geometry-and-trigonometry

[gritty flare]

@magic turtle answerz B. 80 degrees for you

[magic turtle]

correct

[sick veldt]

Is my dilation correct?

[sick veldt]

<@&286206848099549185>

Need your judgement on my 5 question test

this is #1

[sick veldt]

this serves dead haha

[hard gale]

yas

this one is ok

[sick veldt]

okay

This one I'm having issue with

I got (-3,4) (0.6) and (2,4)

[serene field]

Hint: take the coordinates of each vertex of the triangle and multiply it by the scale factor.

[sick veldt]

when multiplying 2 to the coords

I did

lol

and then after that

I added (2,2) to all three of the scale factored coordinates

that didn't work cause I got 14 as the y for the second coordinate

so I decided to subtract each of those three coordinates by (2,2)

and got this graphed

@hard gale

[hard gale]

i guess you just screwed a calc somewhere, the two other points are fine

this one is odd tbh

[sick veldt]

yeah

FACK

yeha idk what I did wrong

2(0,6) = (0,12)

then

(0,12) - (2,2) = (-2,10)

oops wrong one

[hard gale]

ah i see

[sick veldt]

yeah

I messed up

[hard gale]

i just haven't done this shit for long times lel

[sick veldt]

i calculated

-3,4

but it was -3,3

looks like this now

what do you think

[hard gale]

looks bettre

[sick veldt]

ik but is the math correct and all cuz with dilations it can look alike and whatever but the calculations matter

[hard gale]

the math is ok

however just think to compute the coordinates with the new origin first

for some transformations it matters (like rotations)

[sick veldt]

This one idk

I keep getting decimals for my x

What should I do here

last question

[hard gale]

you should substract the coordinates of the origin first tbh

it's like with functions, as in usually f(g(x)) =/= g(f(x))

[sick veldt]

Okay so what I got for the scale factored coordinates are, (-2.5,2) (1.5, 4) and (2.5, 2)

so just subtract these three by (-3,0)?

[hard gale]

what i mean is substract -3,0 from the coords of all the points then perform the dilation on those new coords

[sick veldt]

k

I got this

(-5,4) - (-3,0) = (-2,4)

(3,8) - (-3,0) = (6, 8)

(5,4) - (-3,0) = (8,4)

^ calculations

REEEEEEE is it right?

cause for the second part with the x I did, 3 - (-3)

@hard gale cmonnnn

almost done haha

[hard gale]

yea so now do the scaling

(a huge pack of flour fell in the kitchen and it was everywhere lel)

[sick veldt]

LOL

idk if this is right tbh

[hard gale]

and now retranslate back

[sick veldt]

what

[hard gale]

1st step : we do as if the origin was (-3,0)

2 : we perform the scaling

[sick veldt]

did that already

[hard gale]

you still have to get the coordinates with the original (0,0) origin (since (-3,0) became our new (0,0) in 1st step basically)

[sick veldt]

I'm confused

(-1,2) (3,4) and (4,2)

what do I do with these coords

since they have already been factored

jesus

Can someone help

I've been on this 5 question quiz for an hour and a half

lol

[main spire]

Quiz help

[flint bronze]

[scarlet needle]

If youre out of coleslaw, use sine law

[teal mortar]

hi guys im super dumb

it doesn't describe where to rotate the shape

i mean it does tell us to rotate the shape 180* clockwise but... at which point do we rotate it from? it never said the origin

i assume you would rotate the shape around either the non coloured point or around the origin but I don't necessarily know how to do it!

translations and reflections are easy but not rotations for me...

[narrow canyon]

@teal mortar I would say assume the origin unless the question specifies a location

[teal mortar]

how do u rotate around the origin im having a hard time trying to plot the points

[narrow canyon]

do you need assistance in understanding rotations easier

[teal mortar]

yes please

[narrow canyon]

ok

[teal mortar]

someone said you rotate around the non coloured dot but i said that doesn't make sense because the shape might go outside of the actual cartesian plane/graph thing

[narrow canyon]

give me a second please

[teal mortar]

okay np

[narrow canyon]

Lets assume we are rotating around 0,0 the origin

[teal mortar]

yes

[narrow canyon]

do you know where A would be visually?

we call it A'

after the rotation?

[teal mortar]

no

would it be in quadrant 3

[narrow canyon]

one second, I will get a visual

[teal mortar]

ok

[teal mortar]

i see.

wait

howd you know how big the circle will be

[narrow canyon]

the radius to point A

[teal mortar]

ah I see

should I do that for every other shape?

[narrow canyon]

no need, there is a faster way once you see the trick

[teal mortar]

hmm

im trying to see the trick hold on

[narrow canyon]

do you know what color is the 180 rotation?

[teal mortar]

green

[narrow canyon]

ok good

[teal mortar]

would the shape just look the opposite

kinda

[narrow canyon]

what are the coordinates of the green dot?

[teal mortar]

(3, -3)

[narrow canyon]

how does it relate to the original location of A?

[teal mortar]

uh

it's diagonal from point A

[narrow canyon]

coordinates

[teal mortar]

erm

oh

point A is -3, 3

so the green is 3, -3

[narrow canyon]

what do you notice

[teal mortar]

so does that mean each one is just opposite?

the x switches with the y

[narrow canyon]

check it out and see

[teal mortar]

😮

i see it !

okay

would the story be different if it was rotating counter clockwise?

