geometry-and-trigonometry

[flint pelican]

So 16+8=24 but the answer is A

I’m lost

[proper echo]

@flint pelican I can try to do 55 for you, but doing homework myself atm

[peak locust]

@upper karma let's start with the left triangle

[dark sparrow]

@proper echo don't do that

[peak locust]

it's isoceles, so the bottom two angles must be equal

[proper echo]

Aight

[peak locust]

and the angles must add to 180 degrees

what are the bottom two angles

[idle bloom]

For 56 @flint pelican :your rotating the triangle around the y-axis, so your height will be 5 you worked out that c (the radius) is 12. So just do (12^2x5)x(1/3pi), you should get your answer.

[upper karma]

@peak locust 65

[peak locust]

correct

now, 65 degrees and the obtuse angle in the triangle on the right

add up to equal 180

what is that obtuse angle equal to

[upper karma]

115

[peak locust]

yes

[upper karma]

im just wondering how you figure out the other angle

[peak locust]

and now you have another isoceles triangle, so do the same thing you did for the first triangle

to find 2

[upper karma]

I already did the work for all of that

the two other angles have to add up to 65

[proper echo]

To 130*

[peak locust]

no, 65

[proper echo]

Wat

[peak locust]

so each of those angles is 65/2

or 32.5 degrees

[upper karma]

that’s the answer?

[peak locust]

ya

[upper karma]

i was confused on that part

[peak locust]

they add up to 65

and they're equal

[upper karma]

ik

[proper echo]

But the angles of those triangles are equal

[upper karma]

but having a decimal as an answer

[peak locust]

decimals are fine

[proper echo]

<2 is 65 degrees not 32.5

[peak locust]

I will bet 40 000 dollars that it is not 65 degrees

[upper karma]

?

the triangle as a whole has to equal 180 @proper echo

[peak locust]

this angle is not 65

115 + 65 + 65 = 245, which is way more than 180

[upper karma]

@upper karma I did that question before

sat practice

[proper echo]

O wait

My bad

[upper karma]

stopped

[idle bloom]

Right, let's start from a clean slate right. 180-65 is 115. That means that the other 2 anlges in that triangle are 115/2. so the angle that says 2 is 57.5.

[upper karma]

nah

115 is the measure of the angle on the bottom left

anyways last question

[proper echo]

That's also simple

You know that ths angle is 62

And the other angle is also 62

And he other other angle is also 62

And you got 2 equal angles

So same thing again, different numbers

180°-angle-other other angle

[upper karma]

[proper echo]

You have 2 isosceles triangles

[upper karma]

ohohohohohohohohohohhhoh

what do the double lines mean

congruent

[proper echo]

The double lines are anither way to mark a line

[upper karma]

so they mean nothing

[proper echo]

No offense, but I think you're trolling

[upper karma]

maybe

[upper karma]

👺

[proper echo]

Aight, now I need help

[upper karma]

Aight, now I need help

[proper echo]

I need to find CM

[upper karma]

🤡

[proper echo]

Help please 😭

[harsh panther]

Is there an intuitive explanation that shows the connection between the two focus definition of an ellipse and the stretched out circle version?

[fringe dirge]

As the two foci get closer together, it becomes more and more circly

[harsh panther]

that is the stretched out circle version thingy right

oh okay

you mean when the focus coincide it is a circle so stretching out a circle is the same as pulling apart the focus?

how do we know they will be stretched out in the exact same way?

[fringe dirge]

Using the foci

It's all the points that have the same distances from both foci

As in the sum of the distances to each foci are the same

[harsh panther]

the above is just the definition of the two focus method of representing an ellipse.. how exactly would it show that separating the foci is equivalent to stretching the circle method of representation?

[fringe dirge]

I mean you said intuitive

[harsh panther]

okay

fair enough

[fringe dirge]

You can do it rigorously with a little bit of linear algebra

[harsh panther]

any links?

[fringe dirge]

https://math.stackexchange.com/questions/3200569/geometrically-explained-why-do-linear-transformations-take-a-circle-to-an-ellip

[harsh panther]

thanks a lot

you are amazing

[upper karma]

yes?

[idle bloom]

If I had a question about the equation of the circle and a line intercepting that at points A, B. Would I ask this channel about calculating the length of AB ?

(I don't actually have that question, just trying to get a really strong feel for what fits in where.)

[graceful hemlock]

@idle bloom Yeah!

[idle bloom]

ok thanks 😄

[bright nexus]

https://gyazo.com/8e84e794c8dae82ab6f328c68ec4246c

can someone help on how the formula should be layed out?

[silent plank]

do you know how to find the midpoint of 2 given points

[bright nexus]

yeah

[silent plank]

let the unknown point be P(a,b)

[bright nexus]

?

[silent plank]

what would be your equations relating P,X and M

[bright nexus]

what is p ?

oh

ok

[silent plank]

arbitrary point you're trying to find

[bright nexus]

okay

i get it now

@silent plank thanks

[tepid vine]

hey can someone help with my homework

it is completely illogical and very poorly explained in the textbook

k

"Illustrate each tangent ratio by sketching a right triangle, then labelling the measures of its legs.
a) tan B = 3/5"

[peak locust]

ok

what is tan

[tepid vine]

tangent

😹

[peak locust]

like what is it though

[tepid vine]

3/5

B

i dont know

it doesnt make any sense

[peak locust]

do you know sohcahtoa

[tepid vine]

yes

[peak locust]

then use that

and tell me

what is tangent

[tepid vine]

use it to do what

tan3/5?

