geometry-and-trigonometry

[olive solar]

again, supplementary angles are your friends here

yeah i got x=15 as well

so since youve found the measure of that angle to be 79

you can find y and z

take the angle measured as 3y+2

and see how you can form a 180 degree angle from that

[wind heart]

so like

180 - 79

109

109 / 3

• 2?

Or am I doing it completely wrong?

[olive solar]

close, somewhat

don't rush through it like that

so you have 180 = 3y + 2 + 79

which goes into 180 = 3y + 81

which goes to 99 = 3y

[wind heart]

ohhhhhhhh

[olive solar]

i'm assuming you accidentally got 111 for 180-79 instead

anyways, i think you'll be fine with finding y from this

and finding z should be of a similar difficulty level

[wind heart]

I got it, thanks

for the help

[olive solar]

[mossy plinth]

[heady shuttle]

Anyone willing to do tutoring for 30 or less minutes in Trig? I happen to get stuck a lot when trying to utilize my identities.

And we would utilize the mathematics voice channel?

[heady shuttle]

<@&286206848099549185>

[terse sage]

Just ask your questions and I'm sure someone will help you

[heady shuttle]

Yeah, though I just feel like I am missing something, and like to have a bit of guidance on exactly what I am misunderstanding.

[upper karma]

[maiden rain]

Guys I know that the function sin(x) is symmetric at the origin.. because it's an odd function.. But I don't understand this question.. what is f(x) = x - sin x ??

"x - sin x " <<< what is that

[umbral snow]

Do you know the definition for an odd function?

@maiden rain

[maiden rain]

I know if it's odd by looking at the graph

[umbral snow]

The graph helps, definitely. However, there's an algebraic way to check as well, in case you don't have a graph

[maiden rain]

I remember something that has to do with f(x) = -f(x) or something

[umbral snow]

An odd function is a function that satisfies
f(-x) = -f(x)

That is, it's a function that you can pull a negative out of

[maiden rain]

And how would this help me with the question?

[umbral snow]

Does f(x) = x - sin(x) satisfy the definition of an odd function?

Try computing f(-x), it should be interesting

[maiden rain]

f(x) = x - sin(x) < Can you tell me what's that 2nd x ?

[umbral snow]

Same as the first, they're both x

[upper karma]

how do i solve this ?

[tawny tendon]

you can make nice little right triangles and use inverse trig functions

[drowsy walrus]

How do I approach this?

[somber coyote]

xItzDia:

[rapid nexus]

im pretty sure this isn't the chat for logic stuff

for this question do I solve for sin or cos?

nvm

[quiet mason]

ya but this is english ?

[white cradle]

what even

[dark sparrow]

the handwriting is hard to read

[white cradle]

and its not even math

[dark sparrow]

@keen scaffold what is this

[worthy root]

I dont get the first sentence

[dark sparrow]

honestly the "more formal" statement may be easier to grasp

[worthy root]

What is that?

Ohk

👌

[sudden locust]

In this video I show Why the angle sum of a triangle is 180 https://youtu.be/nPYRo4oG7N8 Hope you all have a great tuesday! 🥰👍

[quiet mason]

stephen hawking lmao

[sly marlin]

and you use 5 minutes 18 seconds to show that

[quiet mason]

lol

you could have made a video about 180(n-2)

where n is the number of sides

[silent plank]

did you prove that alternate angles on || lines are equal?

[dark sparrow]

it's for pEoPlE wHo ArEnT eXpErTs @quiet mason

[quiet mason]

lol

[sudden locust]

@silent plank No, not sure how to prove it. Tried to explain the reason behind it using intuition

[crude hornet]

why is trigonometry so hard

[dark sparrow]

what exactly are you finding hard about it

[dark sparrow]

...

how is this trigonometry

[crude hornet]

hol up

it isnt?

[mint sandal]

what is Z class?

[crude hornet]

my god im worse than I though I was

isnt this geometry?

[sly marlin]

oh are you finding alpha?

[dark sparrow]

well it's hard to tell what this even is bc you haven't given the problem statement, only a fragment of its solution

[sly marlin]

it seems more calculus than trig

[crude hornet]

okay il take a screenshot of the question

[tawny tendon]

this is calculus

[upper karma]

Need help on first question

[dark sparrow]

i see you've rewritten the equation of line AB as y = -2x + 6

you may notice that A and B are its x-intercept and y-intercept, respectively.

[upper karma]

Yes

But, what would I do next

[dark sparrow]

next as in

after what

[keen scaffold]

Oof wrong image sorry

This one from before

[upper karma]

;-;

[calm lintel]

i’m so confused 🥺

[sly marlin]

which of these answers make sense?

are there perpendicular lines here?

@calm lintel

[calm lintel]

oh i figured it out 🙏

[coral sapphire]

Think this was answered in a question channel before?

[calm lintel]

loll

[flint mango]

yeah :p

[calm lintel]

thank you though i was just frustrated and posted it in 2 cause i didn’t know which one

[sly marlin]

just post in 1 channel please

[calm lintel]

got itt

[upper karma]

I'm currently taking algebra 1 and really want to learn geometry/algebra 2 so that I can skip it in HS. It seems that most people take geometry after algebra 1 and then algebra 2. Would it be fine taking geometry even though I'm not finished with algebra 1?

[unkempt jay]

both geo and alg2?

or do you jut wanna skip one

[upper karma]

just one

I really doubt I could learn both

gotta make a 90+ on a test that is assigned to those with a high enough grade in math. with a 90+ you don't have to take the course in HS and it counts as if you already took it

[unkempt jay]

????

HWAT

is this in america???

[upper karma]

yeah

georgia lmao

[unkempt jay]

what state?!

wtf

thats a very abusable thing

anyways

[upper karma]

yeah

[unkempt jay]

you could self learn geometry

[upper karma]

alright

yeah that's what I'm planning on doing

[unkempt jay]

you know where to start or how to do it?