[narrow canyon]

yes and no

[teal mortar]

how so?

depends on how many degrees?

[narrow canyon]

lets say we only wanted to go 90 degrees clockwise

there is another pattern

[teal mortar]

lemme see i

it

[narrow canyon]

VERY NICE

[teal mortar]

okay hold on.

so for A if u rotated it 90 degrees clockwise it'd be (3,3)

oh!

all the numbers are positive?

so they're all in quadrant 1

[narrow canyon]

i do suggest you look at the coordinates for 90 degrees clockwise counter clockwise as well

[teal mortar]

so B would be (7, 5)

[narrow canyon]

focus with point B

[teal mortar]

i just got point B

(7, 5)?

which means C would be (10, 10)

[narrow canyon]

b is currently at (-7,5)

[teal mortar]

yeah

but if you rotate it 90 degrees clockwise wouldnt it be (7,5 )?

[narrow canyon]

nope

[teal mortar]

..

[narrow canyon]

different trick for 90 degree rotations

[teal mortar]

erm

im tryna see it hold up

[narrow canyon]

ok, let me know if you want a hint

[teal mortar]

for what i see

none of the numbers look like theyre going into the negatives?

[narrow canyon]

yep

[teal mortar]

ok im guessing here but

B would be

(5, 7)?

[narrow canyon]

yes

[teal mortar]

idk why

but i just guessed and it looked about right

[narrow canyon]

try this

to get to B now, we can go up 5 and to the left 7

[teal mortar]

erm.

i dont understand

[narrow canyon]

rotate the paper you have 90 degrees either way it doesnt matter, and travel the same up 5 and over 7

starting from 0,0

[teal mortar]

oh

i see

from 0,0 going up 5 and left 7 gives you B

[narrow canyon]

keep rotating the paper 90 degrees

[teal mortar]

erm

im not really rotating it im just looking at it XD

[narrow canyon]

ok ok

[teal mortar]

but i do know

if i rotate the paper again

[narrow canyon]

to get to be we go up 5 and over 7 to the left

[teal mortar]

i go 7 right 5 down

[narrow canyon]

go on

ah i see

[teal mortar]

then after do i go 5 down and 7 left?

[narrow canyon]

ignore B for now after you rotate the paper

[teal mortar]

oh

uh

hm

so wait hold on

the trick for 90 degrees...

theyre blurry hold up

[narrow canyon]

ok lets try a different simpler approach

[teal mortar]

okie :3

so the trick to 90 degree clockwise rotations..

would A be 0, -5?

nevermind

it would be 5, 0

[narrow canyon]

yessir

[teal mortar]

but if that's 5 and 0

i have to figure out the rest omg

[narrow canyon]

i have an example, one sec

see if you see the pattern for 90 degree rotations

[teal mortar]

nevermind !

i just saw something

XD

since i found out A

A'*

i can plot out the rest of the points lemme send a pic when i did it

like this ?

@teal mortar

[narrow canyon]

that looks pretty good to me, do you see any patterns in the coordinates and how they change from A to A', B to B' ect?

[teal mortar]

alright so

what i notice is

A: (0,5) B: (6,3) C: (9,8), D (1,10)

^ for original pic

shape* but the coordinates for A' B' C' and D' are: A' (5, 0) B' (3, -6) C' (8, -9) D' (10, -1)

so like the numbers are opposite and the y number becomes a negative.

i also notice that rotating a shape 180* counter clockwise is the same as rotating it 180* clockwise i think

[narrow canyon]

keep going

[woven wigeon]

nice

[teal mortar]

what do i say

xD

i have to find out 270* ccw and 270* cw rotations too! oh boi

[narrow canyon]

is 270 ccw similar to a different rotation you have already done

[teal mortar]

90* cw

i assume

[woven wigeon]

uhh, one quadrant is 90degrees so u can keep that in mind but u should know lo

[teal mortar]

yea

[woven wigeon]

knowing quadrant degrees helps a lot for me

when i learned geometry

[teal mortar]

yeah

hold up.

[narrow canyon]

🤔 yesssssss?

[woven wigeon]

yesu? :V

[teal mortar]

checking a something

sorry my english atm is really bad cuz im tired but i wanna do this because i think im starting to understand it now

[narrow canyon]

you got dis

[teal mortar]

here!

[woven wigeon]

yes its good

[teal mortar]

the drawing in quadrant 2 (top left) is my 180 turn

it said counter clockwise

tho

but i just rotated it clockwise instead

would it make a difference or no?

[narrow canyon]

wonderful, if you want a challenge, try doing the rotations without a picture at all, only use coordinates and the patters you see

[teal mortar]

o boi i dont know if im ready for that XD

so it doesnt make a difference if i rotated 180* ccw or 180* cw?

[narrow canyon]

ah but you are, you are already seeing patterns in the coordinates,

[teal mortar]

yea

well to be quite frank

i just find A'

the coordinate ^

then i figure out the rest of the points by just like plotting them according to the points i see that are already listed for the original points

[narrow canyon]

this is good -> 👻 Chr🅾ma 👻: so like the numbers are opposite and the y number becomes a negative.