[peak locust]

there aren't many ways to use sohcahtoa

it literally just tells you what sine, cosine and tangent are

[tepid vine]

tangent 3/5 is 0.01

[peak locust]

we're not looking for tan(3/5)

[tepid vine]

ok then what are we looking for

[peak locust]

i'm literally just asking you what tangent is

[tepid vine]

why

[peak locust]

because you need to understand it

to do the question

[tepid vine]

i dont know what it is

[peak locust]

if I give you a right angle triangle

with 3 side lengths

how would you find the tangent

[tepid vine]

what is the tangent

[peak locust]

you said you know what sohcahtoa is

[tepid vine]

sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent

[peak locust]

ok, there you go

tangent = opposite/adjacent

[tepid vine]

ok

[peak locust]

the tangent of an angle is the opposite side/adjacent side

if tan(B) = 3/5

then the opposite side to the angle

is 3

and the adjacent side

is 5

and so draw a right triangle that has two sides like that

[tepid vine]

ok

what are the measures of its legs

the lengths?

[peak locust]

yes

[tepid vine]

ok so when i label the 3 and the 5, can they be on the hypotenuse?

i feel like no

alright so it wants me to label all the lengths

how do i find the hypotenuse

oh pythagoras

[peak locust]

I already said it's the opposite and adjacent

the hypotenuse is not involved in the tangent

and yes, pythagoras is how you find the hypotenuse

[tepid vine]

thank you

i dont understand this stuff

what the hell is tangent

its opposite over adjacent

yes

but wtf is tan 60°

that is not opposite over adjacent its a number

[spark stag]

its the tangent of 60 degrees

as in

if you have a right triangle with a 60 degree angle

the tangent of 60 degrees is the ratio of the opposite side to the adjacent side

[tepid vine]

ok

that makes sense yes

[faint hinge]

can someone explain this to me ive looked up the answers but still dont get it

[spark stag]

note that tangent doesnt care about the raw size, just the ratios of sizes

[tepid vine]

what is the raw size

[spark stag]

like

[tepid vine]

and the ratios of sizes

[spark stag]

5 metres or 10 metres or 20 or whatever

[peak locust]

3 cm and 5 cm are raw sizes

or 3 km and 5 km

or 6 m and 10 m

but all of them have the same ratio

so they all have the same tangent

3/5

[tepid vine]

😐

[spark stag]

lets say we have tan(30 degrees)

then if you draw a right triangle

where one angle is 30 degrees

it doesnt matter HOW big or small you make that triangle

as long as it's a right triangle, the ratio of its sides will be the same

[tepid vine]

right

ok so how do calculators calculate tan30

[spark stag]

they use a method called CORDIC

it's fairly complicated

and not really feasible for humans

we usually get by by knowing how to find a few "special angles"

and maybe using identities to figure out a few more

and besides that, relying on calculators

back in the day, there would be books full of reference tables for trig functions

[peak locust]

0, 30, 45, 60, 90 degrees

[spark stag]

so that you can look up the value you're looking for

[peak locust]

those are the special angles we are supposed to know

[tepid vine]

no 15 or 75?

[spark stag]

they CAN be calculated by hand - e.g. via taylor series

but its generally impractical

15 degrees and 75 degrees can be calculated by using identities, usually

[peak locust]

ya

[spark stag]

since sin(15) = sin(45 - 30)

[peak locust]

you can, but people don't generally don't memorize them

[spark stag]

just find an appropriate identity

and solve from there

[tepid vine]

ok so how do you know whether 60° is greater than or less than 1 without using a calculator

i already used it and found it was greater

[spark stag]

you dont really need to worry about that rn though

do you mean tan(60 degrees)?

[peak locust]

you can actually use half angle and sum of angle identities to find exact values of infinitely many angles, but that doesn't matter

[tepid vine]

o yes

[spark stag]

remember that tangent is the ratio of opposite to adjacent

so we have to think

"will the opposite be longer or shorter than the adjacent?"

it can help to do a quick sketch for problems like these

i tried to make the bottom-left angle roughly 60 degrees

and we can see that its opposite is clearly longer than its adjacent

so $\frac{\text{opposite}}{\text{adjacent}} > 1$

[somber coyote]

Namington:

[tepid vine]

lol

[spark stag]

(in general, if an angle is between 45 and 90 degrees, its tangent will be greater than 1.)

(again, though, you shouldnt have to memorize that - you should be able to work it out.)

[tepid vine]

ok the word measure kinda makin me mad rn

why not say length

the textbook is exclusively using measure

[peak locust]

measure is a pretty well defined thing in math

that is a generalization of length

for your purposes, you can just replace measure with length

[tepid vine]

oh wait never mind it says determine the measure of each indicated angle to the nearest tenth of a degree

ok now i am stuck again

measure of the angle

so i found the length of GF with pythagoras algebra thing

then did tangent 3.5/GF

which was 0.01 something

and then invtan of that was only like 0.6

that angle is not 0.6

did i do something wrong

[tepid vine]

apparently am supposed to do invtan first?

