[dense sky]

30

[gritty flare]

yes

8 is the same youll do it

while you do ill see 9

tell me the anewer you get on 8

[dense sky]

Is it 16

@gritty flare

[gritty flare]

ye it is 16

[dense sky]

Awesome

[gritty flare]

okay now 9

[dense sky]

Alright

[gritty flare]

Can you tell me what that tells us about GH and JK?

the problem?

[dense sky]

Isn’t it just 3-10

[gritty flare]

huh?

3-10?

[dense sky]

Is the answer 7

[gritty flare]

yes

well imo it is 7

Gj gg

[dense sky]

And is the next one 3

[olive plover]

do we ask questions here about trigonometry or #❓how-to-get-help

[devout harbor]

Both

[dense sky]

@gritty flare Dont leave me ;-;

[gritty flare]

ye it is 3

well you are done

[dense sky]

Their is more

Please

I need more help

;-;

Can you help with this

[devout harbor]

Are you O levels?

[dense sky]

??

[devout harbor]

just asking

[dense sky]

What do you mean

[devout harbor]

Nothing

[gritty flare]

omg thata a lot

[dense sky]

Are you willing to help ._.

[devout harbor]

You need to try yourself first

[dense sky]

Yes but no

[gritty flare]

Okay

Another thinf for you

two Tangent lines coming from the same point until the touching to the circle are equal

lets say we have two tangent lines coming from point O and touching the circle at A and B

them OA=OB

this should be enough to solve this problem

[dense sky]

So

[devout harbor]

^ Iscoceles triangle

[dense sky]

DZ=ZW?

[devout harbor]

Yes

[vale nimbus]

what is O-levels math

UK thing?

[gritty flare]

No no

NO NO

[dense sky]

WHAT IS EQUAL

[gritty flare]

Okay lemme draw it to you

[devout harbor]

Yes @vale nimbus

[vale nimbus]

noice

what are u taking?

[devout harbor]

I'm not takin anything I was just asking sk

[vale nimbus]

ooh

my bad

[devout harbor]

np

[dense sky]

Well I’m in geometry I

Wait

[dense sky]

Geometry II I think

lol sorry

[gritty flare]

OB ans OA are tangent lines

and A and B arw where they touch the circle

[dense sky]

CZ is tangent

[gritty flare]

Now what I want you to do on your paper is

mark where the tangent line DW touches the circle

and name it some letter name

and tell me what you named it

[dense sky]

X

[gritty flare]

Okay

then the thing I told you

What is the same thing in youe problem

[dense sky]

Is this Pythagorean’s theorem

[gritty flare]

nope

[dense sky]

Is their a formula for this

[gritty flare]

I alrdy told you

[dense sky]

WAIT

Is it 16?

[gritty flare]

Lemme think

Nope

its not 16

You have to use the property i fucking told you

I wouldnt tell you if it wasnt used

[dense sky]

So ZN=5

Is it

13

[gritty flare]

[dense sky]

Bruh..

[gritty flare]

Ye it is 13

[dense sky]

Actually?????

[gritty flare]

But are tou fully sure you solved it

100%

I dont think you understood the whole thing

so im gonna explain now

[dense sky]

So I was correct?

[gritty flare]

Okay

By the property I gave you

ZC=ZN
DC=DX
WN=WX

Do yoy understand why this is?

[dense sky]

Yes

[gritty flare]

Next by the problem DZ=12 and ZC=5 so DC=7
ZN=ZC=5; by problem ZW=11 so NW=6
DW=DX+WX
DX=DC=7
WX=WN=6

DW=7+6=13

👍

Youll be able to solve next one by the same way

[dense sky]

Ok I’ll do it

Check out the next one

[gritty flare]

Okay did you get thr answer on the next one?

[dense sky]

N

O

[gritty flare]

cmon sude

its like literallt the same as the 11

[dense sky]

Is it a low number

[gritty flare]

Just numbers are changed

What answer did you get

[dense sky]

6

[gritty flare]

thats correct

[dense sky]

Really?

[gritty flare]

They increased numbers

but the side decreased

ya

[dense sky]

I had the answer for awhile

[gritty flare]

It was a simple trick to make you douvt yourself