[woven wigeon]

yeah, just finding one point is enough to fill out the rest

[teal mortar]

Original shape: A. (0, -1) B. (8,-4) C. (6,-9)

and so as soon as i found A'

(0, 1)

i was able to find out the rest of the numbers

[woven wigeon]

lo i dont care too much about the patterns, i just visualize it... which is my preference

[teal mortar]

so B would be (-8, 4)

C would be: (-6, 9)

thats my strategy

[woven wigeon]

1000 iq

[narrow canyon]

so what do you say the pattern is for the coordinates in that one?

[teal mortar]

A' : 0, 1
B' : -8, 4
C' : -6, 9

all the numbers on the left are negative

all the numbers on the right are positive 😛

[narrow canyon]

but you have a 0

[teal mortar]

erm

well

[narrow canyon]

🤔

[teal mortar]

that stays the same

0 isn't a negative or positive

it just kinda just stays as 0

[woven wigeon]

neither

[teal mortar]

(i think)

^^ yea

[woven wigeon]

0 is just 0 loo

[narrow canyon]

can I suggest slightly different wording?

[teal mortar]

yeah

please do im not good with wording im sorry

[woven wigeon]

dont worry, this isnt an english class

lo this is math

[narrow canyon]

I would say the sign of the x coordinate is opposite

[teal mortar]

yes

im still doing more questions im trying to get the hang of this 😛

[woven wigeon]

then there's me who doesnt git 10 trig problems

[narrow canyon]

I would strongly suggest you keep looking at how the coordinates change and keep getting a better understanding of it

come up with your own "rule" to follow that always works

[woven wigeon]

lo perfect description

[teal mortar]

i just gotta find that correlation

1

bottom left pic is the 2nd shape after rotating it 90* ccw

[narrow canyon]

close...

[teal mortar]

whats up

[narrow canyon]

thats a reflection

[woven wigeon]

oof

[narrow canyon]

over the x axis

[teal mortar]

oH

i looked at it and i said

wow that looks like uh

a mirrored photo

lemme refix.

just wondering

if the original A is ( -2, 4)

does that mean A' would be (-4, -2) or (-4, 2)

nevermind

[narrow canyon]

plot both, one looks right one does not

[teal mortar]

(-4, -2)?

yeah (-4, -2) looks better

[narrow canyon]

so again I urge you to come up with a rule for the coordinates

(-2,4)-> (-4,-2)

[teal mortar]

mhm

okay so what I got so far

[narrow canyon]

how would you describe the change and repeat it for the others numerically, without the graph

[teal mortar]

hmm

how would i

im th⭕nking

well some numbers like the x switches with the y

[narrow canyon]

YESSSSSSSSSSS

[teal mortar]

some of them go from negative to positive and switch and stuff

[narrow canyon]

AND!

[teal mortar]

um

[narrow canyon]

MORE!

[teal mortar]

stuff

wait

[narrow canyon]

bring it all together

[teal mortar]

lemme plot the points

so i can get a general idea

[narrow canyon]

yes good

[woven wigeon]

good good

oi jake, what level of math are u up to atm?

[teal mortar]

grade 8 math for me

😛

[narrow canyon]

I am a licensed math teacher

[woven wigeon]

owo

kk

[narrow canyon]

and chroma should prepare for questions where you do not get a graph

[teal mortar]

yea

okay so basically my general idea

is like

[woven wigeon]

no wonder u were so enthusiastic

[teal mortar]

the numbers switch from x to y and vice versa, the numbers also go from negative to positive and vice versa

[narrow canyon]

this sounds better and better

[teal mortar]

i.e. moving a shape 180* cw

original points: A. (-3,3)

B: (-7, 5)

C: (-10,10)

now if you were to rotate that 180* cw or ccw you'd get

(-3, -3)
(-7, -5)

(-10,-10) so basically rotating it 180* cw or ccw makes the numbers all negative?

[narrow canyon]

hold up

[woven wigeon]

hmmm

[narrow canyon]

one sec

[teal mortar]

i dont think it works like that tho

im stupid

[narrow canyon]

the previous problem said 90 degrees

[woven wigeon]

dont worry, i feel retarded at times too

[narrow canyon]

ahh you see

[teal mortar]

...?

[narrow canyon]

this one is now saying 180

[teal mortar]

1st question I showed you showed rotate it 180*

2nd question I showed was rotate 90* clock wise

3rd question I showed was rotate 180* ccw

4th question I showed was rotate 90* cw

i mean ccw for 4th question ^^

but i dont think my hypothesis for rotating it 180* makes all the numbers negative or something

[narrow canyon]

will the ptterns be the same for them all, or will they have different patterns?

[teal mortar]

damnit its hard!!! i just see patterns

they have different patterns

according to where they are?

[narrow canyon]

good good

[teal mortar]

like where the shape is?

(i.e. quadrant 1, 2, 3 or 4)

[woven wigeon]

if ur coordinates were (+,+) rotated 180* it'll be (-,-)

i think

[narrow canyon]

yep

[woven wigeon]

oh yes

[teal mortar]

what if it were (+,-)

would it be (-, +)

[woven wigeon]

no

[narrow canyon]

try a point

[woven wigeon]

oh wait

[narrow canyon]

3,-4

[woven wigeon]

i read that wrong

[teal mortar]

REEEE

ok what do i do with the point

[narrow canyon]

use a graph you have, plot 3,-4 then -3,4

does it look right?

