geometry-and-trigonometry

[upper karma]

oh

is it 7?

[wind coral]

yep

now you can find the height properly

[upper karma]

so now i use bxh/2?

[wind coral]

did you find the height?

[upper karma]

no

[wind coral]

then we cant use bh/2

yet

[upper karma]

so a^2+7^2=25^2

[wind coral]

correct

[upper karma]

ahh

wait lemmie do it rq

so a=24

[wind coral]

yep

that should be the height

now we can use bh/2

[upper karma]

ohhh

so 7x24/2?

[wind coral]

7 is the base of the right triangle

we are finding the whole triangle

[upper karma]

ohhh

so 14x24/2

[wind coral]

yep

[upper karma]

ahh

thanks

[wind coral]

np :)

[upper karma]

how do i do these

5 is x=srqt y^2 + 100 right?

and y=10?

[serene moon]

well because of 45 degrees yes y = 10

but for the other cases you should learn the trignometric ratios of some special angles

[upper karma]

ohh

[serene moon]

like for 30 45 and 60 degrees

[upper karma]

oh

[upper karma]

for 6 is it y^2+7^2=x^2

[upper karma]

and y=7?

[serene moon]

uhm how?

[upper karma]

I did the same thing that i did for 5

[serene moon]

have you read about right triangles?

[upper karma]

yea

[serene moon]

what does the pythagoras theorem state?

[upper karma]

uhh idr

aren't we supposed to us phythag

[serene moon]

https://youtu.be/HM8cDiN2jMs

try this

[serene moon]

phythag is probably a short for pythagoras theorem

[upper karma]

yea it is

[upper karma]

how isnt this correct?

[serene moon]

the side opposite to the right angle is not x

[upper karma]

wym

[serene moon]

try watching this

[upper karma]

I did

[serene moon]

isnt y opposite to the right triangle?

[upper karma]

it is

I wrote it wrong

ahh

[serene moon]

yes

[upper karma]

so it's x^2+7^2=y^2?

[serene moon]

yup

[upper karma]

ahhh

[serene moon]

but you cant find x and y with this information

[upper karma]

why

[serene moon]

how would you proceed?

[upper karma]

solving it

7^2 becomes 49

then u subtract it form both sides

and take the square root

from both sides

and then ur done?

i think ur right

[serene moon]

I should be yes

[upper karma]

what do i do now then

[serene moon]

have you heard of trigonometry?

[upper karma]

yes

[serene moon]

do you know how to apply it?

[upper karma]

not rlly

[serene moon]

try understanding that first, then this should be a peice of cake!

[upper karma]

ahh

wait trig is cos and sin right

how does trig relate to the question?

[snow crystal]

you still need help with this?

[serene moon]

he does yes

[upper karma]

yes

[snow crystal]

@upper karma ok so find all angles in those triangles and I'll show you something fun

[upper karma]

okay

[serene moon]

yay

[upper karma]

so for 6 we have 30, 90, andd

[snow crystal]

?

[upper karma]

what

[snow crystal]

30 90 and what lol

[upper karma]

arent those angles

[snow crystal]

they are

but what about the 3rd one

[upper karma]

im tryna figure that out

[snow crystal]

you did geometry before trig right?

you should know that the total measure of angles in a triangle is 180 degrees

[upper karma]

yes

[upper karma]

60

[snow crystal]

yeah

[upper karma]

what do i do now

[snow crystal]

so this is a 30, 60 90 triangle

[upper karma]

yes

[snow crystal]

so if you know this stuff you can now figure out how to find x and y

[upper karma]

wait what

how

sorry im sick and i have to do this hw so im kinda confused

[snow crystal]

ok so this is 6.

you know that it's a 30, 60 90 triangle

and your x is 7

[upper karma]

yea

so now i just solve for y

[snow crystal]

and x

[upper karma]

oh

isnt x 7 tho?

[snow crystal]

I'm talking about the x on the picture with both x and y

[upper karma]

ahh

[upper karma]

so i alr made an equation with pythag

[snow crystal]

you don't have to

just use the picture that I just sent

[upper karma]

okay

hm

ye i dont understand

[upper karma]

wait do i solve it with the angles?

[snow crystal]

is this doesn't help you then I don't know what will

I'm sorry but this is extremely basic stuff

[upper karma]

it does but like to solce x and y u need to make an equation, no?

[snow crystal]

you don't have to, you can solve it right away

[upper karma]

oh

[upper karma]

it's my first time ever learning geometry

[snow crystal]

you said that you did geometry before trig

[upper karma]

yea i started this summer

i started trig 2 days ago

[snow crystal]

I mean you know little to nothing about geometry so why'd you start trig

[upper karma]

true

that's why im practicing rn

[snow crystal]

ok but if you don't understand this then I can't help you

I simplified it as much as I could

[upper karma]

i kinda get what u mean

but the someone said u need phytag for this

[snow crystal]

that's bs

[upper karma]

im confused cuz of that

like now i think we need an equation to solve this

[snow crystal]

for triangles with angles 30, 60 90 and 45, 45 90 you don't need pythag

you need to know their properties

[upper karma]

the question asks us to find x and y and to write the answer in the simplest radical form

[upper karma]

so like most of the time to find x and y we use equations

[snow crystal]

just. use. this.

[upper karma]

okay

[whole venture]

He's trying to explain that 30 60 90 triangles have this pattern for all real values of a and because your triangle is a 30 60 90 triangle we can apply this pattern.

Now if you compare this image to the triangle in the problem you will notice that a=7 which lets you solve for the other sides.

