geometry-and-trigonometry

[trail minnow]

i pity

[small raptor]

I feel like an underachiever. I only got to precalc by end of high school and nearly failed it

[trail minnow]

nah

it doesn't really matter how "fast" you learn something

i just wanna do this stuff cause it's fun

[hard gale]

well yk there's other things than math also

[small raptor]

Maybe i did fail it. 🤔

Always amused me how I did better in literature despite being dyslexic

[trail minnow]

actually this reminds me

it's already 11

i need to study

[hard gale]

[small raptor]

Study o clock

[trail minnow]

[vague pagoda]

"The course has two objectives: the practice of precise proof techniques and the understanding of the classical results of geometry. Key contents include basic geometry proofs, harp and ruler constructs, triangular mark points, point potency, Ceva and Menelaos sentences, Euler's line, 9-point circle, homotethy and inversion."

thx google translate!

(a description of the classical geometry course)

[trail minnow]

lol

[hard gale]

harp

i like this name for compass

[trail minnow]

that's quite different from over here

where it is much more elementary and focused on greek shit basically

[vague pagoda]

i see

[trail minnow]

sadly US dumb

[vague pagoda]

"The course is conducted as a self-study under the guidance of a teacher. The content is the theoretical basis of the analysis: the axioms of real numbers, the epsilon delta definition of the limit, and the continuity and differentiability of functions. The aim of the course is to train the student for independent study of difficult material. The course can also be done by self-studying another equivalent level."

what does this sound like to u?

[fossil ledge]

Precalc

[worthy root]

I never had such courses in my sylabi

😭

[vague pagoda]

its not precalc

we dont have such a subject

[granite mortar]

its intro to real analysis

except there is some stuff missing

or not mentioned

[vague pagoda]

yeah its probably not mentioned

[worthy root]

I always used to come first in my remedial class 🤓

[vague pagoda]

"self-studying another equivalent level"

what could this be

[worthy root]

,w remedial

[somber coyote]

Display results online and refine query

Requested by Krishna#4971

[worthy root]

Wolf has really bad defination of words

[vague pagoda]

ofc

[worthy root]

Not you buddy

[vague pagoda]

I know

[worthy root]

Big good wold

Wolf*

[vague pagoda]

who u

[narrow sleet]

@worthy root What?

[vague pagoda]

wolfram alpha

[worthy root]

I want you to do something @narrow sleet

[narrow sleet]

Sell my soul to a demon?

[worthy root]

Cut the Bad

You are a good and helpful wolf

Better than most of hoomans

[vague pagoda]

"The course introduces the mathematical modeling of natural phenomena and the processing of models using a computer. Examples include biology and physics: population models, disease spreading, heat conduction, resistance to motion, and wider entities. At least the numerical solution of the differential equation is treated as a central mathematical content."

[worthy root]

[vague pagoda]

what could this be

[narrow sleet]

I had a backstory of my nickname

So nah

[worthy root]

Ree

Bad wolf

lol

[narrow sleet]

Maths modelling seems fun

[worthy root]

Yup

[small raptor]

Wolf in the streets and a grandma in the sheets

[worthy root]

I agree

[narrow sleet]

😂

[vague pagoda]

@narrow sleet would it be a course worth taking?

[worthy root]

That you feel is good for you

[narrow sleet]

If you gonna do pure science or cs, then yeah

[vague pagoda]

I am considering a math or cs degree

but idk about cs anymore

[granite mortar]

theoretical cs is basically a branch of math

[narrow sleet]

I would say do differential equation first then this

[worthy root]

I will make my own degree

[vague pagoda]

ok ok

[granite mortar]

you can always do both ^^

(i am doing both CS and math)

will drop CS though soon

[trail minnow]

CS isn't real

do chem

[worthy root]

I will do triple degree

[narrow sleet]

Why? @granite mortar

@trail minnow YASSSS CHEM

[trail minnow]

hehehe

chem good

[granite mortar]

im dropping it, because starting masters degree

[worthy root]

I will do a degree in math-ee--matics

[granite mortar]

and i dont want to do both in paralell

[narrow sleet]

Oh

[trail minnow]

just get the bachelors for CS

[vague pagoda]

so these are the options I can take: matrix calc, diffy q, mathematical modelling, basics of analysis, complex numbers and functions, classic geometry, game theory, statistics (in depth), a special course (topic changes every year, earlier topics include history of math, advanced number theory, Fourier analysis and inequalities)

[narrow sleet]

Chem is always good

[granite mortar]

will take a few more CS classes, but then im done

[worthy root]

Cotton what do you want to become

[vague pagoda]

any recommendations

[granite mortar]

in bachelors its ez

[vague pagoda]

idk yet im confuusd with everything

[granite mortar]

i can use same thesis for both degrees

[vague pagoda]

but pls tell me which courses should i take

[narrow sleet]

So you wanna do maths right for degree?

[vague pagoda]

maybe

[granite mortar]

how many can you take

[vague pagoda]

as many as you can fit into your schedule lmao

[narrow sleet]

Pure or applied math?

[granite mortar]

take analysis definitely

[vague pagoda]

idk yet...

[worthy root]

I k

I like applied math

I like application problems

[vague pagoda]

im not experienced with math

[worthy root]

Nor do I

[granite mortar]

if this is real analysis intro, it will give you a taste of math

[vague pagoda]

so I know very little

[narrow sleet]

If applied, I would say diff calc, maths model, game theory and stats

[vague pagoda]

diff calc?

[narrow sleet]

Sry diff eq

[vague pagoda]

lol

diff calc we study anyway

[worthy root]

In which grade are you in ?

[vague pagoda]

going to 9th in less than a month here but I have skipped a grade

So people are 1 year older than me

9th is not high school here

just mentioning this

but we need to apply to high schools in February-March

[worthy root]

Lmao I would listen to logics new album "confession of a dangerous mind" instead of taking all these courses. It would be so much work . 🤓

[vague pagoda]

lmao

work is good

u need to study hard in uni tho

[granite mortar]

is it really work, if its fun

[worthy root]

Anything in excess is poison.