[silent plank]

tan(x) = 3.5/GF
x = arctan(3.5/GF)
you apply inverse tan only.

but for this question since you have the opposite and hypotenuse, you can use one of the other trig functions. (instead of pythag and tan)

[flint pelican]

I can understand this but I just don’t know how to find the period

Wait I think I got it

[shell frost]

yo can someone solve #22?

: )

[silent plank]

what have you tried?

[shell frost]

I tried 1+cot^2of theta= csc^2 of theta

But sin isn’t squared in the problem

So we can’t use that identity

[silent plank]

why do you need to do that?
what is the value of sin(pi/6)?

[shell frost]

Can’t use calculator

We have to show the process

[silent plank]

you don't need a calculator

for this

do you know your special triangles?

[shell frost]

Special right triangles?

[silent plank]

yes

[shell frost]

Yes

[silent plank]

so you should know the values of the trig functions at those angles

[shell frost]

so it’s the 30 60 90?

Cus pi/6 is 30 degrees

[silent plank]

yes

[shell frost]

Ok

Then what

[silent plank]

well what is sin(pi/6) or sin(30 degrees)

[shell frost]

1/2

Right?

[silent plank]

yes

[shell frost]

omgg

[silent plank]

can you do the rest?

[shell frost]

I think so

THANK UUUU

[median crown]

wtf

[shell frost]

what

[mild grotto]

So if I pass for help for an incredibly easy problem will I be judges at all? I dunno why I can’t figure it out... 🤷🏻‍♀️😂

I’ll send a pic here in a minute

[sly marlin]

maybe some bit of your foundation is missing

It happens for some people

@mild grotto So, you know what radians are?

[idle bloom]

Sorry in this image what does S stand for?

(sorry for image quality XD.)

is it referring to a sector?

[dark sparrow]

it's referring to the length of the arc

[idle bloom]

Ah thank you :), only at GCSE level atm XD

[upper karma]

I tried doing 15x3

[idle bloom]

I did that question for my mock exam last year XD

[upper karma]

Not sure

Yes

All sides added together

[idle bloom]

If you look at the rectangle at the end right, you can see the 2 smaller sides equal the one larger side

[upper karma]

I can see that yes

Yes

Right

Right

[idle bloom]

eular/fermat they're identical rectangles btw.

[upper karma]

I think Jack’s right

Okay, so basically make up numbers

You know what I mean

[idle bloom]

or if you know that 2 small sides is a larger side you can say assign the small side the variable: e and the large side: f. so f is 2e and because there are 2 large sides and 2 small, you know that the perimeter of 1 rectangle is 6e. so 6e is 15, so e is 15/6 or 2.5 then count how many large and small sides there are in the outer one. and convert that to how many e's there are. and times the amount of e's by 2.5

Like I said i did it in my mock XD

oh yeah XD

Pardon?

I was trying my hardest to give an explanation and provide some clarity, but I'll leave it for now.

[upper karma]

Do you have to do add up the Xs?

Yes

15

Wdym by outline

15

It’s a triangle

So divide 2

30

30??

No 15

Since it’s a triangle

What shape(

30

It’s 30cm

Perimeter

2x+2y

2x+2y=10?

Sure

I did that already

So, I was right when I said “do you have to add the Xs?”

I got

2x+2y meaning perimeter for 1 rectangle

Ohh my bad

Would it be y+y+x+y+x=15

Where did you get 2x from?

And 2y*

I understand

2x+2y=15

Then we need to find out what x and y is?

@upper karma

So I need to rearrange the equation?

[prime jasper]

what does it mean when people say angles that add up to 180 degrees are supplementary

[mild grotto]

Yes I know what radians are.
Figured it out though, thanks

[idle bloom]

What is a radian?

I know it's 360 divided by 2 pi

but what is it?

[dark sparrow]

take a circle, and a string as long as its radius

wrap the string around the circle so that it becomes an arc

the arc will subtend an angle at the center

that angle is 1 radian

https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif

@idle bloom

[idle bloom]

WOW.

XD

You know i said you were amazing @dark sparrow

add 10000000000000000 extra points of amazingness.

[upper karma]

Prove that if
convex quadrilateral has an axis of symetry, then we can escribe or inscribe a circle on it.

No idea how to do this, also had trouble translating since im not English

[buoyant spruce]

Hello I have 10 questions on my home work
Was wondering if I could help with a few so I can start to understand and do the rest

[silent plank]

do you know all the definitions?

[buoyant spruce]

Yes I do

Just not sure how to solve my teachers learning style does not work very well with me

[silent plank]

which ones do you think are true?

[buoyant spruce]

C and D

[silent plank]

Is there anything else that's true?

[buoyant spruce]

I was considering B but that is it

[silent plank]

would B be true or false and give your reason

[buoyant spruce]

Lemme check my work one more time

[sick viper]

why is that true?

when i use the rage of arctan i get

[dark sparrow]

@sick viper x isn't a constant.

[delicate lake]

180x2/pie =114.592

Just want to make sure I'm doing it correctly

[dark sparrow]

you are not

[upper karma]

^

[delicate lake]

Oof

Wait lol

[dark sparrow]

2π radians is by definition a full circle

[delicate lake]

360 then.. but what is the formula to get it

[dark sparrow]

if you're so insistent on a "formula"... 1 radian = (180/pi) degrees.