[snow crystal]

that's basically what I told him

[upper karma]

yea i figured out what u guys meant a bit later but then i had to go

i just had to subsituite it

[odd topaz]

https://www.youtube.com/watch?v=-KpurfpC-eM

[fossil spade]

what is the law of sines

[dark sparrow]

http://lmgtfy.com/?q=what+is+the+law+of+sines

[snow crystal]

hey, I solved that limit but I used l'hospital rule

without knowing it, you're not gonna be able to solve it

and you also have to know chain rule

[willow night]

It can be solved without l hospital
Tho it involves knowing lim (sinh/h) as h tends to 0 is 1 and same thing for tan.
Multiply numerator and denominator by 5x, group the 2x with tan , the 5x with sin, giving you an answer of 5

[snow crystal]

that's the answer i got

[lost marlin]

Like… a right angle triangle has an angle 30 degrees, 60 degrees and 90 degrees. The length of the hypotenuse is 10cm. What is the length of the base of the triangle?

[lucid talon]

Yep

[lost marlin]

@lucid talon

[lost marlin]

you have to pick a reference angle

if the angle is ADJACENT to the base, you’ll do the cosine of that angle

if the angle is OPPOSITE to the base, you’ll do the sine

without images is a bit difficult to explain

[frozen ocean]

,tex .sohcahtoa

[somber coyote]

Akira

[lost marlin]

yes, that’s it

[lucid talon]

Oh yeah true… I am referring to the Adjacent…

[lucid talon]

Thanks!

[lost marlin]

then you’ll do the cosine of that angle

[lucid talon]

Yep! Got it!

[lost marlin]

x/10 = cosine

[lucid talon]

👍🏾

Thanks for the help @lost marlin !!

[lost marlin]

np, we are here to help

[lucid talon]

And Akira!

[frozen ocean]

np, surprising you're learning sohcahtoa in grade 7th but like I have learned this in grade 10th lmao

canada moment

[lost marlin]

hahahahahahaha

I started trigonometry in 9th grade

[lucid talon]

Hi! I am trying for a maths competition in Australia… it is called Olympiad… it is a hard competition, that’s why I am doing it now…✌️

[frozen ocean]

I see

[lost marlin]

you’ll thank yourself later for learning this earlier

[lucid talon]

😅😄🤝

[grim galleon]

i learned solo in 7th

[frozen ocean]

good for you...

[last quiver]

What's solo ?

[grim galleon]

i mean trig by myself using ixl

my school system kinda sucks

[last quiver]

Ahh okay I thought you meant some math abbreviation

[pastel ore]

Hey anybody got any resources to learn about trig functions deeper? I know the basics, and stuff like the addition theorem for sin, and cos, but the rest like how the sine / cos are calculated (for values with no special properties) are a complete mystery to me, and it feels akward to use them without really understanding them.

[lethal egret]

There’s a few gifs that show

https://tenor.com/view/gyroscopic-scanner-spiral-twist-round-gif-5940117

here’s cosine

Or if you turn your face 90degrees it becomes sin

https://tenor.com/view/math-curve-circle-sine-cosine-gif-4839795

[rose thicket]

you need to know about the unit circle if u want to understand that

[lethal egret]

yes

[wind coral]

!status

[lime crown]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[upper karma]

I meant 1

[wind coral]

Ok, do you know what happens when a triangle is made using the endpoints of a circles diameter?

[upper karma]

No

This school doesn’t really help with anything and I don’t know nothing 💀💀

[wind coral]

That's perfect fine, it makes a 90 degree angle at the circumference

[upper karma]

Ok

[wind coral]

Now you should be able to find angle LKE

[upper karma]

If there’s a 90 and 55 then a and b can’t be true

35

[wind coral]

👍

[upper karma]

Thx

[wind coral]

Np

[upper karma]

You think you can help me on another one?

I cant explain the shape cause it’s like origami type idk lol

[wind coral]

Send a picture if the shape

[upper karma]

I have trouble on these

[thin agate]

its 39

[upper karma]

Thx

[wind coral]

!nosols

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[wind coral]

Let's backtrack before you move on so you actually know how to do the problem

Angle AQD is an inscribed angle

We can use that fact to find what angle AQD is

Using the image I provided above

[upper karma]

Ok

[wind coral]

Can you point out what degree the intercepted arc is?

[upper karma]

80

[wind coral]

On this image, not mine

[upper karma]

Ohhhh ok lol

39?

[wind coral]

Well get to that

[upper karma]

I did 78 x 1/2

[wind coral]

Ok that is the correct process

[upper karma]

Or is it 78 divided by 1/2

[wind coral]

We would take half of 78

78 divided by 1/2 is double 78

[upper karma]

156?

[wind coral]

^

[upper karma]

39 and 156 is half and double 78

[wind coral]

Inscribed angle (the angle were looking for) is half of the intercepted arc

The intercepted arc is 78 degrees

Half of 78 is?

[upper karma]

39

[wind coral]

Perfect

So angle AQD is 39 degrees

[upper karma]

Ye

[lone canyon]

good job

good job

[lost star]

There is a way to solve it using pytag, although is loooong. By extending downsides that 7 units long segment with another 7 long units segment you obtain the base of an isosceles triangle. Because of of it's angles is 60 degree we proove that this new triangle is equilateral wich means all it's sides have same length. y will be 2 times the base and x will be the height of the equilateral triangle that can be found with pytag.

[tall coral]

why do we need geometry just use a ruler and protractor

[wind coral]

Most of the time problems are not drawn to scale

Or if you mean applied geometry, rulers and protractors are not good for exact measurements

[tall coral]

(it was a joke)

[wind coral]

Oh, you sounded a bit genuine

[tall coral]

oops

[wind coral]

You wouldn't believe how many of my classmates said that exact thing lol

[tall coral]

just learn all of trig and geometry lol

[grim galleon]

gimme a few seconds

or should i say

secants

nvm that didnt make sensr

[lost marlin]

AHAAHAHAHAHAHAHAHAHHAHAHAHAHA

[fair heron]

In the triangle ABC, Seek verification

Help me

😭

[frozen ocean]

what have you tried @fair heron

[agile tide]

help

[indigo escarp]

I got this answer

But my friends saying it’s wrong

[willow night]

I see nothing wrong there

[sage bison]

A+B+C = 180

[austere mortar]

yeah, everythings fine, so dont worry

[vital dagger]

Hint 1: ||C=180-(A+B), B=180-(A+C)||
Hint 2: ||cos A+cosB=2cos((A+B)/2)cos((A-B)/2)||
Hint 3: ||cos2x=1-2sin^2x||
Hint 4: ||Law of sines||

[hidden pewter]

yoyo i just need the answer please

[wind coral]

we dont give answers srry

[hidden pewter]

bro its just this one question please

[wind coral]

nope

[hidden pewter]

just give me a hint

oh wait i just did the math

i got 13

degrees

[wind coral]

can i see your work?