[upper karma]

I mean

im taking a course on khanacademy

[unkempt jay]

oh i see

[upper karma]

seems to line up pretty well with what we're leaning in algebra 1

[unkempt jay]

sounds good

[upper karma]

so it probs lines up with geometry as well

yeah

ok

thanks

[vagrant steeple]

can somebody explain how i'd simplify this in terms of sine and cosine

[weary drift]

do you know how tan and cot relate to sin and cos?

[vagrant steeple]

yes

(sin/cos) + (cos/sin) = 1/x ?

[weary drift]

show your work on paper

[vagrant steeple]

that is my work lol

that's all i've got

[weary drift]

get some paper and do it on that, then show me

[vagrant steeple]

if you're not going to help then just move on and i'll wait for someone else.

if anybody wants to help with that problem please dm or @ me

[weary drift]

You put zero effort into solving this problem, so you're right, I won't help you

[vagrant steeple]

i have already typed out what i could given the extent of my knowledge. i am lost on that problem and there is nothing else i can do. if you can't understand that then please stop responding

[unkempt jay]

@weary drift what did you expect him to put on his paper

im just curious idk what else he would write down

[weary drift]

I expected him to at least cooperate and show out his thought process on paper. If he doesn't want to do that, then you can take it from here

[vagrant steeple]

i have already typed out what i could given the extent of my knowledge. i am lost on that problem and there is nothing else i can do. if you can't understand that then please stop responding

[unkempt jay]

but his thought process was convert it to sin and cos

then he was lost from there

eh doesn't matter, i got it @vagrant steeple

[vagrant steeple]

galileo do you know what to do next

thank you

[unkempt jay]

so you said sin/cos + cos/sin = 1/x

[weary drift]

He did nothing but type out a single line of text. Have fun with this one, galileo

[vagrant steeple]

1/x

[unkempt jay]

ignore the 1/x side

lets just manipulate sin/cos +cos/sin

any idea how we could find common denominators here?

[vagrant steeple]

cross multiply?

[unkempt jay]

try it

[vagrant steeple]

sin^2/ cos^2 ?

[unkempt jay]

send what you find

almost

what does cross multiply mean

what would multiply the whole thing by?

[vagrant steeple]

ah

sincos

[unkempt jay]

mhm

so multiply the whole thing my sin, then by cos

and say what you get

[vagrant steeple]

sin^2cos + cos^2sin

[unkempt jay]

what about the bottom

[vagrant steeple]

sincos

[unkempt jay]

close

you would get

[vagrant steeple]

squared?

[unkempt jay]

uh

you might wanna write that out so you can actually see it

wait

so you got

sin^2cos + cos^2sin

[vagrant steeple]

i did

[unkempt jay]

oh ok

hm

ok

[vagrant steeple]

i know sin^2 + cos^2 = 1

so divide both sides of the equation by sincos?

[unkempt jay]

this is what the bottom should be

im trying to put that into words rn lol

[vagrant steeple]

all good lol

wait that whole thing is the denominator?

[unkempt jay]

no

[vagrant steeple]

just the sincos

[unkempt jay]

mhm

oh

i se

the way i said to do it takes to much time

lets restart with

cos/sin + sin/cos

what happens if you multiply

(cos/sin) times (1/1)

just a build up into the explanation, its not a trick question 🙂

[vagrant steeple]

it stays the same?

[unkempt jay]

mhm

because 1/1 = 1

now what does cos/cos =?

[vagrant steeple]

1

or

cos

[unkempt jay]

and if you multiply anything by 1

it stays the same, right?

[vagrant steeple]

yeah

[unkempt jay]

you were right, cos/cos = 1

so, we can multiply (cos/sin) times (cos/cos)

because we are techinically multiplying it by 1

if we multiply cos/sin by cos/cos, what do we get?

[vagrant steeple]

cos^2/sin

[unkempt jay]

almost

the top is right

[vagrant steeple]

sincos on the bottom

[unkempt jay]

mhm

so cos^2/sincos

now lets do the same with sin/cos

[vagrant steeple]

sin^2/sincos

[unkempt jay]

nice

what did you multiply sin/cos by?

[vagrant steeple]

sin/sin

[unkempt jay]

and thats just equal to 1

so its ok

now we can add the two because they're the same value as they were before

but now they have common denominators

[vagrant steeple]

sin^2 + cos^2 = 1

[unkempt jay]

so what do we get when we add sin^2/sincos + cos^2/sincos?

[vagrant steeple]

1/sincos ?

[unkempt jay]

close, this

$\frac{sin^2}{sincos} + \frac{cos^2}{sincos}$

[somber coyote]

Meir:

[unkempt jay]

just fraction addition

what is 4/10 + 3/10?

[vagrant steeple]

you've lost me 😅

7/10

[unkempt jay]

cool

[vagrant steeple]

sin^2 + cos^2 is 1

and you keep that on top of sincos right

[unkempt jay]

mhm

heres what we have so far

[vagrant steeple]

so the answer would be 1/sincos

[unkempt jay]

ooh

you simplified alreayd

nice!

do you think you could relay all the steps to me now?

this might be on a test

you could look back at our convo

[vagrant steeple]

i think i've got it now

thanks, you've been a great help

[unkempt jay]

no problem man

good luck, you can ping me if anything looks at all fuzzy

ill be better about now lol

[vagrant steeple]

alright. i'll come back if i get stuck on another problem

[unkempt jay]

dont be shy to 😄

[frail cobalt]

Can anyone help me with trigonometry? I have a problem I'm stuck on

[weary drift]

[frail cobalt]

An isosceles triangle has an area of 24 square centimeters and the angle between the two equal sides is (5pi)/6. What is the length of the two equal sides?