[upper karma]

$360 \rightarrow 2\pi \ 360 (\frac{2\pi}{360})=2\pi$

[dark sparrow]

also, it's pi, not "pie".

[delicate lake]

Sorry

[somber coyote]

Gryff:

[delicate lake]

What I have here is doo doo?

[upper karma]

Where did you get the 12.3?

[delicate lake]

I was working a different problem

[upper karma]

Think about it in this way.

If I have 360 degrees and I want to make it into 2pi radians.

$360 \rightarrow 2\pi \ 360(\frac{2\pi}{360})=2\pi$

[dark sparrow]

converting between radians and degrees really isn't all that different from converting between feet and inches

[somber coyote]

Gryff:

[upper karma]

^

[silent plank]

don't leave out the degrees

[delicate lake]

Thank you

[median crown]

id do

i do

its ugly af tho

its a true statement proof

so i manipulate the components using rules to form a true statement

[rapid nexus]

working out stuff in radians is so difficult

[dark sparrow]

is it really?

[rapid nexus]

I have my final exam in 3 weeks and we only just learnt it and its the first time I've ever seen it

[upper karma]

3 weeks is a lot of time.

[dark sparrow]

radians are just another unit for measuring angles

[upper karma]

Just like feet and inches.

[dark sparrow]

there is little more conceptual difference between radians and degrees than between feet and inches

[upper karma]

Fair.

Honestly radians takes time to get used to.

It was hella weird when I first learned it.

Took like a week to get used to it.

[rapid nexus]

ehh, I guess. I haven't looked at any questions for it yet, but there is all these things like the unit circle, special triangels etc

[upper karma]

So basically 3 weeks to learn basic trig?

Just go to Khan Academy and you can take like 2 days to learn all of that.

[rapid nexus]

and its 2 weeks of holidays

I just have like, a brain block for some reason, where I just can't seem to get my head around it

[upper karma]

Again, go to Khan Academy.

They introduce it pretty nicely.

[rapid nexus]

https://www.khanacademy.org/math/trigonometry

[upper karma]

Yes.

@rapid nexus https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func

Do the first few categories.

[rapid nexus]

yeah, some of it we have already done last year and the year before, but the radians stuff is all new

[upper karma]

So you learned cos(360) but not cos(2pi)?

[rapid nexus]

pretty much yeah

[upper karma]

Wow that's stupid.

[rapid nexus]

I'm in the top class, so we do AS Cambridge as well as the standard exam board which everyone else does

so only we do trig like this this year

but trig looks pretty fun

[sudden locust]

I think this video might be interesting for some of you geometry-lovers: Pythagorean Theorem, but with a twist.. https://youtu.be/Ir3MUW_VkgQ 🔺

[worthy root]

Good video @sudden locust

[sudden locust]

@worthy root Thank you! 🥰

[winter bison]

Hi

Im stuck with this question

[quiet mason]

post

[winter bison]

"find the degree measure of the angle for each rotation and sketch each angle in standard position"
a.) 2/3 counterclockwise rotation
b.) 5/9 clockwise rotation

Does this question even go in this channel lol

[sly marlin]

2/3 radians?

2/3 degrees?

2/3 full turns?

2/3 half turns?

@winter bison

[winter bison]

It doesn't state here

[sly marlin]

Didn't state at all?

[winter bison]

Nothing

[sly marlin]

then sigh unsolvable

[winter bison]

That's all thats here

:((

[sly marlin]

yeah, it's not solvable

if that's all to the question

(even a careless word left out may let it be solvable)

[winter bison]

Welp

I'll skip this one

Thanks:)

[nimble cosmos]

does sin(x)/cos(x) = to either cot(x) or sec(x)?

[quiet mason]

none lol

tan(x) is the notation for sin(x)/cos(x)

[winter bison]

Radians doesn't always have to have pi right? 🤔

[fringe dirge]

@winter bison What exactly do you mean? Radians are a unit of measure

You can have an angle of one radian

[winter bison]

Ohh

[upper karma]

You can have 2pi degrees, which is 6.28 degrees.

Pi is just a number, a constant.

[winter bison]

Because the given radians always have pi in it

So i thought if there's a pi its radian 😅

[upper karma]

It doesn't have to be, but radians are mostly in terms of pi.

[winter bison]

Ohh so radians are like cm, kg etc.?

[upper karma]

Kind of.

2pi radians = 360 degrees.

That's all you need to know.

[winter bison]

🤔 🤔

[upper karma]

[somber coyote]

euler/fermat:
Compile Error! Click the reaction for details. (You may edit your message)

[upper karma]

Someone yesterday got a problem with 2pi degrees 😂

[dark sparrow]

"a single pi radian"

[somber coyote]

euler/fermat:
Compile Error! Click the reaction for details. (You may edit your message)

[dark sparrow]

and no, an angle in radians doesn't have to be given as a multiple of π

it's not like "2.65 radians" is an invalid angle

[upper karma]

https://discordapp.com/channels/268882317391429632/326138757474680852/626057576097906709

This is his question.

[dark sparrow]

what you're saying is kinda unhelpful

[upper karma]

To convert from radians to degrees (and back), pi is generally used.