[vague pagoda]

math is fun to me, anyway

[worthy root]

I used to work very hard in my class 10 . But I just passed .

[vague pagoda]

though I wonder if my opinion will change when I get to uni

:(

[worthy root]

I only score good in math and sci

They were 90 Mark in math and 75 in sci

[vague pagoda]

Also you need to know that basically everything we learn is arithmetic disguised as algebra

[narrow sleet]

If you like pure maths, do analysis, complex num and func, classic geo

[vague pagoda]

we have no algebra here

[worthy root]

Just passed meaning i got 56%

[vague pagoda]

as a subject

its pre-algebra at most

[granite mortar]

so sad

[worthy root]

You need algebra

[vague pagoda]

"algebra 1 and 2" level stuff comes in high school

I know you need it

[worthy root]

But you are doing calculus , differential as and stuff without algebra. I am sure you would stuck

[vague pagoda]

I mean its taught in high school before calc and vectors and such stuff

[worthy root]

Oh

[vague pagoda]

I know algebra tho

not perfectly tho

[worthy root]

That's fine

I don't either

But I will

I can't become perfect in some months

[vague pagoda]

we learn sohcahtoa (right triangle trigonometry) in 9th grade

[worthy root]

I need time

Like 2 years

[vague pagoda]

also drawing graphs of functions n functions in general

[worthy root]

I suck at graph

[narrow sleet]

Nice

[vague pagoda]

I already did the graphing part last year

[worthy root]

Bullshit looks better than my parabolas .

[vague pagoda]

from our 9th grade book

[upper karma]

Can someone help me

[worthy root]

Atleast bull shit has a perfect shape

But my parabola

[vague pagoda]

my parabolas were good

[worthy root]

I think we must stop chatting here

[astral patio]

Is there an identity for csc(2theta)?

[fossil ledge]

Yes

[gritty siren]

there's one for sin(2θ) so you can just copy it

[fossil ledge]

1/Sin(2x)

Then just apply the sin2x identity

[gritty siren]

I saw that

[fossil ledge]

[astral patio]

ah, of course

thanks

I'll try that

So if csc2theta is 4/3

1/sin2theta is 1/3/4?

1/.75

So if csc=4/3

I got csc2= 8 / 3root7

that good?

[devout shell]

$\csc(2\theta)=\frac{4}{3}$ and you ask what $\sin(2\theta)$ is?

[somber coyote]

⚡Amphy⚡:

[astral patio]

no, sorry

csc = 4/3

I'm looking for csc2

Cool bot 😮

$\csc\theta=\frac{4}{3}$

[somber coyote]

Rokitur:

[gritty siren]

Best bot :p

[astral patio]

Seems difficult to type it all in tho 😂

[somber coyote]

Rokitur:

[astral patio]

bleh, forget it 😦

[astral patio]

Does this look right?

[gritty flare]

You couldve used triangle method to get cot(x) as well.

Also... isnt tan(pi/2) undefined

,w tan(pi/2)

[astral patio]

The initial problem asked me to find tan(pi/2-x)

[gritty flare]

Thats a BIG nono

That division on tangent

You can NOT divide by pi/2

But there is a solutions

[astral patio]

It seems tan(pi/2-x) = cotx though

[gritty flare]

It is

But dont use division by tan(pi/2)

You can not divide infinity by infinity

Thete is a simple way to prove that without your thing

[astral patio]

Do tell, cause this sucked. 😦

❤

[gritty flare]

$\tan(90^{°}-x)=\frac{\sin(90^{°}-x)}{\cos(90^{°}-x)}$

[somber coyote]

Solarkoid:

[gritty flare]

You can continue frkm here I think

[astral patio]

Oh, dang

[gritty flare]

Btw 90 there is 90 degrees or pi/2

[astral patio]

Just changed it to degrees

[gritty flare]

I changed to degrees for simplicity of writing

Yoy keep 90 as pi/2 doe

[astral patio]

So, I should already have tan though, right?

I was originally given cscx=4/3

[gritty flare]

Actually you couldve just solved with a simple triangle method

But nvm that

[astral patio]

So I found tan to be -3/sqrt7

[gritty flare]

Prove that
Tan(90-x)=ctg(x) and youre gucci

[astral patio]

Well, that's how I found tan

I don't know ctg

<--- amateur

[gritty flare]

...noh wait

Lol

Ctg is just some place make cotangent that

Instead of cot

Im sry im a pleb

Basically what i can tell you is
More than half of it is correct

And use different method to prove tan(90-x)=cot(x)

Follow from my proof

[astral patio]

So, I used the triangle method to get cot

super easy

unless I knew those were identities

[gritty flare]

You can use triangle method to get
tan(90-x)

Directly

[astral patio]

a=3, b=sqrt7, c=4

So tan was 3/sqrt7

tan(90-3/sqrt7)?

[gritty flare]

Csc(x)=1/sin(x)=hypotenuse/opposite

You couldve begun from thete

Now

4 and 3 so other side is sqrt(7) as u said

So now you know (which u shud) that
tan(pi/2-x)=cot(x)=adjecent over opposite =sqrt(7)/3

Sign is chosen depending on which quadrant this is happening in

[astral patio]

2

[gritty flare]

So -

[astral patio]

yea

[gritty flare]

I may have messed up cause im doing this on top of my head

Yep i did wait

[astral patio]

I'm missing something simple here. I know tan and cot are flipped.

[gritty flare]

You know what that co means?

[astral patio]

but I'm not grasping how pi/2-x relates

[gritty flare]

That co means exactly that

Complementary

[astral patio]

cot = 1/tan

[gritty flare]

Its exactly how
Sin(90-x)=cos(x)

Which can be proved using thentriangle method

Same goes with all others

[astral patio]

so 1/tan = tan(pi/2-x)

[gritty flare]

Ill show u wait

Imma draw it

[astral patio]

Thanks for your patience

[gritty flare]

I hope you see it well

[astral patio]

Thanks for that, very helpful.