[hidden pewter]

i did it in my head

i see

[ember crane]

pretty sure it is

he's solving for the angle cad not x

[thin sentinel]

@teal bison hehe i'd recommend putting trig identities on a piece of paper so you can look them up quickly

[teal bison]

[torpid skiff]

do you guys do tutors?

[twilit atlas]

do yalls like congruency

i find it hard

[coarse tusk]

I'm having a bunch of trouble with this identity

Excuse the doodling, I needed an outlet for my intense frustration

[teal flower]

@naive shale would you like me to show it to you with AM-GM

[naive shale]

no i got how to use it

infact i used AM-GM only

and it was a 2 step thing lol

[naive shale]

btw which class r u

[teal flower]

Grade 12

[naive shale]

india?

[teal flower]

Yes it's much better

nope

[naive shale]

oh k

[teal flower]

Rewrite 1 as sec^2 x - tan^2 x and factorize

[coarse tusk]

Huh

[teal flower]

$$\frac{\sec x - \tan x + \sec^2 x - \tan^2 x}{\sec x + \tan x - 1}$$
$$\frac{\sec x - \tan x + (\sec x - \tan x)(\sec x + \tan x)}{\sec x + \tan x - 1}$$
$$\frac{(\sec x - \tan x)(\sec x + \tan x - 1)}{\sec x + \tan x - 1}$$

[somber coyote]

NEON

[teal flower]

@coarse tusk this is what I meant

[upper karma]

"Two sides of an isosceles triangle have lengths of 2 and 12. What is the length of the third side?" I'm not asking for help I'm asking if the answer is correct I went throguh the entire learning process again and rethought it out but would the answer be 12? cause that's the only conclusion i came too but i want to make sure

I also need help on this cause I seriously don't understand the unit is on Trinangle inequalities

i'm being serious when i say this and yes i went back, nothing in the study work showed a single problem on this and i'm so confused and idk how to go foward

[teal flower]

The sum of two sides must be greater than the third

[upper karma]

i figured it out

[gentle haven]

A rhombus can be a parallelogram but not vice versa

Right?

[exotic yarrow]

A rhombus must be a parallelogram, but a parallelogram is not necessarily a rhombus (though it is possible)

[gentle haven]

Ok

[lost marlin]

trapezoid -> parallelogram -> rectangle -> rhombus -> square

trapezoids have a pair of parallel sides, parallelogram has its opposite sides parallel and congruent, rectangle has 4 congruent angles, rhombus has 4 congruent sides, and squares has 4 congruent angles and 4 congruent sides

every parallelogram is a trapezoid, every rectangle and every rhombus is a trapezoid and a parallelogram, and every square is a trapezoid, parallelogram, rhombus and rectangle

👍

[whole venture]

@gentle haven

[gentle haven]

ohk

[silent plank]

that flow chart isn't accurate

[split terrace]

Its okay its just to give a general idea

[upper karma]

Can someone please point me in the right direction on where to start with this question. I am having a brain fade.

Thank you

[silent plank]

wrong ideas are generally bad

[smoky jetty]

is this perhaps more accurate? from Math Monks

[silent plank]

better, but classification of trapezoid is off

[smoky jetty]

should there be right-angled trapezoids?

[upper karma]

ramonov can you help with my above problem?

[silent plank]

traps are quadrilaterals with at least one pair of parallel sides

[smoky jetty]

right

so all parallelogram are trapezoids?

[silent plank]

yes

[smoky jetty]

dang

how "has" one pair creates misconception with "atleast"

then this should be the correct one?

[kindred helm]

https://youtu.be/wO61D9x6lNY i found this interesting

i had to watch it twice just to get it

though i dont get the sharp corner thing

[teal bison]

@thin sentinel

what chapters are there that you think are harder than 7.5?

[thin sentinel]

the ones i marked in red

and probably partial fractions

differentiation is actually quite simple if you don't mind memorizing some simple rules

and parmesan equations are pretty easy too

[teal bison]

i see

darn math is actually difficult

[thin sentinel]

hehehe

[smoky jetty]

are those syllabus from what grade?

[teal bison]

from a levels so it should be the last year of high school equivalent but this doesn’t include anything from the ‘further math’ syllabus though

which is a different syllabus also taken in last year of high school

[thin sentinel]

from a US perspective this is roughly precalc through about half of calc bc

[teal bison]

oo

what about these?

[thin sentinel]

that is a wide range

like

it's very rare for diffeq (with integrating factors and stuff) to be taught in high schools

[smoky jetty]

ngl it seems to me like lessons ranging from 7th-11th grade

[teal bison]

yeah it does look like it contains a couple of gcse stuffs

[smoky jetty]

but who knows, im not familiar with us syllabus anyway

[teal bison]

that’s not the us syllabus that’s the uk

[teal bison]

i see

[thin sentinel]

my high school had it but only after i left

[teal bison]

my life would be completed if i could do those kind of math

this one looks pretty interesting too

[smoky jetty]

https://tasks.illustrativemathematics.org/content-standards/tasks/1505 hey, I found this article concerning which definition of trapezoid is agreed upon. What could u say regarding it?

[thin sentinel]

the stuff at the top? the proof stuff? that's what math is all about

that's like the actual interesting bits of math

the rest of it is just backdrop and building blocks

[teal bison]

how long do you think it’d take before I get to that level?

[thin sentinel]

usually first or second year of uni

[smoky jetty]

real math is all about proving? 0_0

[thin sentinel]

yep

hang on let me get one of my math homeworks

[smoky jetty]

and I've barely proven anything

[thin sentinel]

most people haven't except some two column proofs in geometry

[smoky jetty]

I heard two columns is just a bunch of trivial stuff?