But radians nor degrees don't have to be anything.

[winter bison]

Yea i have a formula to convert

[dark sparrow]

y'all keep saying "a formula to convert"

[winter bison]

[dark sparrow]

as if they aren't just two different units for the same quantity

as if one would need a "formula" to convert between feet and inches

[winter bison]

What's the right term

Or correct way to say it

[dark sparrow]

the right term for what

the correct way to say what

[winter bison]

For what i said

Ok gotcha

[dark sparrow]

not really, dimensional analysis is a wee bit more than that

[winter bison]

[thorny bough]

I have to calculate the uncertainty in theta, which is found using arcsin. and i have the hypotnuse and opp side length as well as their individual errors, can someone tell me how to find it, from what i understand i need to use deriv of arcsin?

[umbral snow]

Let's say you have y = f(x). You can write the derivative like so:
dy = f'(x) dx

That is, for very small changes in y and x, this equation approximates:
Δy = f'(x) Δx

Uncertainty counts as a "small change" so this equation can work to approximate uncertainties

[thorny bough]

so if my height is 3.8 and legth is 100 i just have to do 1/(1-(3.8/100)^2)?

deriv of arcsin?

[umbral snow]

Oh this is multivariable

[thorny bough]

um

[umbral snow]

You have two variables you have the uncertainty of

[thorny bough]

correcta

correcta

correcta

lag

[umbral snow]

Do you know the multivariable total derivative by chance?

[thorny bough]

although its a basic physics lab for 1st yr students i doubt multivar would be needed, we havent even needed to use derivatives yet

uh i took it last year so maybe?

i forgot a lot of stuff

[upper karma]

I need some assistance

[upper karma]

Yes

[idle bloom]

So do you know what topic it's on?

[upper karma]

Wdym?

[idle bloom]

Like do you know what you have to use, like trigonometry or Pythagoras, that type of thing

Oh wait, I can tell it's a trig question nvm.

"hyp", "adj"

Right Brief explanation, you know the length of your adj is (6.5-2.3) or 4.2m

and we want the hyp.

we also know that the angle is 5 degrees.

Now, do you know a trigonometric ratio that you can use?

with that information?

@upper karma

[upper karma]

SOHCAHTOA?,

[idle bloom]

Yeah, but which one out of that uses the hypotenuse and adjacent?

"Cosine(theta) equals adjacent/hypotenuse remember.

then just re-arrange that to make the hypotenuse the subject and use a calculator to find the answer 🙂

substituting in your values.

[upper karma]

Safe

[tired bison]

How would I go about doing this without a calculator?

[fringe dirge]

Do you know what cot is?

[tired bison]

Cotangent

I know how to solve this using a unit circle, but I'm supposed to know how to do this without using any resources

[fringe dirge]

And what's cotangent

[tired bison]

1/tan

cos/sin

[fringe dirge]

So what do you need to figure out the values of

[tired bison]

I need to find the exact value of that equation

[fringe dirge]

I know

I'm asking what values you need to figure out, so that you can figure out the value of cot(-11pi/6)

[tired bison]

I have no idea

[fringe dirge]

cot = cos/sin

[half quest]

i I tried this but I'm not sure how to do it. I tried changing sin to cos-90 but that didn't work out very well

im timed please help

[fringe dirge]

Is this a test?

[half quest]

kinda

an online times quiz i started by accident

but it'll be marked

[winter bison]

Convert the radian measure to exact degree measure
b.) 2radian

Would this be 360/pi?

[umbral snow]

Ya

2radians × |360 degrees / 2π radians|

[winter bison]

Woa

I used
2radians x 180/pi

How do i show that its a degree tho

[upper karma]

@winter bison wdym

[dusty sphinx]

https://i.imgur.com/DxlD7Ck.png
I'm not sure what to do! 😭

help!

[dark sparrow]

using a Pythagorean identity

do you know what those are

[dusty sphinx]

i watched some youtube videos

[dark sparrow]

i didn't ask you what you did or didn't watch

[dusty sphinx]

kind of

[dark sparrow]

there is no kind of

either you know the identities or you don't

[dusty sphinx]

I GUESS I DONT

[dark sparrow]

$\sin^2(x) + \cos^2(x) = 1$ no bueno???

[somber coyote]

Ann:

[dark sparrow]

what even do you know at that point if you're missing something as basic as that

[dusty sphinx]

like

UH

i know like sin cos tan and how to use them to like find trig functions

and stuf flike that

i guess

[dark sparrow]

i just gave you the one identity needed to do your problem

[dusty sphinx]

yeah

[dark sparrow]

so then

what are you waiting for

[dusty sphinx]

when i plug it in do i square sin..

[dark sparrow]

I DON'T FUCKING KNOW, DO YOU???
DOES IT SAY "SIN^2" OR DOES IT NOT

[dusty sphinx]

OK

IM SORRY

I KNOW IM BEING DUMB RN

[supple abyss]

[vagrant steeple]

can someone help me with figuring out the equation 😅

y = 5sin( ???)

[dark sparrow]

5 sin(x/7), given that its period appears to be 14π

[vagrant steeple]

how did you get 1/7 from the period?

[dark sparrow]

y = 5sin(x) would have a zero at x=π

so this is stretched horizontally by a factor of 7 compared to that

[vagrant steeple]

okay, i get that

does the period on this guy go from the points i marked?