[gritty flare]

So basically you use that

And youre done!

[astral patio]

Familiar with Gaussian elim?

[gritty flare]

I dont like to use it

Its nice doe

So not rly

[astral patio]

Yea, my homework assignment requires me to do all the problems with it for practice 😦

I feel like it takes a magic eye

Gift of foresight

[gritty flare]

Oh that is true. Its like a minigame puzzle

So its kinda fun

[devout shell]

Why not use elimination?

Substitution is only really viable with 2x2 systems

Anything past that, elimination is the way to go

[astral patio]

I can do sub, it's systematic. I'm having trouble just coming up with things for elim to work. I'm still working a problem, but I can post it when I'm done. I'm probably making it harder than it has to be.

Ok, not only did I make this long and drawn out, but the answer is wrong.

Can anyone tell me where I went wrong? Maybe I'm performing one of the rules incorrectly.

[devout shell]

Oh man maybe I can get to this later

[astral patio]

oh man, watching this vid...I think I overdid it.

Gonna try again.

[silent plank]

your error was from 7→8. (should be -4)

also from 3, i would use LCMs to immediately eliminate another term

R2 > 5R2 + 3R3

[astral patio]

I just retried it. I'm screwing this whole thing up 😭

[silent plank]

still couldn't get it in your 2nd attempt?

[astral patio]

Just going in circles

[devout shell]

you are sure that your original system is correct?

[astral patio]

yea

[devout shell]

why the heck they make you go all the way to the identity matrix

you only have to get it to be upper triangular then you are good lol

[astral patio]

I don't know. I did that on my own.

Video I just watched only zero'd out the lower left triangle

[devout shell]

yes, that works

you went all the way to the identity matrix, which works but more work involved

[astral patio]

I've gone through like 6 whole 8x11 sheets trying to get this one problem. 😫

[silent plank]

ur allowed to switch rows, so just do whatever looks most efficient to get 0s

[devout shell]

can you show the original system of equations?

[silent plank]

the original looks fine,

just that small error i mentioned above

[devout shell]

looks like romanov will work with you on this one

[silent plank]

doing R2 -> 5R2 + 3R3 from your stage 3
gets 0 -10 0 = -70
0 1 0 = 7 (y = 7)

combine that with R3 to get z,
then combine them all to get x

[astral patio]

Eurika!!

@silent plank Sorry, I just couldn't grasp it. I yolo'd it, and now I have the concept.

[devout shell]

upper triangular is the way to go, you see why it's much easier to do that?

[astral patio]

Yea, but it took me forever to see the pattern.

I knew what the ultimate goal was, but I couldn't figure out the strategy of getting there. Basically starting in the corner and working your way over.

[narrow sleet]

You just need to practise more

[astral patio]

Yep, doing more problems now. Thanks guys.

[devout shell]

elimination is very systematic

using terminology such as pivots will help formalize the process

wait until a zero shows up in a pivot position

[upper karma]

even more formal ||use elimination/permulation matrices and do multiplication every step ||

[devout shell]

ultimate form: PA=LU

[upper karma]

yas

[devout shell]

just solve Lc=b and then Ux=c

ez day

[upper karma]

find A^1

[devout shell]

the cross out line makes it seem like it says find A^1

[upper karma]

hee hee

[cinder owl]

hey I have a question

can someone help me with number 31?

[fringe dirge]

What have you tried?

[small raptor]

The given parallel should be your key focus as the properties tells a lot about the angles.

You can even extend the lines if you need to

[astral patio]

I'm working some geometric sequence problems: 18, -6, 2, -2/3...

I figured out the ratio is -1/3

I plugged in the known data into the formula: a10 = 18(-1/3)^10-1

I used 10, because the question asks me to find the 10th term

I don't understand the 10-1 part

What's the -1 for? Isn't that just 9?

[narrow sleet]

Yes but you wanna realise in a neat formula

Where Tn = ar^(n-1)

[astral patio]

So, what would each step look like?

Let's just say from a1-a2

It's just 18 x -1/3 "n" times, right?

er

Not 18

But each subsequent answer

[narrow sleet]

No, it's 18 × (-1/3) "n-1" times

Because T1 is just 18, you didn't multiply any "-1/3" in it

[astral patio]

So 18x(1/3) = -6

then -6x(-1/3)= -2

[narrow sleet]

Yes

That's how you form a geometrical progression

[astral patio]

I just keep doing that all the way to 10 times

I'm not actually doing anything with that n-1, right?

[distant sonnet]

?

[astral patio]

That's just telling me how many times to go down the chain, no?

[narrow sleet]

No

T10 is saying the 10th number

Not the number of times

,rotate -90

[astral patio]

oh, of course

Thanks!

[narrow sleet]

👍

[astral patio]

I got a10 = -2/2187 LOL

Crazy answer

[devout shell]

the terms are rapidly decreasing so makes sense lol

[astral patio]

I did something wrong here.

[dark sparrow]

yeah you did

how did that 1 become a 9

[astral patio]

uhhh, good question...one sec

I think I had in my head 10-1

[dark sparrow]

yeah well there's your fuckup

[astral patio]

So that's 17

Isn't that a11?

[dark sparrow]

why would it be a_11 if you calculated a_10?

[astral patio]

Look at my breakout underneath

at each step

[dark sparrow]

you went from a_6 to a_8

skipping a_7

[astral patio]

Much ❤

[astral patio]

I feel I'm getting the hang of these. Can someone look this over please?

[placid tide]

https://cdn.discordapp.com/attachments/593146984911601684/600030727924482069/image0.jpg

1. plx

[silent plank]

what are you actually having trouble with doing?