[thin sentinel]

it's... it's teaching you how to apply theorems to carefully, methodically prove stuff

which is not inherently bad

but it's tedious

mathematicians don't need it spelled out to them that a = b implies b = a

[smoky jetty]

i see

idk why but the theorems seem like a must to remember when doing two columns

[thin sentinel]

yeah bc you have like 200 of them

[teal bison]

[thin sentinel]

working on it

[smoky jetty]

I once saw recommendation that comp math proofs introduces real math better

although i have no single idea, lmao

[thin sentinel]

here's one from "real analysis"

[smoky jetty]

wait.. ~200 theorems in euc-geo?

[thin sentinel]

idfk we had a lot

maybe 90

it was like 3 pages that we had photocopied from our book so we could refer to them

[teal bison]

[smoky jetty]

just for the two column thing?

[thin sentinel]

right

[thin sentinel]

don't worry about the words

focus on the structure

see how it's about an even mix of words and symbols?

that's from my sophomore year and I was still using a lot of symbols

[smoky jetty]

im self-studying some geo concepts cut-out from our previous grade. Would u say it's necessary to learn the two column thing?

[thin sentinel]

here's one from senior year, much more words and fewer symbols because i'd learned not to symbol barrage

[thin sentinel]

two column is an okay way to structure a proof for beginners

and that sounds disparaging but i'm not trying to be

there are better ways, but the important part is that every step should be justified

by either a previous result or some axiom

i haven't really ever used it since geometry

[smoky jetty]

so proofs should actually have more words

?

[thin sentinel]

yeah

[smoky jetty]

i sometimes put reasons to steps in solutions I do at problems, but idk if thats proving at all

[teal bison]

[thin sentinel]

that's good yeah!

[thin sentinel]

all that proof is saying is that if i give you some number of dots you can draw little tiny circles around each one

[smoky jetty]

lmao

[teal bison]

woah

i have a challenge for you

[thin sentinel]

even if those dots are on some wacko surface like you've drawn them on a Klein bottle or something

[smoky jetty]

i've heard many times how challenging it is to discuss such to general audience

[teal bison]

wait I forgot what I wanted to ask

never mind

[thin sentinel]

oh that's a good way to do it

"expand then equate coefficients" is a theme that will show up a lot

[smoky jetty]

but do u think it's fine if i leave out learning two-columns rn?

[thin sentinel]

if you're self-studying? yeah probably fine

[teal bison]

am I just naturally bad in math or can I actually become good at it ?

[thin sentinel]

you're not naturally bad at math what

i've seen what you're doing

neatness and practice

and collaboration

and some level of persistence and stubbornness

[smoky jetty]

from your experience, where do u think would someone experience to actually prove in HS?

[thin sentinel]

you'll go over some proofs in calculus

[teal bison]

o

[thin sentinel]

generally you're not expected to know them but they can be interesting

[smoky jetty]

been thinking the same way ever since last year, and i'd agree with hayley

[thin sentinel]

tbh in high school i was competition brained

[smoky jetty]

ig i'll follow your words for now. tho im looking forward to proofs someday in the future (given enough time )

[thin sentinel]

so i just wanted to know how to do stuff not necessarily why it worked

and i wanted to be f a s t

[smoky jetty]

oohh interesting

did it give you a positive feedback?

[thin sentinel]

i think there are a lot of benefits to being able to do stuff quickly

like

have you taken algebra?

[smoky jetty]

i did basic in 7th grade, and sucked at it, literally

[thin sentinel]

hmm ok

so if i gave you something like $5x + 4 = 19$

[somber coyote]

Hayley

[thin sentinel]

sorry, i don't mean to make this a grill session

my point is just - the faster and smoother you are at each thing, and the less you have to think about the steps, the more you can focus on the next one

[smoky jetty]

from realization when taking math more seriously, i thought it was coz i didnt paid much attention to why i did the stuff i do before

[thin sentinel]

there are also a lot of problems with only focusing on what to do without understanding it

which i had to deal with when i went to college

[smoky jetty]

i'd say u do the common step of isolating them, but i personally dont know the property why i do that, lmao

[smoky jetty]

i was told that

[thin sentinel]

so i think ideal is a balance

because if someone in e.g. calculus II looks at that equation and has to think about it for more than like two seconds before they know exactly what to do, they'll really struggle with the complicated shit that they're going over

[smoky jetty]

like tbh, i started self-studying last year, like whatever concept i didnt know in school, i'd look into deeper whenever i have time, but just proceeded when i really couldnt get something and gets mentally frustrating

[thin sentinel]

it can be, yeah

it's very rewarding to have your brain finally go clunk and you get it

but before then it's a lot of struggle

[smoky jetty]

ikr!

i remember spending a day building intuition over basic combinatorics last month

[thin sentinel]

good! yeah small practice is the way to go for combinatorics

and lots of things tbh

[smoky jetty]

yeah i agree

ngl, i see similarities with your words to the guidance I followed before when doing math lmao

[thin sentinel]

i'd say if you're struggling because you don't get the current concept that's a good place to be (it sucks to be there. i know)
if you're struggling because you do'n't understand the language they're using or the steps they're skipping over, then you may need to review or practice some things (which is also a sucky place to be)

i also never really understood a topic until about a year after i took the class, especially if i was teaching it to someone else

heck even in here as i was helping someone with differential equations (which I took uhhhhh a few years ago) something went clunk in my head

like two weeks ago lol

[smoky jetty]

i completely relate, even rn

sometimes I feel the urge of giving up self studying coz i know i have limited time left but I have hard time getting smth

[thin sentinel]

geometry, right? i'd say get a lot of scratch paper and maybe even some modeling clay

[smoky jetty]

but ig i just believe that learning math wont hurt in the long run

[thin sentinel]

you want multiple forms of instruction, not just reading

[smoky jetty]

algebra actually

[thin sentinel]

well the modeling clay can still help

as a stress ball if nothing else :P

during my algebra class

we had all these silly jingles for the formulas and rules we were learning

[smoky jetty]

i did pretty well on geo (excluding proof stuff coz our school didnt teach us), but ig coz I could visualize the concepts better?