[dark sparrow]

that'd be half the period

[vagrant steeple]

the other half isn't in the graph though

so do i have to figure that out for myself

like finish the graph or something

[dark sparrow]

once you have half the period, you can... yknow... double it...

to get the whole period

[tacit condor]

can someone please help

with iv

[fringe dirge]

What's your guess on what the locus is?

[sly marlin]

@tacit condor Well, the first 3 parts might help

[tacit condor]

yeah solved it:)

[upper karma]

If I have an isosceles triangle, would you say for finding the height, non-base side squared - (.5*base) squared = height squared?

is that an approiate way to simplify the math?

[nocturne musk]

Hello

Can someone help me this?

[weary drift]

👍 @upper karma

[peak mesa]

Anyone knows about quaterions?

https://www.mathwarehouse.com/transformations/images/isometries/triangle-rotated-90-degrees-as-isometry-animation.gif

i want to do this

But it's complicated xd

i need to rotate a Vector around another Vector (by a angle)

[upper karma]

What are the answers to #11 idk what they’re asking for

[upper karma]

<@&286206848099549185>

[umbral snow]

@peak mesa
If you're working in 2D, you only need complex numbers. 3D requires quaternions tho

[peak mesa]

@umbral snow im using this

for 3d

but seems the "origin" variable is always the same.. it rotating in cordinate (0,0,0)

https://gyazo.com/8567a654c85e9a0f7e0f336fea5c221f

The cordinate of player is changing

but its stuck

[umbral snow]

Though your sim is 3D, it looks like a 2D rotation

[peak mesa]

yes

im rotating only x and z

for yaw

[umbral snow]

The means by which you are doing it is a linear transformation. Note that all linear transformations fix (0,0,0)

[peak mesa]

There it is, I don't know what to do xd

[umbral snow]

You can't get away from rotating around the origin with this one, unless I'm misunderstanding the method?

[peak mesa]

If I am in the location (0,0,0) he rotates right, but the problem is that the rotation should always be done at the player's location and he is doing in the location(0,0,0)

[umbral snow]

If you want a linear transformation that also allows translation, you need an extra entry in your vectors for "origin displacement". Then it's a 4D system but that's probably needlessly complicated

[peak mesa]

4d is for quaternions ik

I do not know what else to do, advise to use quaternions? It's just that there aren't many useful examples on the internet for this. It's usually all about game engines.

[umbral snow]

Nah. Quaternions can't do anything matrices don't do better lol

I can't say I know a ton about game development sry

[peak mesa]

Yes, but can you help me figure out what the problem is in this case? I've been in this problem for a few hours

[umbral snow]

Okay, so you want it to rotate around a different point than above?

[peak mesa]

vector rotating around a vector pivot

https://www.mathwarehouse.com/transformations/images/isometries/triangle-rotated-90-degrees-as-isometry-animation.gif

look at edges of triangle

its like this i want

its by distance etc

[umbral snow]

That's what you have

[peak mesa]

so im diff the x and z

true

but

e goes always to (0,0,0)

[umbral snow]

e?

[peak mesa]

?

i dont know what im do wrong

im substracting

[umbral snow]

What's vec? The player?

[peak mesa]

origin its the position of player

vec its the edge of cube

so i want to rotate vec around position of player

[umbral snow]

@peak mesa
origin - vec is the vector that goes from the box to the player. I think you want the negative of this

Yeah, I think that's your issue

Do vec - origin instead

[peak mesa]

i know the problem

its fov and distance

i print in 3d space my location

and he is the right place of (0,0,0)

but the values changes

so i guess its the base distance of objects

fov

[umbral snow]

Because you add origin on at the end, you end up creating a 2origin - vec vector, which isn't something you can use

[peak mesa]

the math is correct

https://gyazo.com/2527486950d5fcab0aceb7756d200d42

Look at the addicional point there

its my location printed

its incorrect

its the problem

the cube is rotating around the point that the 3d space think is the correct location

i will see this tomorrow

thks for all good night

[umbral snow]

At least check vec - origin

[upper karma]

Idk I was confused about what the question ias asking

[jovial axle]

i need help 😦

i need two wheels that have the same radius and area, but one has 4 spokes and one has 2 spokes

so im thinking dont change the radius of the inner 'hub' that all the spokes connect to

and dont change the outer radius obviously

dont change width of the spokes

so only change the length of either of the spokes to make the total area the same

hopefully that makes sense 😦

i sort of got it down to an expression

where the wheel has some inner hub radius that's omitted, and some outer radius thats omitted, and has a radius expressed here being the same as the length of a spoke:

$r_2(2w-r_2)=r_4(4w-r_4)$

[upper karma]

can anyone help me with a trig problem?

it involves graphing and reference angles and sstugg

stuff*

[jovial axle]

[upper karma]

so secθ=-5 and cscθ<0

I need to draw and label the reference angle

[silent plank]

what have you thought about?

[upper karma]

idk if this is correct but

I think x=-1 and y=-sqrt(24)

and r = 5

because sec=r/x meaning that r=5 and x=-1

since r can't be negative

and then I plugged into the pythagorean theorem and got sqrt(24)

and since csc <0 then r/y < 0

and r is positive so that makes y negative

[umbral snow]

@jovial axle
I'm not sure I get it. Does a spoke affect the area?