[frail cobalt]

Anyone?

[silent plank]

what formulas do you know for finding the area of a triangle?

[silent plank]

what are they asking you to do?

[frail cobalt]

Isosceles triangle: 2 sides are congruent and the base isnt.

The angle in where the 2 sides meet is 5pi/6 (150 degrees)

Find the length of the 2 sides.

[silent plank]

what formulas do you know for finding the area of a triangle?

[frail cobalt]

Area : 24 cm^2
A : 1/2 * b * h

[silent plank]

any other formulas (that involve trig)?

[frail cobalt]

My teacher is garbage. I cant find any in my notes and I wrote down everything.

You go to his office for help and he acts like you're a dunce no matter what.

[silent plank]

are you familiar with
Area = 1/2 ab sin(C)

[frail cobalt]

I've heard of it but I dont remember how to use it. Learned in highschool.

[long sapphire]

$\frac{1}{2}ab\sin(C)$ is just an application of the original $\frac{1}{2}bh$ formula

[somber coyote]

Jiramide:

[silent plank]

lowercase letters represent sides, capital letters represent the angle opposite those sodes

[frail cobalt]

But I dont have any side lengths.

[silent plank]

assign them a variable

what do you know about the legs of an isosceles triangle?

[frail cobalt]

2 are congruent. Meaning it would be (1/2)x^2sin(C)?

[silent plank]

yeh

(Area=)

[frail cobalt]

So 48/sin(5pi/6) = x^2?

And x would end up being sqrt(96)

[silent plank]

yeh. Can you simplify that radical?

[frail cobalt]

4*sqrt(6)

I feel absolutely dense.

[ocean junco]

Hi, I know it’s late but could someone explain this to me? I have a quiz on arcs and chords tomorrow and I have no clue on what to do.

[silent plank]

constructing a few lines to the centre may help

[ocean junco]

alright. How should I go about it then?

[silent plank]

whats the relation between mAngle BOE and mAngle BDE

[ocean junco]

They share common points?

[silent plank]

yes, more specifically they are subtended by the same arc

where are those angles formed?

[ocean junco]

the joints of the angles are formed on the arc

I think

[silent plank]

where is angleBOE

[ocean junco]

the center?

[silent plank]

yes

what about angleBDE?

[ocean junco]

the arc?

[silent plank]

wdym by arc

[thorn linden]

u should probably review ur rules

for circles

[ocean junco]

alright.

i will.

[thorn linden]

this might help

[ocean junco]

In that case, do angle BOE and angle BDE follow the first row and thus are the same?

[silent plank]

no

where is the point O
and where is the point D

[ocean junco]

O is the center and D is on the arc or the edge of the circle

[silent plank]

so which theorem should you be using?

[ocean junco]

Is it the second row in the chart? Because it runs through the center and the circumference?

I’m sorry for giving you guys a hard time with my dense-ness . Thank you for explaining all this.

[silent plank]

wdym by

Because it runs through the center and the circumference?

[ocean junco]

I guess I said that because the second row in the chart is a theorem that connects both the center and the circumference

[silent plank]

the 2nd row specifically involves the diameter

which of those theorems involve
an angle at the center AND
an angle at the circumference?

[ocean junco]

The third one?

[silent plank]

yes

[ocean junco]

Does that make mBDE 50 degrees?

[silent plank]

yes

[ocean junco]

oh, nice! thank you so much for your help!

[odd notch]

if i were given this how would i go about starting to find A?

[dark sparrow]

this is a right triangle

you might consider recalling the definitional mnemonic known as SOH CAH TOA

[odd notch]

opp/adj?

[dark sparrow]

c isn't the adjacent leg to angle A

that'd be b, not c

[odd notch]

opp/hyp

[dark sparrow]

yes, sin(A) = a/c

[odd notch]

then to solve for B it would be 90-A right?

[dark sparrow]

sure, you can do that.

[odd notch]

how about to find b?

[dark sparrow]

there are at least three ways of doing so

don't overthink it

[odd notch]

so i did c^2-a^2 then sqrt the answer

[dark sparrow]

you used the Pythagorean theorem, great

so why did you need to ask me

when you were able to do it

[odd notch]

for confirmation i guess after you explained i was overthinking it.

[odd notch]

how would i go about solving this one?

[dark sparrow]

make a picture

[maiden rain]

Is the range of the function CSC(x) = (−∞,−1]∪[1,∞) ? or we don't include -1 and 1 ?

[olive pulsar]

can someone explain to me why cos x - sin x = 0 can lead to tan x = 1?

my guess is that
cos x - sin x = 0
cos x = sin x
0 = sin x / cos x

im asking bc this appeared in a marking scheme and i dont understand why

[silent plank]

what do you get when you divide cos(x) by cos(x)?

[olive pulsar]

1

but this is sin x / cos x

[silent plank]

what do you mean this is cos(x)/sin(x)?

[olive pulsar]

i mean in terms of trig identities

0 = sin x / cos x
therefore sin x / cos x = tan x
and tan x = 1

** sorry i meant sin x / cos x

[dark sparrow]

how did you go from cos(x)=sin(x) to 0=sin(x)/cos(x)

[silent plank]

^

[dark sparrow]

@maiden rain why would we not include -1 and 1 when csc actually returns those values for x=±π/2?

[olive pulsar]

im just speculating here bc i dont understand the reasoning

this appeared in the official markscheme and i dont know why

[dark sparrow]

can you show the mark scheme

like the whole thing

[olive pulsar]

referencing the 4th line of question 8

[dark sparrow]

at no point does "0 = sin(x)/cos(x)" actually appear in that paper...