[thin sentinel]

which dang it they're stuck in my head 15 years latr

[smoky jetty]

yeah i remember relying on those

but when self stuyding, i figured that knowing the basic why's would also lead to some patterns of those things. but it's really time consuming for me

[thin sentinel]

it can? but i don't think about the fact that 17 is prime, i just know it is

i'm also very competitive so self studying without a class to feel superior to wouldn't work for me

[smoky jetty]

yeah i agree

[smoky jetty]

thats interesting

are u in college?

[thin sentinel]

not anymore

i got my masters a few years ago and didn't want to keep going for phd

[smoky jetty]

oh wow, i didnt know u were that nerd

[thin sentinel]

[smoky jetty]

what did u take for masters?

[thin sentinel]

CS but i was taking math through it

i taught a class on cryptography

that was a fun class

[smoky jetty]

welp, u seem to enjoy math so thats pretty neat!

off topic: if i have a not-so-good alg background, should I go for graphs of linear equations and rely solely on geo knowledge?

[thin sentinel]

hmm

when you're doing graphs of linear equations you'll probably need to be somewhat comfortable with equations like the one i wrote above and solving for variables

you can try a geometric approach

but the modern era is largely built on symbol manipulation

[smoky jetty]

dang idek what those are

[smoky jetty]

what could this be

im having hard time understanding graphing linear eqatuons with 2 variables. so im thinking i should study alg first before it

[thin sentinel]

it would very much help i think yeah

i would struggle to teach someone who didn't feel at least somewhat familiar with algebra how to graph and analyze linear equations

[smoky jetty]

the only algebra I got used to was those often used in hs geo

the rest, I planned to self study back from the beginning this coming week

so would u say it'd be better to skip it for now?

[thin sentinel]

solving sets of equations with multiple variables is pretty important going forward but for now it really depends on what else you want to look at

[upper karma]

Can anyone help?

[smoky jetty]

but should equationf of a line and its forms be fine?

[whole venture]

As far as I've seen every person who actively does math is struggling. Whether it's a elementary schooler or an undergraduate (I don't know about graduates but I assume that they are struggling too).

[pliant basin]

hey guys how do i find angles using trig?

and what’s the difference between sin and sin^-1?

[edgy wagon]

With inverse trigonometry functions,

[edgy wagon]

sin^-1 is the angle,

So for example,

sin^-1(sqrt(2)/2) = pi/4

While sin(pi/4) = sqrt(2)/2

sin^-1(opposite/hypotonuse) = angle

[pliant basin]

oh i see

what do i need to find angles tho?

[edgy wagon]

To use inverse trig functions to find the angle, you need to know the lengths of 2 sides of the triangle,

Wait, I’ll draw a picture,

So if you want to find angle x,

You need the lengths of A and B,

Or B and C,

Or A and C,

[pliant basin]

and how do i find it? sinx=b/a and then just cross multiply?

[bold saddle]

sin^-1 (or arcsin) is the opposite of sin. For example:

sin(30) = 0.5
sin(90) = 1
sin^-1(0.5) = 30
sin^-1(1) = 90

if you want to find angle you need to have any 2 of the 3 sides of triangle:

a = sin(x) = B / A
x = sin^-1(a)

a = cos(x) = C / A
x = cos^-1(a)

a = tan(x) = B / C
x = tan^-1(a)

a = cot(x) = C / B
x = cot^-1(a)

[frozen ocean]

,tex .sohcahtoa

[somber coyote]

Akira

[wet ether]

I wanna learn college level mathematics,chemistry and physics. I currently study using youtube(prof. Leonard-maths). Can some one please help me. If u can guide me with this it'll be a great help

[frozen ocean]

Khan academy

[nova slate]

seems like programmation

[smoky jetty]

What do u know about diameter and radius?

[eternal nimbus]

Can I just treat 6cm as a base of a right angle triangle then use tan ?

[wind coral]

Yeah

But for this you would use inverse trig operations

[ember stratus]

Los Angeles is located at (34°N, 118°W), and Osaka, Japan is at (34°N, 136°E). If a plane flies the great circle route from Osaka to Los Angeles, what is the highest latitude that the plane reaches during this flight?

[eternal nimbus]

bruh how do I do part C

[ember stratus]

here is thesolution which i don't understand without a diagram: https://math.stackexchange.com/a/4665352

[lost marlin]

what do you mean by perspective view?

[lost marlin]

not really understanding

can you draw it?

[rustic yew]

guys

im confused

can someone help

<@&286206848099549185> do u know how to do this

I got 182.21

[wind coral]

can we see your work?

[rustic yew]

alr

well u use sine ratio right

cause opposite and hypotnuse

@wind coral

[wind coral]

yeah

go ahead and do so

[rustic yew]

then u divide 54 by sin 38

and then I got 182.21

[smoky mantle]

wont it be cos

[wind coral]

your in radians

[rustic yew]

wut that?

[wind coral]

soh cah toa

[rustic yew]

ye

[wind coral]

switch your calculator to degrees

[rustic yew]

alr

[wind coral]

thats why your getting 182

[rustic yew]

alr thx @wind coral !