[proud bramble]

Hey can someone help me with a general trigonometric problem

[dire rampart]

[proud bramble]

Nevermind I foudn it

Thank you for your time though haha sorry 😃

[stoic wraith]

https://www.sebz.xyz/i/firefox_July_14_2019_CreamyIberianmole.png
I've come up with 3.0031x10^13 as the distance from earth to the star and I'm given that for either point in time the value of the adjacent side (earth to sun) is 9.3x10^7. I've tried using arcsine to get the parallax but I'm getting domain errors on my ti-84. I'm not sure if I'm on the wrong track or if I'm just inputting my data incorrectly. Any ideas?

[chrome fiber]

are you sure your finding the arcsin of opp/hyp?

[stoic wraith]

I've tried both ways just for the hell of it, hyp/opp opp/hyp and I get a domain error

I'm not sure if I need to perform an operation to make the values smaller or if it's an issue with my calculator.

Just checked, I'm in degree mode, for a second I thought I might have been in radian mode.

[upper karma]

Hi can someone help me figure this problem out?

32

unless there's no solution. which I'm pretty sure might be the case since I only have the volumes.

[stuck torrent]

When the side length is scaled by a factor of s, the volume is scaled by s^3

[upper karma]

ok

[stuck torrent]

and I think the scaling the question is asking about is the original s

[upper karma]

ok thx. the answer was 6:1 for left to right

[narrow sleet]

Yes

[upper karma]

Hi guys, can I get some help with this question?

This is the way they solved it (part of it), but I don't understand this. Wouldn't this be the solution if it would be cos2x + sin(5pi/2) = 1 NOT cos5x?

[keen aspen]

Hmm?

They are rewriting cos(5x) as 1-2sin^2(5x/2)

They are using the double angle for cosine

cos(2x)=1-2sin^2(x)

[upper karma]

yes but wouldn't cos(2x) be 1 - 2 sin^2(5x/2)? and not cos(5x)?

[keen aspen]

Okay, let me show you this

cos(2u)=1-2sin^2(u)

Right?

[upper karma]

yes

[keen aspen]

Now let u=5x/2

cos(5x)=1-2sin^2(5x/2)

[upper karma]

ohhhhh

i got it now

thank you

[keen aspen]

Np

[upper karma]

Ill see if I can get to the same final answer as them now

[upper karma]

?

<@&286206848099549185>

[obsidian moon]

change tan into sin/cos

[upper karma]

how would i do that

[narrow sleet]

tan x = sin x / cos x

[upper karma]

shit

i still dont understand

like i know

that

[narrow sleet]

Move -2sinx to the other side so it's tan x + 2 sin x = 0 then tan x = sin x / cos x then factorise sin x

Then you can try to do the rest

[trail minnow]

@upper karma do you know the unit circle?

[upper karma]

yes

[fossil ledge]

I would just use the Sin double angle identity?

[trail minnow]

so you know that sin(x) corresponds to the y axis and cos(x) to the x axis?

[fossil ledge]

You’ll get sinx = -sin2x

[upper karma]

yes that makes seense

sense

[trail minnow]

can you see from this diagram why tan x = sin x / cos x?

[upper karma]

yeah

[trail minnow]

👍

so from there you can see that if $\tan \theta = - 2 \sin \theta$, $\frac{\sin \theta}{\cos \theta} = - 2 \sin \theta$

[somber coyote]

hegel:

[upper karma]

yeah

yeah

i can visualize that

[trail minnow]

from here just multiply out the cos

and use the double angle identity to simplify

[upper karma]

whats double angle identity

[trail minnow]

ah

these identities are important to know

[upper karma]

oh yeah i have those written down

tbh im just trying to pass this class

but its not sin(2a)

its sin (theta)

[trail minnow]

theta and a in this case are just variables

they are interchangeable in this case

it's like when sin formulas use x vs theta

anyway you can see the sin(2a) formula is

2 sin(a) cos(a)

and above we have

$- 2 \sin \theta \cos \theta$

[somber coyote]

hegel:

[trail minnow]

so we can convert this into $ - \sin 2\theta$ right?

[somber coyote]

hegel:

[upper karma]

i think

[trail minnow]

so just to rewrite

we have right now

$\sin \theta = - \sin 2\theta$

[somber coyote]

hegel:

[trail minnow]

now looking at our question https://media.discordapp.net/attachments/326138757474680852/600328960760348691/6610c47ed9280b2c190646323c74adc4.png

[supple abyss]

not the best choice

[trail minnow]

how can we find the solution to this equation in the interval 0 < theta < 2x?

[supple abyss]

it was better left as $2\sin(\theta)\cos(\theta)$

[somber coyote]

CaptainLightning:

[trail minnow]

really? i find this easier to work with lol

[silent plank]

wolf mentioned it was easier to factorise sin(theta)

[supple abyss]

yes

the big brain play

[fossil ledge]

Oh yea

That’s so much easier

[trail minnow]

factorizing is probably the correct choice here : p

[fossil ledge]

Factorizing is massive brain play

[trail minnow]

$\sin \theta - \tan \theta = 0$

[somber coyote]

hegel:

[trail minnow]

$\sin \theta - \frac{\sin \theta}{\cos \theta} = 0$

[somber coyote]

hegel:

[fossil ledge]

Still multiply the cos

[trail minnow]

$\sin \theta(1- \frac{1}{\cos \theta}) = 0$

[somber coyote]

hegel:

[silent plank]

wrong signs. and its 2 sin(theta)

[trail minnow]

oh oops

$\tan \theta + 2\sin \theta = 0$, $\sin \theta(2 + \frac{1}{\cos \theta}) = 0$

[somber coyote]

hegel:

[upper karma]

um damn

im kinda getting a lil confused here

[trail minnow]

yeah sorry we kinda went off on our own here lol

[silent plank]

ignore most of the stuff before the most recent equation

[trail minnow]

yes that was dumb and inefficient

[silent plank]

steps so far
convert tan to s/c
move 2sin to the left
factorise out sin (don't eliminate directly or you'll lose solutions)

[upper karma]

how do u factorize sin

[narrow sleet]

a - a/b = a(1-1/b)

[upper karma]

uh

[silent plank]

$\frac{\sin \theta}{\cos \theta} + 2\sin \theta = \sin \theta( \frac{1}{\cos \theta} + 2) = 0 $

[somber coyote]

ramonov:

[silent plank]

and then solve for theta

[upper karma]

How would I find the cosin of 195 degrees

[silent plank]

are you looking for the exact value?