[teal mortar]

ya

the plots are diagonal from each other XD

if i started with -3, 3 then 180* would be -3, -3?

cuz thats what i just got

[woven wigeon]

(3,-3)

[teal mortar]

wiat

i wrote it wrong my bad

yeah so i was correct

[woven wigeon]

its good

[teal mortar]

if your thing was (-,+) and you rotated it 180* ccw or cw you'd get

(+,-)

[woven wigeon]

yeah, points are basically diagonal to each other

[narrow canyon]

and earlier we said +,- goes to -,+

[teal mortar]

i assume it'd be vice versa if it was (+,-) then it'd be (-,+)

mhm.

there's so much to remember for like making up my own rules!

[narrow canyon]

so how can we describe this generally for all 180 degree rotations

[teal mortar]

erm

the x and y would be opposite

or something like that ?

[narrow canyon]

opposete, say more

[woven wigeon]

so if the points were in quadrant 1 and were rotated 180; the rotated points with be in quadrant 3

[teal mortar]

depending on which one is negative and positive

[narrow canyon]

what does opposite mean

[teal mortar]

i.e if the number is (-4,5) and you rotate it 180* then the opposite would be (4,-5)

[narrow canyon]

ah, opposite sign for x and for y

[teal mortar]

but if your number was (4,-5) then after rotating it it'd be (-5,4)

yes.

[narrow canyon]

that is 100% always correct

[teal mortar]

if your numbers were (4,5) then i think it'd be (-4,-5)

and vice versa.

[narrow canyon]

uh

[teal mortar]

(-4,-5) = (4,5)

idk XD

im just making everything opposite signs

is my hypothesis correct

[woven wigeon]

hyes

yes

[teal mortar]

okok ok lemme write this

i feel good nr

rn

[narrow canyon]

but only for 180

[teal mortar]

yes

that only applies for 180

now i gotta figure the one for 90*

[narrow canyon]

now the 90 degree ones are a little bit trickier

but you got this

[teal mortar]

might take longer

i should be sleeping rn

[narrow canyon]

use your abilities and graphs to plot known points and look at the coordinates

[teal mortar]

but screw sleep

XD

jkjk

i really value it but i also dont

ill start to value it more as i grow older.

seem right?

[woven wigeon]

lmao i sleep an average of 6 hours

[teal mortar]

i sleep about 7

[woven wigeon]

cries

[teal mortar]

and i need about 8

[woven wigeon]

ok, now for 270 degrees xd

[narrow canyon]

very well formatted

[teal mortar]

270 degrees = 90 degrees

my wording is bad but thats what i first thoguht of

[narrow canyon]

kinda yes

[teal mortar]

270* ccw is 90* cw

[narrow canyon]

better thankls

[teal mortar]

270* cw is 90* ccw

and 360* is just 360

the figure remains in the same spot

[narrow canyon]

which is also 0

[woven wigeon]

smh i was just testing

[teal mortar]

mhm.

[narrow canyon]

hell yeah

[teal mortar]

seem good for 90* so far?

or whats up with it

oh crap

[woven wigeon]

seems good

[teal mortar]

i dont know what happens if the numbers are (-,+) and if the numbers are (+,-)

REEEE

oh lawd have mercy

[woven wigeon]

(-,+) ---> (+,+)

[teal mortar]

wait..

[woven wigeon]

i think..

[teal mortar]

wait hold up

(+,-) -----> (-,-)?

[woven wigeon]

yeah

[teal mortar]

and so (-,+) ------> (+,+)

[woven wigeon]

wait

[teal mortar]

or am i just wrong

or its just the opposite

90* is much more complicated than 180*

[woven wigeon]

(+,-) -> (-,-)

[teal mortar]

270* degrees is some how related to 90* i think

yeah tahts what I got

[woven wigeon]

xdd

[narrow canyon]

let me give you a few 90 degree cw examples
4,5 -> 5,-4
-1,3 -> 3,1
-2,-5 -> -5,2
4,-3 -> -3,-4

[teal mortar]

.

thats if both are positive

wait

nvm

[narrow canyon]

what do you notice

[teal mortar]

yeah

so

[woven wigeon]

just know the quadrants, it rly helps by a ton

for me

[narrow canyon]

the pattern is more than just signs

[teal mortar]

both positive ones: (+, -)
negative x and positive y: (+,+)
both negative ones: (+,+)
x positive and negative y: (-,-)

so

hmm

negative x and positive y is = to both negative?

x positive and y negative is = to both negative

both positive = x positive y negative

[narrow canyon]

focus on just the numbers not the signs for a moment

[teal mortar]

its hard

[narrow canyon]

what happens

[teal mortar]

the signs kinda make sense

1. 4,5 -> 5,-4
2. -1,3 -> 3,1
3. -2,-5 -> -5,2
4. 4,-3 -> -3,-4

1. the x and y switch spots and y becomes negative

2. both numbers become positive

3. both numbers become positive

[woven wigeon]

idk if my method helps but here :V

[teal mortar]

4. both numbers become negative

holl up noice noice

[narrow canyon]

try to avoide breaking it up into different examples

[teal mortar]

b00m

[narrow canyon]

look at all 4 examples and make one rule that works on them all

[teal mortar]

now what's different about cw

erm

im not good at doing stuff like that sorry

i do notice one thing in common.