[wind coral]

np

[rustic yew]

I got the answer now

[smoky mantle]

im dumb nvm

[wind coral]

all good dw

[grim galleon]

QUICK TELL ME WHAT COT FORMULA IS

nvm

[violet shadow]

Guys

how do you derive the sum and product formulas

Like the SinA +SinB ones and then SinASinB ones cause I always forget them

[cosmic violet]

@violet shadow Here's a proof of cosine product formula

In line 2 the cosine angle sum/difference identities are used

[lost marlin]

guys, one question. in those m+n.sin(a.x+b) functions, why does the b being positive deslocates the graphic to the left, and the b being negative deslocates the graphic to the right? wouldn't it be the opposite? in my head, the b being positive would have to deslocate the graphic to the right, since it is the positive side of the plane

[pastel verge]

is this silicon Valley highschool

[teal bison]

@thin sentinel am at differentiation now 🗣️🗣️

[wintry spire]

yo

can anyone teach me basic trigonometry right now

i didnt pay attention in school for a week and im a little lost

sin cos tan bla bla bla i dont get it

[silent plank]

look up a vid

[violet shadow]

no like derive it

as in if you forgot what the formula was sort of thing

[nova rose]

yo guys should i study proofs, or should i do that when I actually need it in school. i like being ahead of things like this but idk how important proofs are

[upper karma]

How do I find the length of a chord without an angle

is the only way using the chord formula?

[silent plank]

depends what other info you're given

[glad tinsel]

Can anyone help me out

[upper karma]

midpoint of chord, centre and radius

so the chord formula works but is that the only way

[silent plank]

wdym by midpoint of chord

oh

as in you're given coordinates of the midpoint and centre?

what's this "chord formula" you're referring to?

[upper karma]

no clue

Ive worked it out just can't work out why its 2*sqrt (r^2 - d^2)

why minus when pythagoras is +

[silent plank]

you don't know the chord formula you keep referencing?

pythag gives the relation between the three sides of a right triangle

a^2 + b^2 = c^2
with hypot c and legs a,b

which one yuo solve for depends on what you're given

solving for an unknown leg
a^2 = c^2 - b^2
a = sqrt(c^2 - b^2)

[upper karma]

my books assume all this knowledge and while I know the pythag theorem ive not used it in years

ive just been being stupid

makes sense now I actually drew the circle lol

[weary hound]

Math assumes previous things you learnt when you learn anything new

Also btw do remember pythagorean theorem you'll need it for highschool and even university calculus at the very beginning

[dense tulip]

I need help! How do I do this without a Calculator. I know how to find The degrees that’s easy but I don’t know how to find the sides without using a calculator

[wind coral]

Image?

[wind coral]

Well we know sin(25) is .4 right?

What is the ratio for sin?

[dense tulip]

Opposite/hypotenuse

[wind coral]

Yep so sin(25)=0.4=opp/hyp

We have a side length already

Is that side the opp, adj, or hyp?

[dense tulip]

Opp

[wind coral]

Yep, so sub In 8 for opp here

Do you see where this is going?

[dense tulip]

I know the formula for it

I guess don’t know how to solve it without without a calculator

[wind coral]

Well what did you get when. You subbed in 8 for opp?

[dense tulip]

Sin(25)=8/hyp

Then hyp•sin(25)=8

Then I divide it so I get 8/sin(25)

And then I get stuck

Ohhhh now I get it

Sin(25)=.4

Ty

[wind coral]

Np :)

Now you cam use Pythagoras to solve for the other side or do the same strategy

[violet shadow]

do u guys have tricks to memorising exact trig values in radians

[upper karma]

yeah I'm good with it lol, just forgot about using it. 5 years ago was highschool for me

obvs use it to find distance and polar coordinates and stuff but my knowledge has become a case of using software to do stuff for me and not doing it myself

that is sorta what its like post university anyway, but the knowledge is still important for troubleshooting and understanding

i did 5

is it correct

for #5

someone told me to use (x,y)->(-y,x) instead of (x,y)->(y,-x)

nvm

fixed the problem

[grave pond]

That's the most approximate trig table I've ever seen.

[upper karma]

minus is better lmao

[lone axle]

If i'm using real coordinate space, do i just treat time just like i would treat any spatial axis? I've seen (x,y,z,t) being used to represent coordinates and stuff like that, but i'm just not good at this type of stuff

[dense tulip]

How do I find the measures of question b without using a calculator

[wind coral]

Use the same method I told you before. You can find c using Pythagoras. Then use trig ratios to find a or b

[lost jungle]

What channels can I watch to teach myself geometry and are centroids involved in geometry

[violet shadow]

Is there a quick way to find the equation of a circle with 3 points?

[shell sleet]

how to prove Guldinus theorem in a simple way(plz

[dark sparrow]

https://en.wikipedia.org/wiki/Pappus's_centroid_theorem

this?

@shell sleet is this what you're talking about?

[silk dove]

Hi, what's the proof that the circle is the shape with the most area in relation to it's perimeter? just a thought that came across my mind today

[dull light]

isoperimetric inequality

[shell sleet]

yes thank u

[dull light]

or at least when n=2

[cosmic violet]

If you did the steps of the proof backwards (from the bottom line up) it is a derivation. But not an obvious one, it would be very difficult to know what to do next without already somewhat remembering what the formula was

Probably easier to memorize the formula, and then if you’re unsure, try to rewrite it as sin(a)cos(b) to check if you remembered correctly

[dense tulip]

Hello people, I need help once again. I know how to do (a) and (b) but I’m stuck on (c) and (d)

[silent plank]

have you drawn a diagram

its pretty much just interpreting the table again

which gives the relation between the function,ratio and angle

supposedly the ratio you'd get would be in the column of the appropraite trig function and you can get the angle from that

[dense tulip]

Oh I see because I divided 22/20 and I got 1.1

Which matches with 65 degrees

Going back to this one again I know the answer for (b) but which is a=55 b=35 but how do I know which one is which

Like how to do that a=55 and not 35 and Vice versa

[wind coral]

well we can find angle a using tan. tan(A) is equal to opp/adj correct? we know opp=10 and adj=7, so we can sub those values in for opp/adj getting us tan(A)=10/7. the decimal representation of 10/7 is approx 1.43. so tan(A)=1.43. you can use the table to figure out the rest im sure.

[upper karma]

how do i figure this out

nvm

[upper karma]

agreed?