[fossil ledge]

Cos(180 + 30/2)

Use half and sum identities

[upper karma]

I got square route of six plus square route of 2 over 4

[fossil ledge]

Essentially rewrite in terms of 0,30,45,60,90

Sounds like a reasonable number

Can not confirm tho

[silent plank]

easier to simplify it to

• cos (195 - 180) = -cos (15)
  = -cos(60 - 45)

yeh that seems right (sry missed the minus sign)

[dark sparrow]

@upper karma first off, it's square ROOT, not square route. second, would it really kill you to actually write that in notation, using sqrt() for square roots?

cos(195°) < 0, though, so your answer is definitely incorrect

[upper karma]

Well it’s already in so

Thanks anyways

[worthy root]

Heu

$2sin^2x-3sinx+1=0$

[somber coyote]

Krishna:

[worthy root]

What are a,b,c of this quadratic

[devout shell]

define x := sin(x)

then you will see

[fringe dirge]

maybe use y = sin(x)

[worthy root]

Ok

[devout shell]

was about to say y instead lol

or w, or something that isn't a, b, c, x, y, or z lol

[worthy root]

So

a=2

b=-3

c=1

[devout shell]

yes

[worthy root]

Ok

How many solutions it can attain over interval (0,\pi)

[devout shell]

solve that quadratic

[worthy root]

Ok

[devout shell]

sub back in sin(x) and then solve for the solutions in that interval

[worthy root]

y=1

Or y=1/2

sin(pi/2)=1

sin(30)=1/2

So 2?

@devout shell

Eeh

Sin(150) as well

3 solution

[devout shell]

sounds good then

I didn't check but sounds like you did it right

[dark sparrow]

@worthy root you're being inconsistent in your use of radians and degrees

stick with one

don't mix the two

[worthy root]

Yea sorry

[summer plume]

Hi, so I was hoping someone could better explain to me why the answer is what it is, but I was also hoping to post it as a picture. Is that alright?

[fringe dirge]

[dark sparrow]

[summer plume]

Why is it COT instead of TAN?

[sly marlin]

tan = opposite / adjacent. cot = adjacent / opposite. Multiply that by opposite and you get the distance between P/Q and the bar.

[summer plume]

So, in order for me to find the distance, I have to multiply the opposite. Having me to use cot rather than tan, because if I use tan that'll lead me to multiply using the adjacent. Resulting in an incorrect answer. Right?

[indigo orbit]

need help >.>

[small raptor]

what does the given tell you?

[tawdry pivot]

,rotate

[dark sparrow]

please don't tell me you're expected to make a two-col proof

[indigo orbit]

I am ;(

[worthy root]

Lol

SAS congruence

[upper karma]

I completed the calculations but Im having trouble with the questions can anyone provide assistance please and point me in the right direction

[upper karma]

i hate two column proofs. thankfully, for my class they're outdated and not mandatory

[mighty narwhal]

[mighty narwhal]

I am unable to do these geometrically, but I made an interactive desmos "playground" so you can play with this setup and gain intuition
https://www.desmos.com/calculator/cdpeydy2tm

[upper karma]

@mighty narwhal by evaluate, do they usually want you to take the definite integral with respect to those two points

[mighty narwhal]

Yea

[upper karma]

I was thinking about doing that and plugging those radian values into cosine to evaluate it with x values

is my intuition alright there?

[mighty narwhal]

Whats the exact problem?

[upper karma]

Let me get on my laptop

[mighty narwhal]

Ohkay

Well thats easy

f(x) is already described in terms of x

So you just integrate it (indefinetly)

$\int \sqrt{1-x^2}dx$

[somber coyote]

DarK:

[mighty narwhal]

Done

,w integral from 0 to 1 of sqrt(1-x^2) dx

[somber coyote]

Display results online and refine query

Requested by DarK#2404

[mighty narwhal]

A(0) is 0

?

b??

Wait what

wrt theta?

It will be

$\int -\sqrt{1-cos^2\beta}sin\beta d\beta + \frac{\pi}{4}$

[somber coyote]

DarK:

[mighty narwhal]

For the area wrt beta

(Theta)

(I used beta instead of theta)

[gritty siren]

[mighty narwhal]

Its not really trivial

You can get it by looking at the wrt x case

$\int \sqrt{1-x^2}dx$

[somber coyote]

DarK:

[mighty narwhal]

Then observing, that x is cos(theta)

So you sub in x=cos(theta)

[gritty siren]

Why are you calculating an indefinite integral in the first place?

[mighty narwhal]

and you get the ugly one wrt theta

Because why not ._.?

[gritty siren]

calculating $\int_0^xf(t)\d t$ seems more intuitive

[somber coyote]

Tuong:

[mighty narwhal]

Well, true
and also you can just do

$\int_0^{\cos\beta} f(t)dt$

[somber coyote]

DarK:

[mighty narwhal]

To get it wrt beta

But I always prefer indefinite integrals for some reason

x=cos theta
dx= sin(theta) d(theta)

Sub in, and you got the indefinite integral wrt beta

But the problem asks you to do it geometrically, not with integrals

So dont confuse yourself with trig subs and other things you dont learn yet

[gusty drum]

Hello

I need help with law of sin

can someone help

@daring baneryone

[devout shell]

lol they got pinged on accident again

also, why do you think pinging everyone is a good idea?

[gusty drum]

i am desperate

[dire rampart]

bruh

[upper karma]

!help

.help

How do I use the bot

I need to flip these images

!rotate

/rotate

$help

[formal bolt]

Send the images

,rotate 180

[upper karma]

Thanks

,rotate 180

Lmao

,rotate 180

[small raptor]

So... any reason for this image?