[maiden rain]

Oh right, I got 1 out of csc(90) , Thanks Ann

[olive pulsar]

yes thats why i said it was /my guess/

i dont understand how cos x - sin x = 0 leads to tan x = 1

whats the reasoning

[dark sparrow]

cos(x) - sin(x) = 0

add sin(x) to both sides

what do you get

[olive pulsar]

cos x = sin x

[dark sparrow]

now divide both sides by cos(x)

what do you get

[olive pulsar]

sin x / cos x

[dark sparrow]

no

[olive pulsar]

which equals tan x

[dark sparrow]

no

[olive pulsar]

cos x / cos x = sin x / cos x

[dark sparrow]

yes.

[olive pulsar]

the first half = 1
the second half = tan x

so 1 = tan x

[dark sparrow]

well there you have it

[olive pulsar]

ah ty

[plucky jay]

Hi, I have a question regarding sequences.

[quiet mason]

ok wait

brandons trolling

#precalculus #precalculus

anypne of these

[plucky jay]

Oh lol

Thanks I had a feeling xd

[maiden rain]

I know the domain of tan = R-{(n)pi where n is odd number..

[dark sparrow]

no it's not

what you said both includes pi/2 (which it shouldn't) and doesn't include pi (which it should)

[maiden rain]

Wait it should be R-{sin=0}

But I don't know how to translate that

[dark sparrow]

no, it should not

[maiden rain]

Sorry I meant cos(x)

[dark sparrow]

ok so when does cos(x) equal zero

[maiden rain]

When it's at pi/2

[dark sparrow]

pi/2 is by far not the only point

[maiden rain]

or 3pi/2

[dark sparrow]

there are infinitely many points

[maiden rain]

Yeah

But I don't understand the answers here

It's definitely one of the 2 at the bottom

[dark sparrow]

the notation in the answer options is somewhat dodgy but yes

[maiden rain]

I'll go with the one that has pi/2

Is it the 3rd or 4th ? I'm not sure :/ ?

[wary turtle]

The 3rd one. Like Ann said, "R - nπ" doesn't include π in the domain, but includes π/2, which shouldn't happen since tan(π/2 or 3π/2) = ∄. @maiden rain

[maiden rain]

@wary turtle What's " ∄ " ?

[dark sparrow]

tan(π/2 or 3π/2) = ∄.
bad notation

he meant "doesn't exist"

or rather "is undefined"

[maiden rain]

I wanna cry 😦 , I didn't realise what " n " meant until now 😦

I totally understand it now. I feel so bad.. I wanna get better I'm frustrated 😢

[honest bay]

I need to get tan of ABC

Any tips?

[dark sparrow]

,rotate -90

[wary turtle]

Sorry. I was quite in a hurry when replying, but yeah, it meant "doesn't exist".

[proud valve]

uh can anyone help me

with vectors

https://media.discordapp.net/attachments/435980077680033812/631612745669804033/image0.jpg?width=332&height=442

[crisp grove]

@proud valve that's too small

[proud valve]

oh someone explained it to me already

im fine now

XD

[crisp grove]

np

[proud valve]

thanks tho

[ebon plume]

hey, can anyone help me with this problem on angles

[silent plank]

what have you tried?

[ebon plume]

i tried to add the angles together but them realized that wouldn't work. I'm honestly just confused with this. My entire homework is just problems like this one.

[silent plank]

what would the sum of those angles be equal to?

[ebon plume]

22x + 4 ?

[long sapphire]

you should have a sum that doesn't depend on a variable

[silent plank]

yes but also what is the angle sum of supplementary angles

[dapper escarp]

^

do you know what supplementary is

[ebon plume]

supplementary is two angles that equal 180 degrees

[silent plank]

not quite

[ebon plume]

what else is there?

[silent plank]

what you typed implied that they are both 180 degress

[ebon plume]

i guess. I'll be honest I'm very confused by this

[silent plank]

the angle sum of supplementary angles is 180 degrees

and you are told that angles 14x and 8x + 4 are supplementary
are you able to form an equation with this information?

[ebon plume]

yes, wouldn't it be 14x + 8x + 4?

[long sapphire]

thats an expression

an equation is a statement in the form x = y

[silent plank]

but what numerical value is it equal to

[long sapphire]

what does 14x + 8x + 4 equal to?

[ebon plume]

since 14 and 8 are like terms could you add them?

[silent plank]

numerical value
the angle sum of supplementary angles is 180 degrees

[ebon plume]

i understand that the angles sum will be 180 degrees but I don't understand how I am supposed to get the numbers to it

[silent plank]

using an equation

convert
the sum of (14x) and (8x + 4) is 180 degrees
into a mathematical equation

[dapper escarp]

the angles together are 180 degress

you make an equation

[ebon plume]

would 14x + 8x = 4 be a proper equation?

[silent plank]

no

well it would be an equation since it has an = sign,but not the correct one for this equation

seriously...
what numerical value to you get when you add your two angles?

[dapper escarp]

do you know what 14x + (8x + 4) would be

[median crown]

[silent plank]

i understand that the angles sum will be 180 degrees
...

[dapper escarp]

[dapper escarp]

@ebon plume

[dapper escarp]

now you just zoom in into that u

lol

[ebon plume]

I thought that if I did 22x + 4 that's wrong

[silent plank]

not an equation

[dapper escarp]

how would that be wrong

[silent plank]

but what numerical value is that equal to

i understand that the angles sum will be 180 degrees

[dapper escarp]

contradictions everywhere

oof

[ebon plume]

I'm just very confused man. I don't know what numerical value it'll add up too. That's about what my problem is at this point

[silent plank]

i understand that the angles sum will be 180 degrees
i understand that the angles sum will be 180 degrees
i understand that the angles sum will be 180 degrees

[median crown]

i understand that the angles sum will be 180 degrees
i understand that the angles sum will be 180 degrees
i understand that the angles sum will be 180 degrees

[dapper escarp]

...

feel like you're trolling at this point

[median crown]

Literally read it

[dapper escarp]

very simple basic question

can an angle be 0 degrees

[median crown]

Yes

[dapper escarp]

oh ok thanks

[median crown]

You guys got it now?

[dapper escarp]

oops

wrong ping

[median crown]

i understand that the angles sum will be 180 degrees

[dapper escarp]

@redd#4951

he left

damn

he left the server

i have a heavy feeling that was a troll tho

[white cradle]

lmao

[median crown]

You bots

[dapper escarp]

indeed

[median crown]

You literally told yourself the answer

[dapper escarp]

🤖

he contradicted himself like 92 times

[silent plank]

the guiding questions aren't hard
if they really needed the help, they probs wouldn't leave

[trim gyro]

All you needed to tell him was 22x + 4 = 180

It honestly felt like you were the troll here.

Probably left cause he realized there's no point asking for help here 😛

[flint sentinel]

he contradicted himself so many times lmaooo

[trim gyro]

What did he contradict exactly?

He obviously had no idea about what he had to do.

If I had to guess, he was probably in 6th grade.

All I see here is bunch of retards ganging up on a kid

[dark sparrow]

sounds like he didn't know what the word "sum" means

[trim gyro]

"i understand that the angles sum will be 180 degrees but I don't understand how I am supposed to get the numbers to it"

He didn't know how to make the equation. That's it.

Congrats, you proved you have a slight longer dick than a prepubescent child

[sudden locust]

In this video, I go in depth on Midpoints. Hope some of you find it valuable and that you enjoy your Thursday! 🥰👍https://youtu.be/9Yt6iW8OipA

[dark sparrow]

what kind of depth is even possible on that

[sudden locust]

I managed to make 5mins about it 😉

[quiet mason]

"😉"

[sly marlin]

actually, I'm inclined to disagree, but you didn't really go into depth yet

For example:
The midpoint of the hypothenuse of a right triangle is the circumcentre
Parallelogram diagonals intersect at their midpoint
The midpoint of one diagonal of a kite lies on the other diagonal
If I connect the midpoints of two sides of a triangle, I get a line parallel to the third side.
If I draw the circle passing through the midpoints of the sides of a triangle, they also pass through the base of the altitudes, the midpoint of AH, for vertex A and orthocentre H, and the circle is tangent to the incircle and 3 excircles

@sudden locust Consider this depth

not deep enough

still can go on

If you take the altitude of a triangle (orthocentre H, base of altitude M) and extend it to the circumcircle intersecting at X, then M is the midpoint of HX

The nine point centre is the midpoint of the line connecting the orthocentre and the circumcentre

If you connect each vertex of a triangle with the midpoint of the other side, you get three lines that are concurrent, intersecting at the centroid

[silent plank]

i would actually watch the video if it included all that

[sly marlin]

same tbh

Hey, let's embark on a fact collecting journey about midpoints

who's up?

[quiet mason]

and the video starts with pictures of stephen hawking,benedict cumberbatch,elon musk

[sly marlin]

nah, we don't need that

[quiet mason]

yes

physicist,actor,entrepreneur

[dark sparrow]

btw

[quiet mason]

lol

math video

[dark sparrow]

can someone give me a TL;DW of the vid

[eager pendant]

the midpoint of a and b is (a+b)/2

[quiet mason]

lmao

[sly marlin]

and coordinates

and probably 1 minute of shameless plug

[eager pendant]

the midpoint of a and b is (1/2, 1/2, 0)

[quiet mason]

what plug did he give tho

"subscribe "

?

[eager pendant]

and the midpoint of an arc is like -vw when the other coords are v^2 and w^2 but that's kinda boring

[sly marlin]

6:05 to 6:51
Drop a like, subscribe, notifications, and long outro

[crisp grove]

it's just a 5 min video!

Ah he's already dead 😭

[sudden locust]

@crisp grove Haha! Great pic 😅

Was pretty much me, just woke up from a nap so you are pretty much spot on!

@sly marlin Eyy, thanks for you insight. Appreciete it buddy 🥰👍

[quiet mason]

uhh

[sudden locust]

What up? 😉

[quiet mason]

funny

[sudden locust]

What is funy? The picture from @crisp grove ? If so I agree 😅 👍

[vague pagoda]

hm

[deft sleet]

Hey guys i need some help in solving a task i cant wrap my head around

[dark sparrow]

[deft sleet]

This

I need to find D

If anyone are wiling to help thank you so much

[silent plank]

is that 61°?

[deft sleet]

yes

[silent plank]

do you know what type of triangle you have?

[deft sleet]

according to my teacher it is not a right triangle

[silent plank]

do you think that it is?

[deft sleet]

well all the other tasks that have right triangles are marked with 90° and are not in a circle

even if it looks like the hypotenuse goes through the diameter

I do know the answer but i do not know how to get to it

the answer should be 11.8 but i don't know how to get there

[silent plank]

that didn't answer my question about whether you think its a right triangle

[deft sleet]

Well I do think it is but my teacher said its not

[silent plank]

what was your justification?

[deft sleet]

the hypotenuse looks like it goes through the center as a diameter

[silent plank]

bad way to explain it
angle at the circumference subtended by the diameter is 90°

[deft sleet]

okay

[silent plank]

so yes, it is indeed a right triangle. no idea why your teacher is saying it isn't

[deft sleet]

i didnt completely understand that but i get the gist of it

(not native english speaker)

[silent plank]

and you can find the diameter using trig

[deft sleet]

okay but, how?

[silent plank]

do you know your trig ratios?

[deft sleet]

We have different words for it in Norway

What are Trig ratios

[silent plank]

sin, cos, tan

[deft sleet]

I know sin and cos

We havent learned tan yet

[silent plank]

(tan would be sin/cos)

[deft sleet]

alright

[silent plank]

which trig ratio do you think you should use here?