[upper karma]

WHAT IS THIS

https://cdn.discordapp.com/emojis/604762352616996884.webp?size=48&name=MikuShock&quality=lossless

[sturdy jackal]

$(874\cdot\frac{w}{2}+x\cdot y\cdot22^{4}+z)$

[somber coyote]

Dmahonjr06

[sturdy jackal]

$874\cdot\0.5+234256xy+z$

[somber coyote]

Dmahonjr06
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sturdy jackal]

$437+702768y+z)$

[somber coyote]

Dmahonjr06

[sturdy jackal]

-702768y=437+z

$y=\frac{437+z}{-702768}$

[somber coyote]

Dmahonjr06

[graceful vortex]

If you know that the diameter of the sun is 864,000 miles and the diameter of the moon is 2160 miles. What is the maximum distance that the moon can be from earth for a total solar eclipse to happen when the sun itself is at its maximum distance, that being 94,500,000 miles?

If someone can works this and give me their answer it would be appreciated

i have an answer that looks good, but i want to know if others also get it

the book gives problem, but does not tell answer

I got less than or equal to 236250 miles

[frozen ocean]

The second picture isn't related to geometry and trigonometry

It's calculus

[graceful vortex]

can you help me with my question please?

[wind coral]

just send it, also dont ask specific people for help.

[graceful vortex]

its just above her message...

[wind coral]

oh i did not see it

[upper karma]

Wrong

Akira it is the same trigonometric series

[frozen ocean]

Unfortunately English is my 4th language so I don't think I'm able to understand that question 😛

Word problems I mean

[frozen ocean]

Oh cool thing but you know what

I've never learned something like this in high school Canada

They teach that in early university

This could be complex analysis based in Canada

But I'm pretty sure it's calculus

[upper karma]

But its a good thing

[teal bison]

@thin sentinel

[thin sentinel]

just step by step

[teal bison]

the torment arghhh

maybe i could forgo some details of this topic

and focus on scoring well for the rest of the topics

[thin sentinel]

it's good practice

[teal bison]

there’s stats and mechanics angwayyy

back

@thin sentinel

what do you think of these stats & mechanics topics? which are the difficult ones?

[teal bison]

yeap am gonna try it again later

[frozen ocean]

I know

But like

[teal bison]

this the year 1 content

[upper karma]

Do you wanan vc about it

[teal bison]

this the year 2

[frozen ocean]

If you asked types questions like that to your math teacher in high school, they'll get mad at you 💀

[upper karma]

Its not fair can i dm u tho

[frozen ocean]

I don't call though

Or vc

[upper karma]

Ok

Added

[pulsar garden]

hi guys after 9 months of euclidean geometry autodidact im here to ask something

how is possible that Euclid proved his own theorem with constructions

i mean how can a mathematician say with only the insight "i think that if i do that construction it works"

for constructions i mean building segments, parallel lines, median and etc...

[toxic cliff]

https://cdn.discordapp.com/emojis/1002496712910323722.webp?size=64

[pulsar garden]

i can say that's not the kind of constructions that im talking about

and u did not answer my question

but i doubt that u can answer to that

[lyric sonnet]

15a. || 75j is the velocity vector and it will take 4000 seconds|| I guess

[harsh junco]

What's the formula to find the height of this?

[sonic willow]

H=3

[pulsar garden]

how do u do that in a square?

[pulsar garden]

he asked the formula

[harsh junco]

I didn't want the height

[pulsar garden]

don't give him unless he wants the solution

[sonic willow]

Then pitago drip

[pulsar garden]

tell me

how do u do that in a square?

[harsh junco]

I just didn't know the formula

[pulsar garden]

how do u find a diagonal of a square? u know atleast that?

[harsh junco]

Thanks anyways though

nvm it

[pulsar garden]

i can help wait

[harsh junco]

I'm fine

[sonic willow]

Use pitago 2 times

[pulsar garden]

if u want to learn then welcome

if u don't want then bruh

[frail ridge]

How do you find the length of the other sides of a right triangle if you are only given an angle and a side that is not the hypotenuse?

[wind coral]

can you send a screen shot

or if your just asking in general, use trig functions

[frail ridge]

More clear now?

[wind coral]

yeah, use trig functions

[frail ridge]

That's the thing, im only starting out with the basics and im pretty sure there is a way to solve this but I don't know how

[wind coral]

well lets find b first

do you know how to start?

[frail ridge]

No? But im guessing you have to plug a and theta into cos

[wind coral]

not quite

have you heard of soh cah toa

[frail ridge]

Yeah, that's what im learning

[wind coral]

ok, do you know what it means?

[frail ridge]

But you can't just use an angle and one side to find the missing side in a trig function, right?

[wind coral]

you can

[frail ridge]

Yep

[frail ridge]

How then?

[wind coral]

so sin(x)=opp/hyp, cos(x)=adj/hyp, and tan(x)=opp/adj

currently we want to find b correct?

[frail ridge]

Yep

And we have adj

And theta

[wind coral]

what side is b, opp, or hyp?

[frail ridge]

Opp

[wind coral]

great

what trig ratio involves opp and adj?

[frail ridge]

Sin

[wind coral]

sin involves opp and hyp

so not quite

[frail ridge]

Oh

Cos then

[wind coral]

are you guessing?

[frail ridge]

Nope

[wind coral]

refer back to this

[frail ridge]

Its tan is it?

[wind coral]

yeah, can you tell me why?

[frail ridge]

Since its toa, tan(x) = adj / opp

[wind coral]

yep, now lets move one to the second step

sub in the values we currently know

we know x is pi/3

[wind coral]

tan is opp/adj

[frail ridge]

Tan ( pi/3) = n / 1

Is that right?

[wind coral]

why n? were looking for side b

aka the opposite

[frail ridge]

Oh right, forgot we actually gave the opp a name

So tan (pi/3) = b / 1

And since its b / 1, we can just do b

Now what?

[wind coral]

yep, we have tan(pi/3)=b

so what is tan(pi/3)?

[frail ridge]

Sqrt of 3

[wind coral]

yep

[frail ridge]

But how did tan(pi/3) get that value?

[wind coral]

youll learn that when you get further into trig

for now just put it into the calculator

[frail ridge]

1.7321

So, that's tan

What's next?

[wind coral]

you should keep it as sqrt3

decimals are hard to work with

so we have the value of the legs correct?

[frail ridge]

Yep

[wind coral]

we can use pythag now

[frail ridge]

Alright

[wind coral]

to find the hypotenuse

[frail ridge]

C is then 2

[wind coral]

yep, thats what i got too

great job we have all the sides now

[frail ridge]

Alright, so this is how trig works

[wind coral]

pretty much

[frail ridge]

What now?

[wind coral]

wdym what now?

we found b and c

[frail ridge]

Yeah

I think that's all

But how do I do this with different values?

[wind coral]

soh cah toa

itll just have different values thats all

[edgy wagon]

Problem in finding area of intersecting circles with same radius that cross through each other’s origin, my answer looks a bit to complicated to be right, someone double check it?

[grave pond]

It has a pi, a 6, and a square root of 3, that looks good enough to me.

[upper karma]

help

pls

[grave pond]

One approach could be to find the side length of the outer hexagon by using the law of cosines on one of the small white triangles.

Another would be to make six copies of the small hexagon, glue one of them onto each side of the original small hexagon, and work how how much the area of the resulting shape differs from the large hexagon.

[wild hare]

it should be nearly 7:1
applying law of cosines, and the formula for the area of a hexagon

[maiden brook]

yes thats right

[dense tulip]

Does anyone know the question to this one

[dense tulip]

Nvm new question

Does anyone know the answer to this one

[dark sparrow]

a few people certainly do know the answer, but we don't give those out here.

[pastel verge]

help pls

[short ether]

alr alr

let me help you with that

[short ether]

so <1 =70-4x and <2=18x-4. And both of them combined should equal 90 degrees.

[pastel verge]

i set the equation up so it equals 45

[short ether]

so gotta solve the equation (70-4x)+(18x-4)=90 to get x and then add them to each angles and ur done

[pastel verge]

and got 6.25

oh

i see

let me do that

[short ether]

x=24/14

i think

im not sure

i used my head

did it work

[pastel verge]

hmm

i think im doing it wrong

i got 14x = 12

oh no i get x = 2

okay cool

[short ether]

oh ya thats correct

my bad

i aint good at calculating :-

[pastel verge]

i got it from here

nah uchillin

i appreciate it

[short ether]

great

if you got anymore than just dm

[pastel verge]

🫡

[short ether]

👌

[pastel verge]

How would i go about this

@short ether

[short ether]

oh this one is a little bit tricky

so you know that a triangle is 180 degrees

yes

i got teh answer88

i triple checked

[nocturne remnant]

Alternatively, sum of angles in quadrilateral:
120 + x + 64 + x = 360

[edgy wagon]

Ah, thank you!

[vocal sleet]

please help.

[wind coral]

Is this a test?

[vocal sleet]

no

why?

its pracitce

[vocal sleet]

.

[wind coral]

Ok, use the fact that angle xyz is an included angle

[wind coral]

Is an inscribed angle* srry bout that

[wind coral]

!nosols

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[worthy latch]

mb

[wind coral]

all good, saying "two time the inscribed angle" is fine though

[worthy latch]

oh ok

[wind coral]

but let the helpee figure out the arc themselves

[worthy latch]

okok

[low hill]

Hello

My name is Steven

[frozen ocean]

#discussion

[vocal sleet]

please help

If KL = 30, LM = 18, MN = 13, then NO = (Blank 1). (Round your answer to one decimal place, if necessary.)

[tidal nova]

Is this a test

[vocal sleet]

no

its practice

[tidal nova]

Ml times mk equals mn times mo

[vocal sleet]

bruh i did that ik the formula for secant this and all but could u like show me how to do it step by step

I feel as if I am doing it wrong

[tidal nova]

Find ml times mk

Then divide by mn to get no

Mo

Not no

Then mo minus mn is no

[upper karma]

ngl It doesn look like a test related qeustion to help you out on what's going to be on the test

[frail ridge]

What is the arc length and why is it important in the circular trig functions?

[still jay]

have you guys ever faced a trigonometry limit before where the function is a trig function divided by some angle

for instance:

$$ \lim_{x \to \frac{\pi}{2}} \frac{1-\sin(x)}{x - \frac{\pi}{2}}$$

[somber coyote]

Lyerix

[still jay]

it's kinda annoying solving these problems

[merry parrot]

0/0 form

apply LH rule

[still jay]

no L'Hopital

[merry parrot]

do you want the solution?

[still jay]

it'd be 0, using L'Hôpital

But I don't want to use that rule, neither would my teacher want me to. I just want to know what is your solution towards this problem besides using LH rule

[merry parrot]

change sinx to cos(pi/2 - x)

[still jay]

ohh ok, I see where this will be going

[merry parrot]

then you can make that form

(1-cosx)/x^2

but here x will be (pi/2 - x)

and it tends to 0

so it is applicable

[still jay]

how is the ^2 there

[merry parrot]

where

[still jay]

wouldn't it be (1-cosx)/x
if x = π/2 - x?

bottom part isn't squared

[merry parrot]

you need to multiply and divide the expression by (pi/2 -x)

[still jay]

(π/2 - x)/(π/2 - x) ?

ohh yeah yeah

[still jay]

what will this tends to anyway if x → 0?

I know only the sinx/x would tend to 1 when x tends to 0

[merry parrot]

1/2

[still jay]

therefore this would be 1/2 ⋅ 0?

[merry parrot]

yup

[still jay]

alright understandable, very much great and simple solution than the other one my classmates had

[still jay]

what's this process called anyway?

sorry for mentioning, I forgot to turn it off

[merry parrot]

no worries, ig they are called reduction formulas in trigonometry, not sure

[still jay]

alright, I'll check that out later

thanks very much man, ur a helper

[merry parrot]

and always try to manipulate your problem in such a way, that it forms a limit that you know

[pastel verge]

How did she find this angle was 90?

[whole venture]

By the vertical angles theorem you get that the angle GHE is 90 degrees and by the linear pair theorem you get that that the angle CHG is 90 degrees.