[formal bolt]

To flip them I think

[umbral snow]

Lol

@upper karma
Do you need these images to be here? Consider deleting them for users on data

[small raptor]

Considering this is a feature of the bot, could they DM the bots for this?

[formal bolt]

@somber coyote refuses to collaborate in DMs

[dire rampart]

it has to get to know u first before dms smh

[formal bolt]

Lol actually I take it back, he does rotate images but won't render LaTex it seems

[small raptor]

Probably a better suggestion than someone cluttering up the chat then.

[upper karma]

How do I delete

[dire rampart]

click delete?

ill get it for u

[upper karma]

I’m not the bot

[dire rampart]

oh

[formal bolt]

Why LaTex doesn't work in DMs? :((

[upper karma]

Thanks

[dire rampart]

u click on the bin symbol

next to the code

[trail minnow]

and that's why : p

[formal bolt]

Where?

[trail minnow]

oh wait wrong channel oops

[dire rampart]

I'd just create a server and invite texit

[formal bolt]

That's really a good idea

I needed a quiet place to experiment

[devout shell]

I have a personal server filled with lots of LaTeX lol

[dire rampart]

same

[formal bolt]

Will you ever invite me Amphy?

[devout shell]

Why you want to be on my personal server lol?

[formal bolt]

Cause reason number 1 I am unable to open a server myself lol and reason number 2 I can be a very good-mannered guest

[devout shell]

I can make another server and let you on it to experiment with LaTeX then, my personal server has personal stuff as you can imagine lol

So I keep my personal stuff to myself as I would like to of course

[formal bolt]

Yeah I was simply joking ahah, I'll figure this out somehow

[devout shell]

I’ll make a server later then

[vagrant elk]

my personal latex server has stuff in it like commutative diagrams that I like to have on hand

for memes

[devout shell]

And get texit on there for you to play with

[small raptor]

Personal Latex server sounds kind of kinky

[devout shell]

[formal bolt]

What does it mean?

[devout shell]

I’ll just send you an invite later, that’s about all you need to know

But get yourself a pfp that’s not the default one

[formal bolt]

I am grateful, I can't believe being this lazy could lead me somewhere

pfp would be?

[vagrant elk]

change your image

[small raptor]

Curious if anybody knows, but how does one go about solving sin(x) + cos(x) = sqrt(2) without using multiple angles approach to solving it, but simply quadratic equation route of solving? Or is that possible without multiple angles approach and the Textbook being a jerk by hiding that route in the next section?

Seems most solving sites resort to a short-hand identity that looks like just multiple angles approach, and certainly, that fits with what I have done thus far by squaring both sides... etc.

[fossil ledge]

you can square both sides

youll get sin^2 + 2sincos + cos^2 = 2

that becomes 1 + sin2x = 2

sin2x = 1

[small raptor]

Yes, I know this. However, the solution comes from the multiple angles approach at this point.

[fossil ledge]

i dont know what multiple angles approach is

there is another way

2sinxcosx = 1

[small raptor]

From this point on, you would go 2x = pi/2 + 2kpi. The divide out. This gets you pi over 4 which is the answer.

[fossil ledge]

sinx * cosx = 1/2

wait what

oh

I do not understand where that 2kpi is coming from

but yea

[small raptor]

2pi is the period, and the k is integer solution or something. I'm a bit rusty as I just did this. 😛

I'm ignoring it for the most part as it's not related to the solution

I guess it's more or less how does one get pi /4 without seeking all solutions using multiple angles as the textbook suggests one can.

[dire rampart]

multiply both sides by sqrt2/2

should help

[small raptor]

Nope that doesn't make any sense to me

[dire rampart]

sqrt2/2sinx+sqrt2/2cosx=sin(x+pi/4)

[small raptor]

I guess I"m not sure where you're getting sqrt2/2 in this regard. May be over my head

[umbral snow]

@small raptor
There are infinite solutions to this equation, no matter what your solution method is. Knowing the solutions when inverting sin is inevitable

[wanton berry]

i have vertical asymptote as 2 but seem like i was wrong

[vagrant elk]

there is a vertical asymptote there with x=2

[wanton berry]

the graph seem a bit off though

[vagrant elk]

how so

[wanton berry]

the asymptotes line seem closer to the bottom graph than the top

[vagrant elk]

so

[wanton berry]

dont it have to be in between the graph?

[vagrant elk]

it is between them

[wanton berry]

I'm just making sure, thank you

maybe i could find a way to prove it

[vagrant elk]

simple: the function is undefined at 2, and some rudimentary examination of behavior as you approach that value confirms it

[brave gust]

I have a question. This is rational functions graph and equation

In the last part next to xmin x max. How did he come up with (2,7) as discontinuous point if X cannot equal -2?

I cannot get a equation to equal 7 unless I sub in -2? 😦

[white mountain]

can some1 help with a simple problem ?

I have the triangle ABC and c = 120 degrees
ac = 2 cm
bc = sqrt(3) - 1 , and i have to find ab

[tawdry pivot]

cosine rule

[idle bloom]

Law of cosines is my first thought

[mighty narwhal]

yupp

@white mountain

[white mountain]

Thank you smart sir

[old wren]

https://gyazo.com/236eeb36748929d2844a911ff3ec4b01

cAN someone help

[devout shell]

Three noncolinear points define a: ?
Therefore R, L, and S define a ? Which makes them ?

@old wren

[old wren]

idk

i failed math this year with like a 10

[devout shell]

do you have your book or anything with you?

[upper karma]

@old wren R, L and S are coplanar

[worthy root]

Both answer are correct

[dim crescent]

Hey, I suck at maths, or even defining the branches of math.

I am looking to see what you call this. Question: I am trying to find/define the angle in which when PURPLE STAR is "Looking" or "Aimed at" the Red circle, what angle would the line be between the other stars that leads to the Red circle.

Re-directed here from General-discussion.