[jovial axle]

@umbral snow yea

because hold on, ill draw

[upper karma]

@silent plank does that seem right to you?

[jovial axle]

like here is a two spoke wheel

so the whole white area is just cut out

no area

[umbral snow]

Oh, and the green is "area"

[jovial axle]

yea

@umbral snow in the end, these will be two discs with the same mass and radius but different moments of inertia

i think this simplifies the process though

[silent plank]

@upper karma
values seem fine. have you calculated the angle and drawn it?

[jovial axle]

as theyll have the same density and height

[upper karma]

it just says draw so I didn't calculate

ill show u my drawing one sec

if it says show arc and angleθ then do I draw the original and ref angle?

[umbral snow]

I see, you can reduce inertia by including more spokes

[jovial axle]

yea

but to be experimentally valuable, they need to have the same mass and radius for us

maybe its easier to change density than to solve this problem

[upper karma]

@silent plank is that correct?

instructions say "draw the reference triangle for θ in the correct quadrant show your arc and angle θ"

[silent plank]

seems they want you to indicate the original angle too

[upper karma]

ok

it would be the one that's like 225 degrees right @silent plank

[silent plank]

in this question it would be a bit more than that

[upper karma]

not for the numbers

like looking at the graph

like ot

it's not the 135 degree one

[silent plank]

refer to them as quadrants

[upper karma]

like this

[silent plank]

yeh

[upper karma]

ok

it says "find the simplified,exact,rationalized value of sinθ

that's just 1 value righ

right*

[silent plank]

hmm, you should also try and make the diagram a bit more to scale

[upper karma]

it would be -sqrt(24)/5

I don't think our teacher cares that much tbh

this is simplified exact and rationalized right

[silent plank]

(instead of making it look like a 45° angle)

sqrt(24) can be simplified

[upper karma]

ah ok

@silent plank so the cos is -1/5

so I did inversecos of -1/5

and got 101.53

this is the ref angle right?

[silent plank]

the reference angle is between 0 and 90.

[upper karma]

so why do I get 101.53 for the inv cos of the cos

[silent plank]

and doesn't care about the sign

so it would just be arccos(1/5)

[upper karma]

ok so 78

[silent plank]

and then you shift it depending on the quadrant to find your actual angle

[upper karma]

how do i find R?

[fiery crypt]

How do you solve this?

[hushed comet]

Do you know the law of sines?

@fiery crypt

[fiery crypt]

Nope

You mean sohcahtoa?

[hushed comet]

yes

that can work

So lets talk about cosine

cos(theta) = adjacent / hypotenuse

we know adjacent, we know theta, we don't know x, our hypotenuse

[fiery crypt]

How will i know the value of hypotenuse?

[hushed comet]

let me do some algebraic manipulations

cos(theta)=adj/hyp

(hyp)cos(theta) = adj

hyp=adj/(cos(theta))

[stable nebula]

Need help with proofing d and e please

need help asap

[silent plank]

were you given a diagram? what's the full question?

[stable nebula]

yeah

I just need to proof d and e

c and d *

That's the question

[silent plank]

when you say 'asap', is this part of a timed test?

[stable nebula]

no, I just have to get it done before my parents get at me

[silent plank]

the question is cut off

[stable nebula]

There's nothign more

says fill in the blank

[silent plank]

Can you show the whole thing? Don't know what they actually want, how they want the answer.

[stable nebula]

Literally what you see above

and fill in the blank

It's a flow chart

flow proof

a. and b. are given

e is the converse of SIA

I need help with c and d

[silent plank]

what's the definition of supplementary angles?

[stable nebula]

Two angles that add up to 180°

[silent plank]

does that answer your question for c?

[stable nebula]

Possibly

Yes it does

Can you help with d?

[silent plank]

what's the relationship between angles 2 and 5?

[stable nebula]

They're same side interior angles

[silent plank]

is that the same as what they have?

[stable nebula]

yes

[silent plank]

so what would be the justification of that statement?

[stable nebula]

I've no clue

[silent plank]

the question is poorly structured

[stable nebula]

I'm sorry, I'm not following

[silent plank]

was the question asking for a proof or reason for the statement?

[stable nebula]

"Use the diagram to answer the question"

It's a Statement/Reason proof

[silent plank]

because the reasoning for d is
they are same side interior angles because they are in fact same side interior angles

i guess you could write given?

what did you mean by

e is the converse of SIA

[stable nebula]

That's the answer

[silent plank]

i've never seen that notation before
what's S|A?

[stable nebula]

SIA is Same-Side Interior Angles

Nevermind, I finished it

Thanks for the help

[silent plank]

you may need to be more specific

just converse of SIA doesn't relate to the other statement nor parallel lines
(imo you should also write it out in full instead of abbreviating it)

[peak mesa]

@umbral snow its not 100% but https://gyazo.com/9fbbec7bce47f2bd7c641afb16f6bd42

one of the problems is the convertor of 3D vector to 2D

im complicating the convertion for nothing..

[peak mesa]

https://gyazo.com/cb6e14579fef038f4218f711b2eeedb4
Done 🙂

[sly marlin]

So, you have the lengths of the medians?

erm...

[dark sparrow]

...

[sly marlin]

what are those angle markings you made?

[dark sparrow]

this is not a good diagram

you'd have been better off just writing out what's equal to what explicitly...

what's G

oh that's a G

it looked like a 6

[sly marlin]

...and ABG totally does not look equilateral

Maybe draw a more accurate diagram

[dark sparrow]

diagram not to scale

@upper karma what?

do you think you're being witty or sth by inserting random Russian words written in translit into your speech

44%? where'd you get that number from

bet you pulled it out of your ass just now

oh you meant that

[worthy root]

Lmao

[dark sparrow]

yeah you just conjugated the verb знать incorrectly lmao

also wow

4 for ч is a blast from the past

call the other ends of the medians A', B' and C', so that the medians themselves are AA', BB' and CC'

consider triangle BGA'

it is not

30-60-90 triangles where one angle is 120° are a bit hard to come by

angle BGA' is 120°

i gave you enough of a hint for you to be able to solve your problem

what's wrong with using trig

how is trig cheating

it isn't cheating and shouldn't feel like it

this anti-trig stance is at best incredibly silly

and at worst incredibly limiting

[somber coyote]

euler/fermat:

[dark sparrow]

let me check

your answer matches mine

please stop doing that, it's honestly just disgusting to look at

[peak locust]

anti-trig stance

that's a new one I must say

[dark sparrow]

@upper karma how is that bullying???

i'm not

the random snippets of broken Russian written in translit are what i'm calling disgusting.

[quiet mason]

noohoy

[dark sparrow]

:?

oh 😒

[hardy monolith]

How will i go about doing this? I think the idea is that you cant use a calculator

[upper karma]

have you done any question yet

[hardy monolith]

I've done the first one

[upper karma]

A?

[hardy monolith]

I think its wrong

Yh

[upper karma]

did you use sin

[hardy monolith]

Can't, its no caluclator

[upper karma]

yes you can do it

haven't you learnt the values of sin(30) (sin60) etc yet

sin(30) = 1/2

1/2 = 5 / x

x = 10

you got it right

[hardy monolith]

Ah ok, that makes sense, i think i must have missed a lesson

[upper karma]

prob did

wait, i have a really good vid ofru

[hardy monolith]

Oh that would be great

[upper karma]

https://www.youtube.com/watch?v=PF2nmCVSUEs

this trick is godly

[hardy monolith]

Thanks so much

u've saved me from a detention

[upper karma]

lmao np

[hardy monolith]

wow that is a good trick

[upper karma]

it really is

watch it a few times

and you'll know trig values z

ez

[hardy monolith]

Ok sorry to bother you but I’ve got this far, what do I do now?

[hardy monolith]

I was asking @upper karma , he knows what i was doing

thnx for rotating it

He will understand trust me

[upper karma]

what trigonometric function do you think you should be using

[hardy monolith]

I thought it would be cos

[upper karma]

okay good

[hardy monolith]

It doesnt make a difference tho

[upper karma]

what side are you looking for

the mathematical name for it

[hardy monolith]

x

the hypotinuse

[upper karma]

hypotenuse yes

we're using sin

[somber coyote]

euler/fermat:

[upper karma]

since we don't have the value of the adjacent

fair enough

but i think it wants working out

it's a trigonometry task lol

homework

[hardy monolith]

umm

[upper karma]

so he has to show working out

[hardy monolith]

yh'

[upper karma]

but we use sin

[hardy monolith]

So whats the next step if ive done my bit right

[upper karma]

no

you used cosine

[hardy monolith]

oke

[upper karma]

use the hand trick

what is sin45

[hardy monolith]

2

square root 2/2

[upper karma]

try again

[hardy monolith]

umm

middle thinger right?

[south lichen]

Does anyone get matrix

[somber coyote]

euler/fermat:

[upper karma]

oh my bad yeah

[hardy monolith]

So

[upper karma]

now rearrange to find hypotenuse

[hardy monolith]

using https://cdn.discordapp.com/attachments/326138757474680852/626824954335330327/73695295149453312.png ??

[upper karma]

as the value for sin45 yes

[somber coyote]

euler/fermat:

[upper karma]

the teacher will want working out lol

have you learnt that yet, lucid?

[hardy monolith]

So how did u get from 45=sqrt2/2 to x=4sqrt2?

Thats the only bit confusing me now

[upper karma]

it's not 45

sin45

which is

https://cdn.discordapp.com/attachments/326138757474680852/626824954335330327/73695295149453312.png

[hardy monolith]

yh sorry

https://cdn.discordapp.com/attachments/326138757474680852/626819544161452036/IMG_7325.JPG

Thanks but i will need to do workings

[somber coyote]

euler/fermat:

euler/fermat:

euler/fermat:

euler/fermat:

euler/fermat:

euler/fermat:

[hardy monolith]

Yeah, i think im fine, thank you

Thanks @upper karma

[idle bloom]

Sorry, I know this might sound like a really silly and basic thing, considering I've done this topic a ton of times, but I always struggle to remember the exact values of the (sin,cos and tan) functions. So basically I'm asking does anyone know a smart way to remember them all and if so thanks 🙂

[dark sparrow]

there's this one thing... the hand trick

e/f i don't think they're asking how to memorize continuum-many numbers