[narrow canyon]

what

[teal mortar]

1. 4,5 -> 5,-4
2. -1,3 -> 3,1
3. -2,-5 -> -5,2
4. 4,-3 -> -3,-4

x and y numbers switched spots

[narrow canyon]

wonderful

and

[teal mortar]

so 4,5 -----> 5,4

[narrow canyon]

what else

yes

[teal mortar]

just negative and positive signs but

i can't grasp onto it

[narrow canyon]

ok

lets focus on the x value of them all

[teal mortar]

i only understand the x and y numbers switch spots

[narrow canyon]

4,5 -> 5,-4

[teal mortar]

yea

[narrow canyon]

4 swaps and becomes negative

[teal mortar]

the x becomes the y in the 90* one?

[narrow canyon]

it changes signs

[teal mortar]

4,5 -> 5,-4

yea

[narrow canyon]

opposite

yea

[teal mortar]

so opposite positions and opposite signs

[narrow canyon]

-1,3 -> 3,1

[teal mortar]

but the 5 remains the same

opposite position

opposite sign

[narrow canyon]

x again is opposite and opposite sign

now look at just y

[teal mortar]

does it work for all tho?

all 90* formations i.e. (-,-) or only (-,+)

[narrow canyon]

y swaps but...

[teal mortar]

y switches positions but stays the same

[narrow canyon]

bingo

[teal mortar]

does that apply to all of them

[narrow canyon]

lets put it all together

and check

[teal mortar]

(-,-) (-,+)
(+,+) (+,-)

[narrow canyon]

they swap

[teal mortar]

does that idea of x opposite side and x opposite sign and y opposite side but same sign work for all

or no.

[narrow canyon]

check it

[teal mortar]

cause i just got this and it seems to make sense for me

[narrow canyon]

1. 4,5 -> 5,-4
2. -1,3 -> 3,1
3. -2,-5 -> -5,2
4. 4,-3 -> -3,-4

[teal mortar]

tbh i cant really check its 11:30pm and i should be in bed ill only have 7h of sleep

[narrow canyon]

ok ok

[teal mortar]

it works.

[narrow canyon]

then before you leave

[teal mortar]

i jsut saw

it works.

the hypothesis works

[narrow canyon]

now thats math right there

[teal mortar]

XD

[woven wigeon]

👏

[narrow canyon]

one sentence for all 90 degree cw rotations

[teal mortar]

but what about 90* ccw and 270* cw and 270* ccw

could one of you guys dm me about it because i gotta sleep soon

like very soon

[narrow canyon]

remember 270ccw is the same as...

90cw

[teal mortar]

ok

so i just say

270 ccw: 90* cw

how do i do 90* ccw

so basically all i need is 180*, 90* ccw, 90* cw?

[narrow canyon]

the wording you just used for 90 cw is almost the exact same for 90ccw

[teal mortar]

almost?

is it just

the opposite

XD

[narrow canyon]

haha

[teal mortar]

im tryna figure out

my brain is just dying at this point but im starting to get a grasp

[narrow canyon]

you will be the best learner if you do this one on your own

take a break after writing down the 90cw one

[teal mortar]

instead of finishing my homework im doing this math concept stuff and its rlly cool and ill share with my class

[narrow canyon]

come back another time

[teal mortar]

wait

[woven wigeon]

sleep is no1 priority

[teal mortar]

can you give me some numbers so i can test my hypothesis

[narrow canyon]

its good to take breaks when you are actually learning hypothesis and stuff

[teal mortar]

for ccw 90*

yeah 😛

[narrow canyon]

will dm you

[teal mortar]

im so excited to share this with class

ok thx

I'm so excited to share this with my class.

[woven wigeon]

happy to hear

[teal mortar]

thanks to u guys u helped me a lot

[woven wigeon]

...but i probably didnt help

[teal mortar]

now i can complete the rest of my hmwk at school before math and ill understand everything

u did help! u helped confirm my theories and stuff

thx ❤

[woven wigeon]

aww thx <3

I’m having problems with #2

[teal mortar]

OH CRAP

IS THAT WHAT I HAVE TO LEARN IN HIGH SCHOOL

[woven wigeon]

yes

these problems has sum algebraic uses to it

but me brain smol

[jaunty plume]

what is another way to write csc(x)

[narrow canyon]

1/sin i believe

[woven wigeon]

yeah

[jaunty plume]

so what is csc(x)sin(x)

[upper karma]

1

[woven wigeon]

yes

[jaunty plume]

yes

[woven wigeon]

yes intensifies

[jaunty plume]

what's another way to write 1

[woven wigeon]

lemme right down the problem to get an idea

hmm

[teal mortar]

imma fail high school math then

[woven wigeon]

unsuuree

[teal mortar]

if math like that looks like that

gn guys

[jaunty plume]

n

[woven wigeon]

gn

[jaunty plume]

hint: combine c^2/s^2 +1

so same denominator

[woven wigeon]

yeah kk

[jaunty plume]