[dark sparrow]

no idea what you're on about

[keen aspen]

First find x

Also be careful which quadrant its in

Cosine is positive which means 1 or 4, tangent is negative, so x is an angle in the 4th quadrant

[lusty quest]

mmm i see, thanks

[dim crescent]

@dark sparrow Consider you have three cameras all trying to look and follow the same position, the camera in the middle drives that operation. Now you need to work out the angle difference between the two that follow the primary camera.

[lusty quest]

i cant seem to figure this one out

isnt it like 5theta -26 = 90 - theta?

[idle bloom]

Well cos(theta) = sin(theta + 90°)

So start with that (remember secant and cosecant can be rewritten in terms of sine and cosine)

[dire sand]

How do I tell if there will be an ambiguous case?

[waxen gorge]

@idle bloom hi

[quiet mason]

remeber complementary angles?

just know that sec k = cosec (90-k)

or in your case sec(theta + 14)=cosec(90-(theta + 14))

@lusty quest

[lusty quest]

@quiet mason ill try it again today, thanks

[gusty drum]

Ambiguous case is like in law of sines when you’re given two sides and an angle

[upper karma]

Can someone quickly explain what’s the reason

[gusty drum]

someone

explain this

The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°. a. Find the length of the diagonal. b. Find the length of the shorter base.

I need help

[upper karma]

Since it is isosceles, the angles are the same and must be 70 degrees.
sin 70=x/7, and that is the height of the trapezoid, or 6.58 feet
cos 70=y/7, and that is half the distance that the longer base is over the shorter base.
y=7 cos 70=2.39 feet
The longer base is 4.79 (rounding) feet greater than the shorter base, so the shorter is 17.21 feet long.
The diagonal: The base of the right triangle for which the diagonal is the hypotenuse is 22-2.39=19.61 feet long. The height is 6.58 feet. Square both and have 384.390+43.268=427.658. The hypotenuse is the square root of that.
The square root of that is 20.68 feet. Diagonal. @gusty drum

[gusty drum]

thx

this is from gogole

[gusty drum]

dumb

[copper valve]

try not to give out free answers to people @upper karma
we want people to learn, not just get their homework marks.

[gusty drum]

I want to learn

[copper valve]

did you read #❓how-to-get-help

@gusty drum

[heady acorn]

O

[upper karma]

@upper karma did you get your answer

Its a parallelogram as opp sides are congruent

Angle K and L are congruent (you should know why at this point)

NGL is congruent to another triangle

Find the triangles congruent using the postulates

I'm not great at geo, but I'm currently learning

[lusty quest]

A student makes the following claim: “Since sin²θ+cos²θ=1, I should be able to say that sinθ+cosθ=1 if I take the square root of both sides."

i feel like it would be true, cause square rooting both sides would remove the square

[devout shell]

lol that's not how square root works when we are dealing with sums

$\sqrt{a+b} \neq \sqrt{a}+\sqrt{b}$

[somber coyote]

⚡Amphy⚡:

[formal bolt]

Expand $(a+b)^2$ by yourself

[somber coyote]

Mat:

[vagrant elk]

h m m

[lusty quest]

huh, ok so i was almost tricked

it was too suspicious for me

[formal bolt]

It's important that you always stay vigilant with students' claims

[astral wave]

One message removed from a suspended account.

[vague pagoda]

Get a trig book

And just solve problems

[hot oyster]

could someone help me with this problem

[fringe dirge]

What have you tried

[hot oyster]

its a test so i i get the results at the end but i dont remember how to set it up

this is a summer school course so i obv struggle with geom

[fringe dirge]

that didn't answer my question at all

[hot oyster]

well i cant really try anything if i dont know how to set up the problem

[fringe dirge]

do you know what the pythagorean theorem is

[hot oyster]

well yes but i think they're asking to solve for x and without knowing the hypotenuse i cant figure it out

[fringe dirge]

well is there some other triangle you can apply the theorem to

[hot oyster]

yes and the dashed line is equal to the square root of 4896 but that information is useless isn't it?

[fringe dirge]

That's not quite the right number

[hot oyster]

36^2 + 60^2 is 4896 and then i take the square root of that right

[fringe dirge]

That's not how the pythagorean theorem works

[hot oyster]

Ohhhhh so 36^2 + a number squared would equal 60 ^2 ?

[fringe dirge]

yep

[hot oyster]

ok so the side is 48

the problem is a bit weird though it doesnt specify what missing lenght

am i finding x or am i finding the dashed line

[fringe dirge]

Now, can you see some similar triangles?

It's pretty clear that you're finding x

[hot oyster]

Ohh its an icosoles right triangle

[fringe dirge]

no

[hot oyster]

that is

oh shoot i am wrong 84 isnt an answer choice

[fringe dirge]

how do you know that that other side is 48

[hot oyster]

i dont you are right

[fringe dirge]

Now, going back to what I said

can you find any similar triangles

[hot oyster]

these two?

sorry for the terrible outline

[fringe dirge]

why are those two triangles similar?

[hot oyster]

thats the thing i have absolutely no clue how they're similar but assuming those are the only 2 triangles to see i thought they were similar

[fringe dirge]

There are more than 2 triangles in this picture

[hot oyster]

oh there are 3

[fringe dirge]

right

so are any of them similar

Go back and look at what you need for two triangles to be similar

[hot oyster]

all of their angles must be equal

and corresponding sides are in the same ratio

[fringe dirge]

okay, but do you need all of those things to be true to have two similar triangles?

[hot oyster]

no only one of them have to be true

[fringe dirge]

Right, so do we have any similar triangles here

[hot oyster]

these 2?

they both have a right angle but thats all i can figure out

[astral wave]

One message removed from a suspended account.

One message removed from a suspended account.

[hot oyster]

is the answer 100?

i think i did it right

@fringe dirge thanks for ur time i forgot to say i know how dumb i was sounding

[upper karma]

@desert vortex why are you confident that it's not A

[desert vortex]

i’m reposting the problem sorry lol

cause -5pi/6 isn’t the same as -pi/6 lol

[upper karma]

well yeah, it isn't

but think about it

if r is -3, e.g let's say we had (-3, -pi/6) and (3, -pi/6)

they'd be exactly pi radians apart

so if you add pi to the angle in (3, -pi/6), it should represent the same point as (-3, -pi/6)

[upper karma]

@desert vortex

[desert vortex]

cause you can negatethe radius?

[upper karma]

yes

also

you can add any multiple of 2pi to the angle

or add odd multiples of pi to the angle while negating the radius

[desert vortex]

ohh okay thank you

[worthy root]

@upper karma why did you use 3 parallel once and then 2 parallel lines to denote equivalence

Does that 3 parallel lines have special meaning

[gritty siren]

[upper karma]

equivalence

= is equality

[gritty siren]

3 in Chinese

[upper karma]

i wish i was chinese

[gritty siren]

[worthy root]

@upper karmabut what is 3 parallel line means

[upper karma]

here i choose it to mean that it represents the same point

[worthy root]

🤔

thinkingbread thonk tinktonk thonkeyes megathink hyperthonk fishthonk catthonk eeveeThink catThink

Is that congruent or something

[desert vortex]

what even is a and b tbh

[devout shell]

That graph is called a cardioid

It has certain requirements on a and b in order to produce that graph

[upper karma]

cool

[upper karma]

cardioid is not exactly the correct term since it is a specific case

it is a limaçon

[spark stag]

^

a cardioid is when there's just a "cusp" and not a "loop"

like a heart shape

(in fact, cardioid comes from prefix cardio-, meaning heart - like cardiovascular)

[lusty quest]

whats the difference between sin^-1 and arcsin^-1?

they both lead to the same answer here

[spark stag]

arcsin^-1 isn't a thing

sin^-1 and arcsin are the same thing

different notations, but identical meaning

$\sin^{-1} (x) = \arcsin (x)$

[somber coyote]

Namington:

[gritty siren]

(sin¯¹ being a bit incorrect)

[spark stag]

well, not incorrect

its standardized

its just inconsistent

[gritty siren]

literally, sin¯¹ doesn't exist

[dark sparrow]

neither do you

[gritty siren]

[upper karma]

if tuong doesnt exist then i wish i was tuong

[dark sparrow]

> Oxide: Be Tuong.

You try to be Tuong and fail.
He's way too nonexistent for you to be him!

[inner sandal]

sin^-1 is correct

f^-1(x) is the notation for inverse function, not 1/f(x)

[stuck torrent]

https://tenor.com/view/ah-shit-here-we-go-again-ah-shit-cj-gta-gta-san-andreas-gif-13933485

[inner sandal]

arcsin^-1(x)

[stuck torrent]

$$\sin^{-1}=\arcsin(x)$$
$$1=\text{arc}\cdot \sin^2 (x)$$
$$\sin^2(x)=\text{arc}^{-1}$$

[devout shell]

\sin

[somber coyote]

Whoever:

[umbral snow]

Beautiful

[somber coyote]

Whoever:

Whoever:

[devout shell]

[hot oyster]

i believe i do sin58= x/58 but i am not sure if someone could clear that up before i submit it i would appreciate it

[devout shell]

AC is the side adjacent to the angle, 51 degrees

explain why you think it is sin(58)=x/58 then

[hot oyster]

Oh so i use cos?

i thought ac was opposite

[devout shell]

you'll have to brush up on reading names of line segments

you do use cosine, but what will the angle be?

[hot oyster]

cos51= x/58

so then i would multiply by 58 on both sides and it would be 58 cos51?

[devout shell]

yes

so then why did you think it was sin(58)?

the angle wasn't 58 degress

[hot oyster]

i meant 51 im sorry

[devout shell]

so the big thing to learn is how to read and match line segment names to the segment

[hot oyster]

yes i will definitely do that

thank you for your time

hang on i got 43.04 as the product of 58cos(51)

but thats not an answer choice

so did i do something wrong?

[devout shell]

you typed something wrong then

I got an answer that matches one of the choices

typed it wrong in the calculator*

that or you have radian mode on instead of degrees I would guess

[hot oyster]

oh i DO have radian

thanks

[upper karma]

guys is geometry hard

im going into geometry honors and im scared

[keen aspen]

No

The proofs might be boring to you

As they were to me

But its not rigorous

[dark sparrow]

idk whether geometry honors involves the nasty bullshit known as two-col proofs

[keen aspen]

🤣

[olive solar]

isn't two-col proofs part of normal geo as well as geo honors?

[upper karma]

im going into 9th grade too

im scared for hs

[small raptor]

Geometry is probably one of the easier maths as it's intuitive for the most part.

[cinder portal]

i wanna disagree and say it's both the easiest and hardest, well depending on how you look at it

[quiet mason]

geometry is the most logical and most difficult part of math

ive done till now

[cinder portal]

but if you're doing 9th grade geometry, take it slow

[quiet mason]

its pure thinking

[cinder portal]

it's going to take some time to learn some things

[quiet mason]

^

[cinder portal]

if you're really unsure about something, please do some googling, or feel free to ask

I took geometry in 9th grade and kinda regret not paying attention

[quiet mason]

or sit and try to figure out yourself

[mint sandal]

geometry is hard

[quiet mason]

which would increase your logic

and reasoning

intuition

[small raptor]

Well, high school geometry was easier than the others. Of course, I say this, I remember everyone around me failed. 🤔

[quiet mason]

by high school geo wym

name me a topic

[cinder portal]

also the first class where you touch the surface surface of proofs

[quiet mason]

from that

[cinder portal]

learning how to go from what's given, and show that something is always true

[quiet mason]

are there any proofs for the laws of congruence

like how SAS and others work

when i started geo those proofs were never in the book

nor in google

[small raptor]

It's been over 10 years. But I recall doing proofs, yes.

I also recall sleeping in class a lot though too.