[deft sleet]

cos?

[silent plank]

nope
where is the 10.3 relative to the 61° angle

[deft sleet]

oh right

sin then

because it is opposite

[silent plank]

yes

[deft sleet]

okay what step is next?

[silent plank]

sin(61°) = opp/hyp = ?

[deft sleet]

alright let me try

THANK YOU!

Thank you so much for taking your time to help me ramonov

[silent plank]

np

[deft sleet]

I appreciate it a lot

My test is tomorrow and now I think that i will do well

[silent plank]

good luck
remember to justify things properly with theorems/identities you should've been taught

[deft sleet]

Yes

I will

And again thank you for helping me

[celest swift]

https://media.discordapp.net/attachments/603212212303298560/631922765301022733/IMG_20191010_203443.jpg?width=1172&height=670

how do i find h

[dark sparrow]

what have you tried so far

[celest swift]

well i got really confused so i`ve been trying to solve this thing for a hour or so

[dark sparrow]

yes but WHAT have you tried?

(also, an hour? this is definitely at least 4 times as long as the problem merits)

[celest swift]

i guess i havent tried anything, well ive tried but i got it all wrong i have no idea of how to solve it now

[dark sparrow]

can you show me your failed attempt

maybe you were going in the right direction and messed up the arithmetic or sth

[celest swift]

i tried Pythagoras but i 5 is the whole ab so, i`m lost rn

[dark sparrow]

ok

well

alright

i can give you a hint

consider the area of this triangle

and to be more specific, this area can be calculated in two ways, one of which involves the height

[celest swift]

two ways so there is another way

[dark sparrow]

well... not quite, i guess.

it's the same method just from different perspectives

[celest swift]

o

[dark sparrow]

to divulge more details would spoil the entire solution

[celest swift]

i c now

i just relized

thank u so much

o wait i think i lost it

okie ill try

[undone shuttle]

There is an equation for that

[somber coyote]

Digicat195:
Compile Error! Click the reaction for details. (You may edit your message)

[undone shuttle]

with that, you can calculate the h

[celest swift]

Did it

Thanks for da tip

[novel flax]

@celest swift
area of a triangle is bh/2
3 could be the base and 4 could be the height
a=34/2
a=6
5 could be the base and h could be the height:
a = bh/2
6=5h/2
12=5h
12/5=h

[celest swift]

Well I saw that later

[glad timber]

Can somebody proof check my geometry proof

If you need help reading the hand writing @ me

[thorn linden]

@glad timber

what does step 3 say

[glad timber]

If you add congruent segments to congruent segments the sums are congruent @thorn linden

[crimson olive]

can someone help me solve for x, q and r are parallel btw

[thorn linden]

5x+21 -2x = 90

cause corresponding angles

[silent plank]

did you mean corresponding angles

[thorn linden]

yes

[silent plank]

what was the reason for 10 @glad timber

[marble parcel]

How do i draw this figure

Would it be like this

[silent plank]

yeh

[glad timber]

@silent plank never mind the proof is wrong

[silent plank]

from what i glanced, you would need to involve congruent triangles

[glad timber]

Yeah I was rushing through it, totally forgot to set the triangles congruent

[marble parcel]

Can someone help me with this proof i did this like completely wrong

[silent plank]

yeh. restart the whole thing.
would you be able to prove that triangle a ABR and ARK are congruent?

you can't just assume #3

[marble parcel]

um they r congruent by sas right

[silent plank]

no

you can't assume they're right angles ie they are already perpendicular

you would need to use a different congruency test

what information are you able to get from AE bisects BK at R?

[marble parcel]

Honestly not sure. Could i use vertical angles to solve the proof?

[silent plank]

what does bisect mean?

[marble parcel]

splitting it into 2 parts

[silent plank]

what's the relation between those two parts

[marble parcel]

they are congruent

[silent plank]

so which segments would be equal from that information?

[marble parcel]

br and bk

ar ar

ab ak

[silent plank]

br and bk aren't equal.
br is a part of bk

[marble parcel]

rk sorry

[silent plank]

is that enough information to prove congruency?

[marble parcel]

wouldnt it be SSS?

[silent plank]

yes

you'd still need 3-4 more steps to prove that they're perpendicular

actually, you could do something tricky

[marble parcel]

wdym?

[silent plank]

nvm about that last comment

[marble parcel]

ok haha

[silent plank]

what would be your steps after proving congruency?

[marble parcel]

oh I usually use cpctc after

isnt there some posulate that when 2 lines are perpendicular they form 4 right angles

[silent plank]

you would only need to show that one of them is right
cpctc?

[marble parcel]

corresponding parts of congruent triangles are congruent

[silent plank]

that isn't sufficient to show that its 90°

[marble parcel]

im not really sure then

[silent plank]

its intuitive why they're 90° but in these proofs you need to explicitly write why.

[marble parcel]

if 2 angles are both congruent and supplementary they form right angles

that would right?

that would work right*

[silent plank]

needs a justification of why they're supplementary

[marble parcel]

well because they r on a line and angles on a line add up to 180

my geo teacher doesnt make us do this in class haha this is way more detailed

[silent plank]

yeh its stupid but you do have to write it
angles on a straight line are supplementary

[marble parcel]

really wowza

okay after that i can say congruent and supplementary angles form right angles

and then vertical angles?

[silent plank]

don't need vertical angles.
you only need to show that one of them is 90° and the lines are perpendicular

[marble parcel]

oh i thought it was 2 angles that are perpendicular

then they form 4 right angles

[silent plank]

when one is 90°, the other(s) will also be 90°

[marble parcel]

makes sense

[silent plank]

if you only had AR and BK,
there are only 2 90° angles and they are still perpendicular

[marble parcel]

do i also need to state that angle arb and angle ark are perpendicular or is stating that they are just right angles okay

[silent plank]

angles aren't perpendicular. perpendicular describes the relationship between lines.
the conclusion would be AE perp BK.
the reasoning would be something like angleARB = angleARK = 90°

or definition of perpendicular lines

[marble parcel]

one more quick question im trying to prove that angle P is congruent to angle S. angle p and s are just the straight lines right?

@silent plank

[silent plank]

it isn't very clear what angle P and S actually are.
they aren't part of any shapes and seem to be just points

[marble parcel]

So I probably drew the figure wrong i guess

[silent plank]

ah. construct lines PR and SQ

[marble parcel]

ohhh

[silent plank]

maybe don't make RS and PQ look perp

since the right angles should be at R and Q

[marble parcel]

R and Q??

[silent plank]

uh angles PRS and PQS

[marble parcel]

they should look like that right

[silent plank]

PR perp RS, means the right angle should be at PRS
similar with the other triangle

don't make RS and PQ vert/horizontal

however, even if the diagram is not to scale, you should still be able to complete the problem

[marble parcel]

Oh okay

[silent plank]

it is implied that angle P and angle S refer to the minor angles
ie angle RPQ and angle RSQ

[marble parcel]

would it be sas?

[silent plank]

no. you don't know whether PT = TS

hint: ||you don't even need to know that RT = TQ||

[marble parcel]

would vertical angles work for this problem?

[silent plank]

yes

[marble parcel]

oh.

[silent plank]

did you get it?

[marble parcel]

i think so? angle rpt and qst are vertical angles

then u use vertical angle theorem to say that they r congruent

[silent plank]

no, RPT and QST are not vertical angles

but there are vertical angles elsewhere in your diagram

[marble parcel]

im so confused

[silent plank]

what's the definition of vertical angles,
and which angles on that diagram are vertical angles?

[marble parcel]

opposite angles of 2 intersecting lines

[silent plank]

which angles of your triangles fit that description

[marble parcel]

did i write it wrong or smt? does it need to be ptr and stq instead

[silent plank]

yes

the vertex of the angle is always in the center when labelling angles

[marble parcel]

jesus i was overthinking that so hard lmaooo

so now i can say the 2 angles are congruent

[silent plank]

you'd have to justify that your triangles are either similar or congruent first

[upper karma]

how can i find sine/cosine from hypotenuse length and angle?

[dark sparrow]

what

[upper karma]

or is that impossible

[silent plank]

did you mean find the unknown sides?

[upper karma]

yes

i know the hypotenuse length and the angle

[silent plank]

do you know your trig ratios?

[upper karma]

nope

[silent plank]

(soh cah toa)

[upper karma]

i dont need a lesson in trig

i just need to know this for something im making

to clarify,

i know the hypotenuse's length

i do not know the adjacent/opposite

i know what theta is

[silent plank]

yes, that would be sufficient

[upper karma]

what are the operations?

[silent plank]

it sounds like if you're doing something like this
that relies on trig rations,
you should learn them

[upper karma]

i know

im a month or two away from being taught in school

it is fine if this requires the inverse operations, btw

[silent plank]

i mean you can literally just google trig,
and come back with stuff you don't understand

[upper karma]

nvm

figured it out

it was really simple

sin and cos of theta * hypotenuse

[dark sparrow]

ratios*

[silent plank]

lol don't know why, comes out as "rations" when i write it as well

[upper karma]

alright

i used this to make an incredibly convoluted and unnecessarily complicated way to compute rotations of yaw and pitch

https://www.desmos.com/calculator/rm12vjltqy

[deft sleet]

Hey guys

I had a test today and it seems that one of the questions are wrong

Could anyone take a look at it and see if the get the sum of 181 degrees

I know a triangle is supposed to be 180 degrees so thats why im worried

[mighty narwhal]

,calc sqrt(4.3^2+11.5^2)

[somber coyote]

The following error occured while calculating:
Error: Value expected (char 17)

[quiet mason]

()

,calc sqrt((4.3)^2+(11.5)^2)

[somber coyote]

Result:

12.277621919574

[quiet mason]

it should be 12.3

btw

[mighty narwhal]

You get 181 because of rounding error

[deft sleet]

could you explain to me what you just did?

okay so it should be 12.3 but why

[mighty narwhal]

We calculated that the hyp is 12.277... with Pythagorean theorem

[deft sleet]

ah okay

[mighty narwhal]

But it says 12.2 on the picture

So when you calculate angles with that, the angles will be off slightly

[deft sleet]

oh okay

but idk if i did it correctly still or not

even if the answer is wrong

some people got 69.5 degrees on the biggest angle

Meanwhile i got 70.5 degrees

What would be "correct" If it was 12.2

[quiet mason]

yes

those people might have done -1 to 70.5

for the sake of marks

[deft sleet]

So 70.5 degrees would be the correct answer?

like i did my calculations right but the 12.2 was wrong?

[quiet mason]

no

the sum is wrong

yes they should give yall marks

or show the calculation that hyp was 12.3

[deft sleet]

That i understand but did i do my calculations right

[quiet mason]

to teacher

[silent plank]

we're all 3 sides given to you?

[deft sleet]

yes

[mighty narwhal]

They did a rounding when presenting lenghts of the 3 sides, so they have to accept the answer if it is off because of the rounding

[deft sleet]

As seen in the picture if you scroll a bit up

[silent plank]

as long as youre using legitimate ratios you should be fine

[deft sleet]

okay

@quiet mason what are marks? (not native english btw)

[silent plank]

since with those side lengths, it isn't actually a right triangle

[deft sleet]

its not?