@me if you need

[woven wigeon]

alright

ahhhh

[jaunty plume]

[woven wigeon]

i got csc^2

and that symbol afterwards

[jaunty plume]

theta

[woven wigeon]

yeah

cos^2(x)/sin^2(x)+1

then u get cos^2(x)+sin^2(x)/sin^2(x)

end result is csc^2(x)

[jaunty plume]

that's right

[woven wigeon]

yay

thanks brutha

[jaunty plume]

wait they put the answer as sec^2 on the sheet

or is that something else

oh

is it multiple choice

[woven wigeon]

its a multiple choice

yeah

[jaunty plume]

nice

[woven wigeon]

i learned more from u than my math teacher lo

probably cuz im slacking off 90% of the time

[jaunty plume]

prob

[woven wigeon]

yeah...

[woven wigeon]

What happens after

[keen aspen]

sin^2+cos^2

=1

1+2sincos

[woven wigeon]

waat

[keen aspen]

Look at the numerator

sin^2 and cos^2

that makes 1

[woven wigeon]

so combining them makes 1

ah kk

thx

got the answer

[quaint plinth]

Hi. I'm new to math.

I had a question.

How come the digits of the constant pi can be 0s?

if it is a 0, how come it doesn't end there and then more digits follow? and there are lots of 0s.

[jaunty plume]

the same way the number 101 has a 0 but doesn't end there

[quaint plinth]

hmm

but why can the digits of the pi have a 0, does that not kill its accuracy?

I was thinking it may be picking the number between 1 and 9 based on how accurate it is.

(and yeah, I don't understand any math, but interested in learning )

[jaunty plume]

idk what you mean

what about the number 0.01

[paper glacier]

0 in this case has a value of its own

[violet flower]

Your a fuckin idiot

No offense

[jaunty plume]

your

nice one

[dire rampart]

who they speaking to lol

[jaunty plume]

idk

[woven wigeon]

Cotx(secx - cosx) = sinx 🤔

[dire rampart]

?

[left folio]

How can i find the trigonometric values of cos(150°);sin(150°)?

[serene field]

Know your unit circle.

[lament bay]

How do I do #3

[upper karma]

Find the slopes of the two opposite sides of a parallelogram and show they are identical?

[lament bay]

@upper karma how when I don’t have the coordinates

[upper karma]

Well, aren't you going to create a coordinate system for the parallelogram?

[lament bay]

How would I do this

I’m like new at this stuff

[upper karma]

Oh, sorry, I keep jumping channels, sorry about delay. OK, can you draw a parallelogram on a Cartesian grid?

[glad ocean]

yes

[upper karma]

OK, do it and then check the slopes of the two parallel lines

[lament bay]

I don’t even know what you’re talking about

Sorry I suck at this

[serene field]

Notice the slopes of the parallel lines in the parallelogram are the same.

[lament bay]

Wait wait @serene field how did you get that?

[serene field]

By definition of parallelogram, opposite sides must be parallel

I just chose equations that gave whole number coordinates.

[lament bay]

So I just gotta draw that and show the slopes for it to be proven right?

[serene field]

I don't know much about coordinate geometry, but going off the name, you may want to instead use the coordinates of the vertices.

Prove that the slopes between adjacent vertices are equal

[lament bay]

Basically do the slope formula

And show they are the same

[serene field]

Pretty much, yeah.

[lament bay]

Ok thanks for your help!

[serene field]

No problem, feel free to ask more questions as you come across them. 👍

[lament bay]

@serene field mind helping me with #6?

[serene field]

You know how we used the slopes of the parallelogram to prove the earlier thing?

[lament bay]

Yea

[serene field]

Pretty much the same thing here.

[lament bay]

I do the same with the sides?

How do I know what points to choose though?

[serene field]

Rather than slope, you're just looking for congruency

Distance formula will do

You can just draw an isosceles trapezoid on a coordinate plane with vertices on whole numbers

[lament bay]

What points should I choose though?

[serene field]

Whatever points you like. Drawing something sideways might make computation slightly harder though.

[lament bay]

Would that one work?

[serene field]

Having your base on the x-axis might make computation easier.

Looks like that will work, though.

[lament bay]

I graphed this one for one of my earlier problems

I’m just gonna finnessed it so I don’t gotta do slope again lol

[serene field]

Since you're looking for congruency, distance is probably the way to go.

[lament bay]

Thanks

@serene field when I show my work I gotta find the distance for DB and AC right ?

Or do AD or BC work?

[serene field]

The sideways things

/ \

Not the parallel bit

[lament bay]

ok I did it right

@serene field do you know how to do #7

<@&286206848099549185>

[lament bay]

@dawn stone

[dawn stone]

yes mate?

[lament bay]

Can you help me with #7?

[dawn stone]

umm

you could take different points that satisfy the equation, and then plot a graph connecting those points?

[lament bay]

Uh wdym

[dawn stone]

like take y=0, then find out the value of x that satisfy the equation

then take y=something else, find the value of x again

similarly, find multiple points in this manner and then join them on the graph

[lament bay]

can you show me?