[mighty narwhal]

y'all stop confusing him even more :c

[silent plank]

its very close to one

[mighty narwhal]

Your answer is good, and the 1 degree difference is only because the problem had the lenghts rounded.
thats all

[silent plank]

depending on which sides you use your trig ratios on, you'll get slightly different angles

[deft sleet]

Alright thank you DarK

Ramonov to my understanding the hypotenuse is wrong and therefore it is not a right triangle due to a rounding error

[silent plank]

yeh. but for the question you would treat it as one

[deft sleet]

Yes

Otherwise i did really well on the test because of your help yesterday ramonov

[silent plank]

,w arctan(11.5/4.3) in degrees

[somber coyote]

Display results online and refine query

Requested by ramonov#0921

[silent plank]

,w arcsin(11.5/12.2) in degrees

[somber coyote]

Display results online and refine query

Requested by ramonov#0921

[deft sleet]

so i fucked up

goddamn it

[silent plank]

,w arccos(4.3/12.2) in degrees

[somber coyote]

Display results online and refine query

Requested by ramonov#0921

[silent plank]

using any of these to obtain the angle will get you mark s

you did nothing wrong

[deft sleet]

I used sin-1 (11.5/12.2)

[silent plank]

yeh that's fine

[quiet mason]

calculators allowedd?

[deft sleet]

Okay so i did correctly

yes calculators were allowed

the test is over now but i wanted to make sure i didnt mess up so i could learn from my mistakes

[silent plank]

it doesn't necessarily mean that the hypotenuse is wrong, just that (at least 1 length is wrong)

[deft sleet]

alright thank you

Should i tell my teacher?

[silent plank]

yes

[deft sleet]

What should i say?

[silent plank]

use exact values. or leave finding an unknow side to the student

[deft sleet]

Alright but what do i tell him is wrong with the question?

[silent plank]

pythag doesn't work,

hence it's not a right triangle.
it wasn't even rounded properly,

for calculations, it is assumed that it is (a right triangle) and will return different angle values depending on the trig function being used

Chuck them that.

[deft sleet]

Alright i will thanks

oh you changed it

[silent plank]

worded it a bit better

[deft sleet]

Ah alright

I will send him that

[quiet mason]

lol be kind tho

[deft sleet]

And the last thing

What are these marks you guys are talking about?

like points on a test?

[silent plank]

yeh

[quiet mason]

yah

[deft sleet]

Okay

[quiet mason]

no

yah

[silent plank]

finding an angle like this is worth 1 point? (2 max)

if they offer more, consider getting a new teacher

[deft sleet]

bahahha

It is our first time with trig like i told you yesterday

2 points is max yes

He is a pretty good teacher but he is "out there"

[silent plank]

dw ur doing fine

[deft sleet]

he went on a trip to himalaya this summer to meditate for a month

Yeah thanks for helping me man

[quiet mason]

K

he went on a trip to himalaya this summer to meditate for a month

lmao

[deft sleet]

Yup

he is an oddball

[quiet mason]

does he teach higher classes?

and does he teach well

[deft sleet]

I think he teaches 1st and 2nd but i am not sure

norway has a different school system

He isnt bad by any means

He is not the type of teacher to just give us the answer, he wants us to work it out ourselves

¯_(ツ)_/¯

Alright i sent it to my teacher

[undone shuttle]

@celest swift you're welcome

[celest swift]

[rapid nexus]

how do i get OC, OA, OB

[dark sparrow]

two of these are given

actually, no

all three of these are given

so to answer your question, you get these by reading the problem.

@rapid nexus

[rapid nexus]

so oa = 6, whats the column vector for it

[dark sparrow]

what do you think it is

it's parallel to i

and is six times as long

give it a little thought

[rapid nexus]

just 6i

[dark sparrow]

yes, OA = 6i

so what's that written as a column vector

[sly marlin]

which of a, p, q can you figure out?

#❓how-to-get-help

btw this is #geometry-and-trigonometry

probably not a good idea here @tribal spire

[dark sparrow]

...

let's take this to #help-0, the only channel in which i didn't delete your copy of the q

[gentle dome]

Is there another name for Euclidean Geometry?

Would it be Plane & Solid Geometry instead?

[thorn linden]

yes

[full ruin]

help

which ones harder

geometry or trigonometry

or algebra II

and also

what’s the hardest type of math

[dark sparrow]

there is no objective answer to either of these questions

[full ruin]

oh

ok

[weary drift]

nice save

[full ruin]

i’m too childish to be in this

there is literally a chat called “advanced math” @dark sparrow so there is clearly some type of math considered the hardest .

[dark sparrow]

not really

i mean like let me put it this way: at university level, you very often can pick two people, and each will be good at one thing and find the other's thing hard

[full ruin]

ohh

that makes sense

but it we are being HONEST

geometry is harder than any algebras

[wary turtle]

Also, for someone without any prior knowledge that leads up to it, of course it can look like the hardest - even though it still can be hard, but it's more subjective.

[full ruin]

all the “metrys” are harder than the “gebras”

shapes are harder than anything else

and circles are THE devil

[dark sparrow]

meh

geo was alright to me but 2-col proofs are so bad even the devil would not take credit

[upper karma]

2-col? @dark sparrow

[sly marlin]

yeah, math statement on the left, reasons on the right

I just let my reasons flow anytime I need them

[hard gale]

an example of [REDACTED]

[novel olive]

If I have a wave function that's being "dampened" over time, but the peaks go down at a different rate to the troughs goings up, what would explain that?

By that I mean this (roughly, as I only have a few points at evenly spaced intervals, not the whole curve)

The different rates I'm refering to are the red vs the purple in this image

The red line (being the closest point I had to the maximum point of the cycle for every cycle) goes down at a steeper rate than the purple line (being the same as red but for the minimum) goes up

And as a note, everything before the beggining of that purple line is kind of unreliable data, so it can be disregarded

[sly marlin]

hmm

you can probably model as e^(-At) sin(Bt) + C

@novel olive

[upper karma]

how to do dis