Kind of confused

[dawn stone]

I told you

take y=0

what do you get the value of x as?

[lament bay]

4

[dawn stone]

|x-2| + 3=5

|x-2|=2

[lament bay]

Do I just use 0,1,2,3?

And then graph it?

[dawn stone]

x-2=2 or x-2=-2

so you get x=4, and x=0

[lament bay]

So it’s a V?

[dawn stone]

so your first two points are (4,0) and (0,0)

[lament bay]

Basically only need 2 points to graph it

[dawn stone]

then you try finding points with different values of y, and finally connect them

You need more than 2 points to graph anything

always

[serene field]

Since this has double absolute values, you may want to check both the positive and negative side.

[dawn stone]

yup, you got 2 points for y=0, then next try y=1, y=2, y=-1, y=-2 and once you feel you have enough points graph it

[lament bay]

|x-2|+4=5

[serene field]

My intuition is saying this is a square/rectangle shaped graph.

[dawn stone]

Yep ^

[lament bay]

Ok

@dawn stone you helped me on this one but I got some questions with the theorem

[upper karma]

hmmm proofs.

what question do u not understand

[dawn stone]

you pinged me, but I don't see your question

I already explained these in the other chan to you the other day right? Where are you stuck at?

[lament bay]

Can you check the ones without theorems next to them since I’m supposed to have one next to everyone ? Also check if the ones I did are right @dawn stone

[dawn stone]

did you just copy the answers to them I gave you earlier? Cuz you don't even have an X in your figure in question 4 yet you've used it in solution

that's bad mate, you won't learn anything that way

[lament bay]

I just imagined it

I’m gonna redo it on paper later

Just making last minute revisions

@dawn stone

[dawn stone]

mhmm, the solutions are fine though alarmingly identical to mine. Anyway looks good, proceed

[lament bay]

Ok that’s all

Thanks

[left folio]

@serene field the unit is 1

[forest hazel]

<@&286206848099549185> how do I solve iii

[spring apex]

ping after 15 minutes of asking the question

not any less

[keen tangle]

did you solve i and ii already @forest hazel ?

[restive wren]

I am stuck on it for a while can anyone help

[keen tangle]

do you know the power of the point theorem?

[forest hazel]

@keen tangle yea I did

Both answers are 0?.5

0.5*

[keen tangle]

how did you solve it?

[forest hazel]

Uh formula sheet and some manipulation

But when it comes to tan 8x

Idk how the heck to convert it

[keen tangle]

yeah prolly formulas for sin(2x) and cos(2x) right?

[forest hazel]

Yea

[feral perch]

you could try to rewrite tan8x to sin(8x)/cos(8x) ?

[forest hazel]

I did formula for tan (2x)

[feral perch]

see if that helps?

[forest hazel]

And dk how to proceed

I did

I kinda uh got stuck

Because there's the 4 there

That idk how to get rid of

[keen tangle]

sin(8x)=2sin(4x)cos(4x)

cos(8x)=cos^2(4x)-sin^2(4x)

[forest hazel]

How do I convert it because there's the stupid 4 there that I cant exactly use

I need to get it down to at least 2x

[keen tangle]

then repeat

cos(4x) you know already

sin(4x)=2sin(2x)cos(2x)

I just realised you can't really determine tan(8x)

you can get |tan(8x)| but not tan(8x)

@restive wren do you still want help with that?

[restive wren]

Yes

[keen tangle]

can you repost?

[keen tangle]

so have you heard of the power of a point theorem

also known as intersecting chords theorem

[forest hazel]

@keen tangle what's your answer for that

Just checking

[keen tangle]

for what?

[restive wren]

I am in high school ,so no

[forest hazel]

The question I posted jn

[keen tangle]

$|sin(4x)|=\sqrt{1-\cos^2(4x)}=\sqrt{1-\frac{1}{4}}=\frac{\sqrt3}{2}$

[somber coyote]

Gonzo17:

[keen tangle]

$|\sin(8x)|=2|sin(4x)|cos(4x)=\frac{\sqrt3}{2}$

[somber coyote]

Gonzo17:

[keen tangle]

I think you can see where this is going

[forest hazel]

Yea

Except my answer sheet has two answers

[keen tangle]

yea, cause we can only get |tan(8x)| this way

[forest hazel]

I think they included a complex number

Fok what is this sch doing

Anyway thanks!

[keen tangle]

ok @restive wren sry for that break

[rancid nacelle]

im trying to make some formula that output the width (widest point) of a regular polygon with the same area as a square with x width.

Is this even posible, not that good at math myself?

-inputing 3 and 100 would be 133,333...
-inputing 4 and 100 would be 100
-somehow inputing infinity and 100 would be 112.83...

[steady hull]

how do i prove this

[soft scarab]

@steady hull why not just evaluate for the values?

[limpid basin]

Kermie is op he got it already

[soft scarab]

i don't understand why he couldn't just evaluate the equation?

[limpid basin]

Probably cause it’s not very elegant to evaluate the values using a calculator and show that they sum to 0

Holy shit my grammar

[soft scarab]

@limpid basin how else would you do it?

using special triangle identities?

[limpid basin]

Sum to product I think

[somber coyote]

luka:

[upper karma]

how do I prove that this works for any real number x?

<@&286206848099549185> any ideas?

[wanton forge]

cos(x) = cos²(x/2) - sin²(x/2) = cos²(x/2) - (1 - cos²(x/2)) = 2cos²(x/2) - 1

[somber coyote]

luka:

$$cos(x) = cos²(x/2) - sin²(x/2) = cos² - (1 - cos²(x)) = 2cos²(x) - 1$$

[upper karma]

$$2cos^2 x - 1$$

[somber coyote]

luka:

[wanton forge]

wait

[upper karma]

that's not x/2?

[wanton forge]

wait I'm tired and thinking (or trying to)

[upper karma]

ok

$$cos(x) = cos²(x/2) - sin²(x/2) $$

hmm

[somber coyote]

luka:

[upper karma]

how do I know that?

[wanton forge]

duplication formula

cos(2x) = cos²(x) - sin²(x)

[upper karma]

ok

[wanton forge]

cos(x) = cos²(x/2) - sin²(x/2) = cos²(x/2) - (1 - cos²(x/2)) = 2cos²(x/2) - 1

[upper karma]

yep

thank you so much!

[steady sleet]

yw

[sick veldt]

are my points right?

Heres my calculation
(5 + x2)/2, (-6, y2)/2
I solve for x2
8 = 5 + x2/2
16 = 5 + x2
11 = x2
Then
Solve for y2
5 = (-6, y2)/2
10 = (-6, y2)
16 = y2

<@&286206848099549185>

[cold plaza]

U can check urself

What’s the midpoint of 11,16 and 5,-6

@sick veldt

Anyway yes it is right

The way u calculate midpoints is by summing the x, then divide by 2

And doing the same for the y

[sick veldt]

ik

what I did

anyways

could you stick around for one more?

[cold plaza]

Sure

[sick veldt]

Thanks

So

Just find the mid-point

then fine the midpoint of the same found midpoint with point A

find the midpoint between point A and the mid-point basically right?

[upper karma]

how do I get $$cos(pi/8)$$

knowing that pi/8 = 1/2 * pi/4

I have to prove that it's equal to $$\frac{\sqrt{2+\sqrt{2}}}{2}$$

<@&286206848099549185> any ideas?

[keen tangle]

there are half angle formulas

[upper karma]

*I need to use the duplication formula

[somber coyote]

luka:

[keen tangle]

so set $x=\frac{\pi}{8}$ just for easier notation

[somber coyote]

Gonzo17:

[upper karma]

ok

[keen tangle]

you know cos(2x) already

[upper karma]

yea

$$2cos^{2}(x)-1$$

[somber coyote]

luka:

[keen tangle]

and on the other hand it's $\cos(\frac{\pi}{4})=\frac{\sqrt2}{2}$

[somber coyote]

Gonzo17:

[upper karma]

ok

$$\frac{\frac{\sqrt{2}{2}+1}{2} = cos^{2}(\frac{\pi}{8})$$

[keen tangle]

what?

[somber coyote]

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

[upper karma]

$$\frac{\frac{\sqrt{2}{2}+1}{2} = cos^{2}(\frac{\pi}{8})$$

any ideas how I correct this?

[keen tangle]

$\frac{\frac{\sqrt{2}}{2}+1}{2} = cos^{2}(\frac{\pi}{8})$

[upper karma]

right

lol

[somber coyote]

Gonzo17:

[upper karma]

yep

so is that it

[keen tangle]

was just missing 1 brace

[upper karma]

-sqrt and sqrt?

ok

@keen tangle doesn't work 😦

[somber coyote]

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

[keen tangle]

$\sqrt{\frac{\frac{\sqrt{2}}{2}+1}{2}} = cos(\frac{\pi}{8})$

[upper karma]

?

you have to do the whole sqrt

[somber coyote]

Gonzo17:

[upper karma]

on the left side of the equation

yep

but what I'm supposed to get is $$\frac{\sqrt{2+\sqrt{2}}}{2}$$

[somber coyote]

luka:

[upper karma]

rip

[keen tangle]

yeah they're equal

[upper karma]

how?

$\sqrt{\frac{\frac{\sqrt{2}}{2}+1}}{\sqrt{2}} = cos(\frac{\pi}{8})$

lol

sqrt for numerator and denominator

[keen tangle]

$\sqrt{\frac{\frac{\sqrt{2}}{2}+1}{2}} = \frac{1}{2}\sqrt{4\Big(\frac{\frac{\sqrt{2}}{2}+1}{2})}=\frac{\sqrt{2+\sqrt{2}}}{2}$

[upper karma]

lol

[somber coyote]

Gonzo17:

[upper karma]

hmm is there an easier way to convert it?

[keen tangle]

I mean, this is pretty much simplyfying

you wanna get the denominators out of square roots

[upper karma]

I can understand $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

can you explain with that method?

[somber coyote]

luka:

[keen tangle]

$\sqrt{\frac{\frac{\sqrt{2}}{2}+1}{2}} = \sqrt{\frac{\sqrt{2}+2}{4}}=\frac{\sqrt{2+\sqrt{2}}}{\sqrt 4}=\frac{\sqrt{2+\sqrt{2}}}{2}$

[somber coyote]

Gonzo17: