is this all possible in 2 mins though?
#geometry-and-trigonometry
lime dune
you don't need to label every single angle
clear anvil
yeah i used 1, but i guess a multiple of 5 apparently was the best choice here
lime dune
and sometimes you can just "eyeball" stuff
clear anvil
what's "eyeball" stuff
i played the smart game and said they're all congruent triangles
which was a correct assumption
lime dune
you can eyeball that congruence assuming the diagram is to scale
clear anvil
but no diagrams are to scale?
at least no geometry problems have diagrams to scale right?
lime dune
when i look at the diagram i also notice lots of right triangles with altitudes to their hypotenuses
they're not necessarily to scale
but a lot of the ones i've seen are
clear anvil
well yes i noticed a lot of right triangles
i guess i gotta do more of these things
u mentioned angle chasing right
clear anvil
i don't do competition math :3
lime dune
(i can dm you some problems on angle chasing if you'd like)
clear anvil
i never did geometry formally lol
i cheat my way through geometry by bashing trig
but wasn't applicable here
lime dune
lmao rip
clear anvil
(i can dm you some problems on angle chasing if you'd like)
i guess, sure
lime dune
aight gimme a moment
empty yew
Is 13,12,5 a Pythagorarean triplet?
merry aurora
yes
empty yew
I can prove this with Pythagoras theorem but I can't prove it with 2m,m²+1,m²-1 formula
obsidian harness
I can prove this with Pythagoras theorem but I can't prove it with 2m,m²+1,m²-1 ...
Not all Pythagorean triples have this form
All primitive Pythagorean triples (those where gcd(a, b, c) = 1) can be written in the form $a = m^2 - n^2, b = 2mn, c = m^2 + n^2$
somber coyoteBOT
south
obsidian harness
For all Pythagorean triples simply multiply a, b, c by some positive integer k
empty yew
Ohh
obsidian harness
Ye
obsidian harness
I can prove this with Pythagoras theorem but I can't prove it with 2m,m²+1,m²-1 ...
This is only for when n = 1
empty yew
Is it hard to find the m and n?
obsidian harness
Is it hard to find the m and n?
No, there are just a few conditions like m > n > 0
And m and n must be odd, even or even, odd: they must have opposite parity
For a primitive triple
empty yew
For a primitive triple
Primitive triple?
obsidian harness
Basically because 12 is the even number, you have 2mn = 12, mn = 6
obsidian harness
Primitive triple?
One where gcd(a, b, c) = 1
So yes (5, 12, 13) is a primitive Pythagorean triple
empty yew
Thanks
obsidian harness
No worries
vocal bison
Can someone help me with number 4
clear anvil
I think the fastest approach would be coord geo
but similarity is pretty quick, right?
clear anvil
I think the fastest approach would be coord geo
find the line between (0,0) and (1,1/2) then find the line that passes through (1/2,0) and (1,1)?
Find the perpendicular distance between them and square the result?
clear anvil
Can someone help me with number 4
maiden brook
Find the perpendicular distance between them and square the result?
yeah or just find the coordinates of two points on the square
clear anvil
yeah or just find the coordinates of two points on the square
which needs some geometry
maiden brook
no not rlly
I just think coord geo will very obviously work cause u r looking for an area of a nice shape, have right angles and midpoints
clear anvil
How do you find the coordinates of two points on the square?
If not for doing what i mentioned
clear anvil
I just think coord geo will very obviously work cause u r looking for an area of...
sure fair enough
obsidian harness
In this case though the area of the black and white region is just (area of semicircle with radius b/2) + (area of semicircle with raidus a/2) + triangle
So you actually don't need coordinate geometry at all
It's useful for many problems but not for all of them
maiden brook
How do you find the coordinates of two points on the square?
system of equations (which works out almost immediately) then distance formula
clear anvil
So you actually don't need coordinate geometry at all
we're doing another problem ig 😭
Lol
clear anvil
system of equations (which works out almost immediately) then distance formula
what's your systems of equations?
can u share
obsidian harness
Ohhhh I see the 1/5 one
It's 1/5 the area of the big square, famous q
Yes you would use coordinate geometry for that, that's 1 way
obsidian harness
Yes so if you realise they are AA similar you're not too far off
clear anvil
It's 1/5 the area of the big square, famous q
it's famous?
Lol
yeah i did the question i got 1/5
i did similarity then ratio of areas = (ratio of lengths)^2
maiden brook
it’s kinda famous
clear anvil
ratio of lengths was sqrt(5) so ratio of area is 5
maiden brook
geometry is fun
maiden brook
y = 2x, y = -1/2 x + 1/2
u see this right?
clear anvil
I don't even geometry too lol
clear anvil
u see this right?
isn't that what i mentioned though
Yeah i do
but then i don't see why it's a system because we're finding the
distance between the two
they're supposedly parallel lines
there's no intersection so no system to solve
maiden brook
sure that always works
but what I did was find two points on the square (which are determined by two respective system), find that distance and square
sounds like a lot but it’s not
clear anvil
You mean these 2?
Yeah but that's like a lot of effort i feel
S_2 is the intersection of those two lines which i have to find the equation for
S_1 is the intersection of another two lines which i have to find the equation for
finally, i have to use the distance formula on S_1 and S_2
THEN FINALLY square that result
i can't do all that in 2 minutes 😭
clear anvil
would take me like 3 minutes
yeah i have 1.5 mins i guess
but yes thanks thanks-
each question is 1.5 mins
maiden brook
for what?
obsidian harness
damn i didn't know it was famous
Yes it was most famously on Brilliant
clear anvil
for what?
my quiz is 1.5 minutes per questions for 30 questions where each question gets more difficult
clear anvil
Yes it was most famously on Brilliant
ohhh i see
maiden brook
school quiz or what?
maiden brook
that teacher is dumb u should not have that much of a time crunch
clear anvil
it's preparation for a standardized exam
which has the same time crunch but like on that exam
they just give you all 30 minutes or whatever and you allocate it however u like
but with a bit of math that averages to 1.5 mins give or take
maiden brook
WAY too short
bruh
kinda ruins things imo
not rlly testing about skill at that point
clear anvil
😭 yeah unfortunately
i don't do geometry either
so it gets annoying to have to do these competition-esque problems in 1 minute
rose raven
my quiz is 1.5 minutes per questions for 30 questions where each question gets m...
this reminds me of that one guy popping up on my yt feed and the videos are "doing x math subject but the problems keep getting harder" and the thumbnails are like really weird
dark sparrow
@sour peak what's troubling you?
sour peak
I think I got it I said 132pi
trail tendon
Help??
ok so first of all you can enter today's date most likely if you look at the bottom corner of your screen you will see it. you can probably enter it by typing because it looks like its on a computer. i don't know how to help you with your name tho, maybe copy a friend's answer?
maiden brook
can someone pls explain mass point geometry?
lime dune
think seesaws
if I put a 5lb weight 10ft from the fulcrum on one side of a seesaw and I have a 25lb weight that I want to put on the other side
how far away should I put it from the fulcrum to balance the seesaw?
lime dune
there is no “”””””rigor”””””” to it
mass of A * distance of A from fulcrum = mass of B * distance of B from fulcrum
this is the most fundamental equation for mass points
we pretend our “points” are weights
and apply this equation repeatedly
maiden brook
there is no “”””””rigor”””””” to it
average science thing
rugged shuttle
How does the a^2 and the b^2 term affect a hyperbola
maiden brook
how would u do this without mass point geometry
maiden brook
there is no “”””””rigor”””””” to it
i understand how to use it, i just dont rlly get why it works
lime dune
again
physics
if two masses on opposite sides of a fulcrum exert equal torques on the lever
then the lever is balanced
maiden brook
how would u do this without mass point geometry
what about this how would u do it without mass points?
lime dune
I think I’ve seen alt approaches where they draw in parallel lines and use similarity? but that gets kinda messy
or, alternately, area ratios
if two triangles have the same base length or height, then the ratio of their areas is the ratio of their heights or base lengths
dusty ginkgo
how would u do this without mass point geometry
vectors
dusky locust
how would u do this without mass point geometry
stupid solution that happens to work is draw a simple triangle that has these properties (like A(3,0) B(0,3) C(0,0) D(0,2) E(1,0)) and the ratio will become apparent
hollow cipher
can someone pretty please tell me what i did wrong
north kindle
Rounding probably
dark sparrow
i have to round it?
show all of your work
then we can tell you exactly where you went wrong
limber musk
Help pls I'm so confused
dark sparrow
this doesn't look like geometry. maybe move to #prealg-and-algebra ?
limber musk
oh ok srry
hollow cipher
show all of your work
dark sparrow
several things wrong with this
one, you misapplied the pythagorean theorem and mixed up the signs
two, 84^2 - 155^2 is not equal to 16969
three, a number isnt equal to its own square root
four, where did you get that 130.2 from? certainly not from memory, right?
hollow cipher
idek
dark sparrow
so you don't even know where you got the 130.2 from?
how can that be?
it must have come from something, right? like a calculator?
hollow cipher
i square rooted 16969
hollow cipher
calculator
dark sparrow
right, and your calculator gave you only 130.2?
limber musk
doesn't it?
dark sparrow
did your calculator give you more decimal places or only one?
hollow cipher
right, and your calculator gave you **only** 130.2?
it gave 130.2651143
hollow cipher
oh
dark sparrow
you really should be a LOT more detailed in your work
with this barebones thing you sent the mistake was nearly impossible to track down
would you like me to tell you how to write out your work properly?
hollow cipher
yes please
dark sparrow
i will write it out on paper so there's no confusion, one moment.
hollow cipher
okayy
limber musk
just checking, this is part c of the same question as before. for max profit employees have to be 0 right??
dark sparrow
wrong channel? but also no.
limber musk
oops
dark sparrow
hollow cipher
thank youuuu
dark sparrow
just to make sure
you understand that this ISN'T just me being a stickler for all-work-shown, yes?
hollow cipher
yea
dark sparrow
like my point is
we all make mistakes. there's no moral value attached to making a mistake.
but when you make a habit of writing out your work properly and not skipping any steps
then you can CATCH your mistakes.
and correct them before bad things happen (ranging from you losing a few marks on your homework to a bridge collapsing)
obsidian harness
What have you tried so far?
If the x coordinate of B on the x-axis is k, can you find an expression for point P in terms of c and k?
austere dew
Hello, I have a problem on this question: Either $ABC$ a triangle and $\Gamma_B$ (respectively $\Gamma_C$) a circle passing through $A$ and tangent to $BC$ in $B$ (respectively in $C$). If the diameter of $\Gamma_B$ $=56$ and the diameter of $\Gamma_C$ $=126$ . what is the radius of the circle circumscribed by $ABC$? I used the law of sines and got a result of 8.001 but this is wrong, I also tested with equations but impossible.
somber coyoteBOT
habibjr.
vocal python
hello i hope i don't bother anyone but can someone explain me this problem and show me the solution
dark sparrow
do you understand what this notation stands for? Y/N @vocal python
i hope i don't bother anyone
these pleasantries are not necessary by the way
merry mulch
The angles of depression and elevation of the top of a tower 20 meter high from top and bottom of a second tower are 60 degree and 30 degree respectively. Find the height of the second tower.
can you check this question weather the answer is 4m or not?
vocal python
do you understand what this notation stands for? Y/N <@1218174339522887740>
i know is rotatation and translation
dark sparrow
rotation (small r), translation (T) and reflection (big R).
do you understand what the numbers underneath each letter tell you?
vocal python
Yeah i think so
merry mulch
The angles of depression and elevation of the top of a tower 20 meter high from ...
Is 2nd Tower taller than the 1st one?
dark sparrow
Yeah i think so
ok, can you explain their meaning in your own words?
for example, in option (a) one of the transformations is $T_{\ang{1,3}}$. can you tell me what this notation stands for?
somber coyoteBOT
Ann
vocal python
ok, can you explain their meaning in your own words?
3 to the left and one up
dark sparrow
ok, that'll do.
er
wait no
you mixed them up.
the first coordinate is the horizontal movement
and you also screwed up the direction
<1, 3> means 1 to the right and 3 up
leftward movement would mean a negative number for the first coordinate
so "3 to the left and 1 up" would be <-3, 1>
merry mulch
The angles of depression and elevation of the top of a tower 20 meter high from ...
Wait is the ans 80m?
Anyone?
merry mulch
Nevermind it's solved now
vocal bison
Ik its a semicircle but i stilldont understand how to find the shaded part
wait nvm imslow
tall coral
what are you trying to find?
vocal bison
what are you trying to find?
Area of shaded region
tall coral
what info do we have on the empty spacing within the semicircles?
vocal bison
um that the dots are teh centers of teh circel
tall coral
ok I think I got it
vocal bison
im confuysed
tall coral
have you found the total area of the subtracted space?
vocal bison
no i think i did it wrong
muted sorrel
is that the whole problem or just a pic of the triangle and circle thingie?
muted sorrel
probably but idk where to find it
muted sorrel
can u type out what's written on top?
everything above the "Area of delta: 1/2 b*h"
the first three lines
vocal bison
area of outside semicircles:
bigger; 1/2pi(1/2b)^2 = 1/8pi b^2
smaller; 1/2pi(1/2a)^2=1/8pi a^2
vocal bison
Uh idk i just did pi r ^2
tall coral
is this outlined shape a semi-circle?
vocal bison
ye it is
tall coral
ok, making that assumption, what do you think the area of the semi-circle not in the triangle
vocal bison
pi(a+b)^2 /4 ?
trail tendon
is this outlined shape a semi-circle?
out of curiosity, it look like one fs, but how do you geometrically prove/know that it is?
vocal bison
out of curiosity, it look like one fs, but how do you geometrically prove/know t...
the dot is the center of the circle
vocal bison
Can someone help me with number 4
^i feel like none of yall scrolled up
tall coral
out of curiosity, it look like one fs, but how do you geometrically prove/know t...
I'm just assuming based on the given info, I don't think you can really prove it's a circle with the given area
tall coral
pi(a+b)^2 /4 ?
you know (a+b)^2 doesn't equal (a^2)+(b^2) right?
nimble yew
is this outlined shape a semi-circle?
Is there a value for the righthand side of the scalene right triangle?
Are we messing with invisible/imaginary numbers?
tall coral
Is there a value for the righthand side of the scalene right triangle?
I don't think so, the sides are just labeled a and b
tall coral
I'm not sure what you mean by invisible numbers, but imaginary numbers are always i
nimble yew
I forgot the term
gentle haven
There shouldn't be imaginary numbers
vocal bison
you know (a+b)^2 doesn't equal (a^2)+(b^2) right?
idk tbh i tried to use pythag to find the hypotenuse of the triangle cuz i thought thag was the diametr then got a+b/2 and then plugged that into pi r^2
tall coral
idk tbh i tried to use pythag to find the hypotenuse of the triangle cuz i thoug...
the diameter would just sqrt((a^2)+(b^2))
trail tendon
Oh lord I'm gonna fail the standardized test omg
what is the standardized test
nimble yew
what is the standardized test
Geometry. The whole skill. In 60 questions.
vocal bison
wut i thiugjt u take the square root of that
trail tendon
Geometry. The whole skill. In 60 questions.
is this standard geometry?
bro idk how to do it 💀
gentle haven
Are the points on the triangle the midpoint of each side
trail tendon
it seems like a challenge problem for geometry maybe but idk
nimble yew
is this standard geometry?
Yeah ig so it's high school level
But my teacher hasn't even taught circles yet
gentle haven
I think ik how to solve it but it uses trig
trail tendon
But my teacher hasn't even taught circles yet
how are you supposed to do that problem?
gentle haven
Is that fine in the problem?
trail tendon
without circles?
vocal bison
um i dont think ur supoosed to use trig
tall coral
wut i thiugjt u take the square root of that
I did take the square root of it, sqrt is an abbreviation
gentle haven
um i dont think ur supoosed to use trig
Oh
nimble yew
Oh yeah that's what I came here for; Do you guys know any websites for geometry that's simple enough to learn in about 4 weeks
vocal bison
I did take the square root of it, sqrt is an abbreviation
iops i didnt se that
nimble yew
Like mostly circles and 3d shapes
trail tendon
Oh yeah that's what I came here for; Do you guys know any websites for geometry ...
khan academy. if you've already tried than try something else. you aren't supposed to learn a semester's worth of stuff in 4 weeks but you can do your best anyway gl...
nimble yew
Yeah I've also tried IXL and idk
trail tendon
Yeah I've also tried IXL and idk
gotta find what works for you
nimble yew
Because it's more like she's taught us surface level thongs and I took a practice test and immediately thought, "Oh my god I'm going to fail"
tall coral
iops i didnt se that
yep, we then just plug in our information.
The find the area outside of the triangle, all you need it the triangle's area and the semicircles area
trail tendon
Because it's more like she's taught us surface level thongs and I took a practic...
surface level?
vocal bison
yep, we then just plug in our information.
The find the area outside of the tria...
wait why do i need the triangles area
cant u jsut find the area outside semi circle and then subtract the inside one
nimble yew
surface level?
Basic things like transformations, planes and points, midpoint, that kind of thing. Nothing deep like finding an equilateral triangle inside a circle or hexagons or 3d shapes etc.
vocal bison
Basic things like transformations, planes and points, midpoint, that kind of thi...
Organic chemistry tutor on yt he has a playlist i think
tall coral
cant u jsut find the area outside semi circle and then subtract the inside one
no, you only need to subtract their overlayed parts
which would be this area
because if we subtracted the whole semi-circle, we'de be subtracting area the semicircles don't even touch
vocal bison
So like the semi circle minus the triangle and then take that and subtract it from the semicircles on the outside
gentle haven
which would be this area
You could use the segment formula to find the areas of the segments
tall coral
So like the semi circle minus the triangle and then take that and subtract it fr...
bingo!
tall coral
You could use the segment formula to find the areas of the segments
I'm gonna assume at the level of this worksheet that the segment formula isn't intended
vocal bison
Is there vids on this because i have more than one problem on this hw
my teahcer jsut handed the hw to us yesterday we had no lesson but i asked and um he said it is easy so i should be anle to figure it out
gentle haven
I'm gonna assume at the level of this worksheet that the segment formula isn't i...
Oh
tall coral
Is there vids on this because i have more than one problem on this hw
I don't think so, but try and use the same premises of trimming area so to speak
tall coral
I mean, they gave you practice for a reason
trail tendon
is the answer ab/2?
tall coral
let me check...
vocal bison
I mean, they gave you practice for a reason
True
trail tendon
wait nope i didnt
to my knowledge 💀
i took the area of the semi-circle with the biggest shaded region, added it to the area of the semi-circle with the smallest shaded region, then subtracted it by (area of semi-circle - area of triangle). the area of the semi circle just happened to be the sum of the areas of the semi circles with shaded regions, so the answer just turned up to be the area of the triangle ab/2
i didn't prove that the area of the semi circle was the sum of the areas, i just noticed they algebraically canceled out 💀
vocal bison
Yall after allat why am i still confused
tall coral
is it ab/2?
yep
tall coral
Yall after allat why am i still confused
what are you confused about?
trail tendon
Yall after allat why am i still confused
i don't blame you
its confusing unless you actually see it in your head
💀
tall coral
it's not like the questions are easy either
took me a while to figure out what was going on
trail tendon
I think this is a particularly hard geometry problem
like
its a lot of geometry application
not too basic
🤷♂️
i mean its not HARD hard
but its maybe hard for high school geometry kinda
idk
😭
tall coral
I mean sure it's not the hardest geometry problem out there, but it's not immedietly obvious
trail tendon
I mean sure it's not the hardest geometry problem out there, but it's not immedi...
yeah
i mean
vocal bison
Tbh i think im just gonna have to ask my teacher on monday
trail tendon
the hardest geometry problem out there probably requires a lot more than geometry
trail tendon
Tbh i think im just gonna have to ask my teacher on monday
thats a good idea
its easier to visualize when someone is literally right next to you
tall coral
I hope I atleast gave you some foundation
trail tendon
they can convey it with drawing, explaining to your needs, ect.
vocal bison
I hope I atleast gave you some foundation
Yeah you def helped
prisma radish
Hi guys can somebody help me solve my confusion in this question?
O is the centre of the circle.
I extended AB to meet circle at P and BC to meet circle at Q. I assumed BP to be x. So now my confusion is whether the equation BC²= AB × BP holds true or not?
And if it does then I get x =2/3
And OB=√46
This Is how I drew the diagram
If I use the theorem 4r²=a²+b²+c²+d² where a b c and d are length of intercepts made by the 2 chords then I get x=4 and OB=√26 which is the right answer. So where did I go wrong previusly
obsidian harness
Hi guys can somebody help me solve my confusion in this question?
O is the cen...
$BC^2 = AB \times BP$ is not true
merry mulch
dark sparrow
,rccw
somber coyoteBOT
dark sparrow
!status @merry mulch
lime crownBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
6
obsidian harness
Cool
wheat basin
The proof of cos(x+y) = cos x cos y - sin x sin y can be proved geometrically on unit circle.
Can a similar proof be prepared for sin(x+y) = sin x cos y + cos x sin y on the unit circle? I have seen proofs of the latter through various figures without the unit circle but can someone provide a proof for the same on the unit circle with both coordinate axes?
upper karma
The proof of cos(x+y) = cos x cos y - sin x sin y can be proved geometrically on...
Very off topic but, how did you get that emoji?
wheat basin
The proof of cos(x+y) = cos x cos y - sin x sin y can be proved geometrically on...
A proof which uses the distance formula and congruency of triangles like that in proof of cos(x+y)
wheat basin
Very off topic but, how did you get that emoji?
Its a character, not an emoji, you can copy it like I did
honest mortar
2
upper karma
Wait, how?
upper karma
Ahh I get it now
honest mortar
huh
trail tendon
much overthink
honest mortar
just add they getting equal
honest mortar
xD
tulip wasp
Are there any books, articles, videos, etc. that go really in depth about the math behind euclidian constructions and origami constructions?
For example, in this video:
https://youtu.be/SL2lYcggGpc
she says that origami can trisect an angle by solving the intersection of 2 parabola, and that origami can solve cubic equations. I want more info on that kind of stuff
Heck, I'll even read an academic paper talking about it
loud moon
vocal python
can someone explain why is not ASA
wicked oak
can someone explain why is not ASA
What are the other choices in the drop down?
vocal python
What are the other choices in the drop down?
Those are the other option
wicked oak
I think its not asa because instead of knowing two angles and one side, you actually know two sides and an angle.
side BA is known, along with side CD, and the thing in the middle crossing through the parallelogram is known, which would allow you to find the angle next to A and the angle next to C, which means two sides of each triangle are known and only one angle for each triangle.
rain trout
can someone explain why is not ASA
It's SAA
visual hare
Could someone help explain a problem to me? I've been stuck on it for a while and my brain forgot all knowledge of circles.
Also, I don't know how this really works, i just joined, so sorry in advance.
Oh wait nevermind, I solved it.
lime dune
yes
dark sparrow
Also, I don't know how this really works, i just joined, so sorry in advance.
for future reference you're supposed to post your problem upfront
dark sparrow
,rcw
somber coyoteBOT
rain trout
rain trout
This is where I've reached.
dark sparrow
simplify cot((A+B)/2) somehow maybe?
if only to make the path to the goal a little more visible
rain trout
Like this?
rain trout
do you know the half-angle identity for cot?
Cot(A/2)?
quartz echo
guys do you know how to solve the cubic eqaution?
dark sparrow
Cot(A/2)?
that is one half of the identity
but yes i'm looking for one that's like cot(x/2) = ...
dark sparrow
guys do you know how to solve the cubic eqaution?
are you sure that you really mean "solve the cubic equation"?
or do you mean something else
like "find a cubic equation that describes the orange curve"
rain trout
quartz echo
like "find a cubic equation that describes the orange curve"
yes yeah
dark sparrow
,rcw
somber coyoteBOT
quartz echo
are you sure that you really mean "solve the cubic equation"?
finding out the eqaution
dark sparrow
anyway uh
rain trout
Does no.10 help?
dark sparrow
@quartz echo i think we should move to #precalculus
dark sparrow
Does no.10 help?
doesn't seem to.
my idea was cot(x/2) = cos(x)/(1 + sin(x))
i'm not sure if that works either
but it does reduce the goal to this
rain trout
but it does reduce the goal to this
Where did this come from?
rain trout
> cot(x/2) = cos(x)/(1 + sin(x))
Is there any identity like this?
dark sparrow
that is an identity...
rain trout
Uhh ok
dark sparrow
oh yeah, a single image on google images is not only an authoritative source but an exhaustive list, OBVIOUSLY.
(sarcasm)
rain trout
So which one is correct?
dark sparrow
what do you mean by "which one"
rain trout
Is cot(x/2) = cos(x)/(1 + sin(x)) or cot(x/2)= (1+cos(x))/sin(x)?
rain trout
oh yeah, a single image on google images is not only an authoritative source but...
What was your sarcasm about actually?
dark sparrow
you presented me with a single google image, which sounded like "this image doesnt list any identity for cot(x/2) so you're talking out of your ass"
that was my perception of it, even though i was mistaken
rain trout
Nevermind. What do I do now?
dark sparrow
i don't know
rain trout
i don't know
Can your verify by any means whether the question is correct or not?
dark sparrow
hm
let's try
let's put A = B = pi/3
clearly the condition 1/sin(A) + 1/cos(A) = 1/sin(B) + 1/cos(B) is true
tan(A) tan(B) = sqrt(3) * sqrt(3) = 3
cot( (A+B)/2) = cot(pi/3) = 1/sqrt(3)
the question is wrong
rain trout
the question is wrong
Phew! Such a relief
merry parrot
let's put A = B = pi/3
what if you put A = B = pi/4? 
dark sparrow
then both sides would be 1 and it wouldnt work as a CE
merry parrot
what does CE mean
dark sparrow
counterexample
merry parrot
the question says 'if' so it's not true for all the values but some specific values of A and B, or am i wrong?
dark sparrow
but the question's condition had plus signs, not minus signs.
you solved a different question.
rain trout
you solved a different question.
Not really
rain trout
dark sparrow
oh, wait.
wait what
hang on a minute
oh that's right, you divided both sides by sin((B-A)/2), which in my counterexample would have been 0.
rain trout
oh that's right, you divided both sides by sin((B-A)/2), which in my counterexam...
Yes.
dark sparrow
can i ask not to be bothered about this again or do you have more things to say that i absolutely have to listen to
rain trout
can i ask not to be bothered about this again or do you have more things to say ...
Hehe sorry if i bothered you
little bay
hey im trying to make a robot leg in this game and trying to get it to walk using inverse kinematics. However i dont understand how it would work when it came to a vertical hip joint
like i understand cosine rule and all the stuff but yea
so like when trying to solve inverse kinematics, your trying to solve for the angles of the joints right?
so if you were trying to find lowercase c, it would be c = SQRT(a^2+b^2﹣2abcosθ) θ being the angle
but if you were trying to solve for an angle it would be C = cos-1 [(a^2+b^2-c^)/(2ab)]
sorry Cos(C) = (a^2+b^2-c^2)/(2ab)
minor dust
vocal python
hello hope everyone well i just here to see if someone can confirm the answer
bleak leaf
.
marble briar
half rampart
Isn’t that a question for help?
half rampart
So I’ve been wondering about this. It not important I’m just curious. Giving any shape X. Take all its sides and extend them out to infinity. Like this
My question is. Is there an EASY way to tell what the area of the extended shape is without making it
austere ember
literary nobody is online in other servers
half rampart
literary nobody is online in other servers
Dang
trail tendon
My question is. Is there an EASY way to tell what the area of the extended shape...
I would say probably no, but i'm not entirely sure if what your asking makes sense
for some shapes you don't have to extend them, you can instead cut off the areas and rearrange them
that may be easier
trail tendon
i don't really know integration too well
half rampart
Nope sorry
trail tendon
i would assume you plugg in 177 for x to get a number, then subtract the expression when you plug -144 for x
i'm pretty sure thats how you do definite integrals
oh
and add C
maybe
naw
i think thats only for indefinite integrals
nvm im not the person to ask lol
trail tendon
i would assume you plugg in 177 for x to get a number, then subtract the express...
but I think its this...
half rampart
@trail tendon do u understand the diagram? I can try to re explain it.
trail tendon
i mean
you're extending the side lengths infinitely
to calculate the areas
and you're asking... if theres an easier way to simply calculate the areas?
half rampart
To calculate the shapes area if the sides were extended. Or if it would make any difference at all like for shape A to B it didn’t make any difference.
trail tendon
so you're not calculating the area of the original shape, you're calculating the area of the shape if you extend all the sides?
half rampart
Ya and see if there is a difference
I don’t care about the actual values I just want to know if there is a difference
dusty ginkgo
So I’ve been wondering about this. It not important I’m just curious. Giving any...
the lines wont intersect again
trail tendon
a difference between what?
half rampart
a difference between what?
Ye
trail tendon
that was not a yes or no question 💀
a difference between what and what?
you want to know if there is a difference between... what and what?
half rampart
K sadly I gtg after this but I’ll try to restate my question
trail tendon
alr
dusty ginkgo
what r u guys typing 💀
trail tendon
i'm trying to type something helpful without making no sense
dusty ginkgo
its been 3 minutes
trail tendon
💀
half rampart
So take any shape you want it didn’t matter the shape. Then take all the sides and extend them out to infinity. Only knowing the area and measurements of the first shape is there an easy way to tell what the extended shapes area will be
trail tendon
ah
dusty ginkgo
So take any shape you want it didn’t matter the shape. Then take all the sides a...
take a triangle
dusty ginkgo
if u extend
no change
cuz no new bounded area
but take something like a
trapezium
trail tendon
if there is no change, you can obviously see if there is no change. but there is no "easy way" to calculate the area if there is a change, besides drawing it in and calculating that area.
half rampart
if u extend
Ya
trail tendon
like
dusty ginkgo
so change may or may not possible
half rampart
Gtg feel free to message me if you get any ideas but again it not important I was just curious
dusty ginkgo
for a n sided regular polygon
u can generalise it
if u want
but that isnt that much of an helpful exercise
trail tendon
Gtg feel free to message me if you get any ideas but again it not important I wa...
I would say as far as I understand your question, the answer to your question is no...
like there isn't really a formula or ratio between the area of a shape and the area of the shape inside the extended lines
i'm not sure if you couldn't make a formula but it would most likely be more difficult than just doing the problems 💀
strange edge
So I’ve been wondering about this. It not important I’m just curious. Giving any...
How did shape D become shape E ?
quaint sequoia
Hello I need help solving this geometry question. I’m solving for “x” but the I’ve tried every formula and method and it’s not working I’m always getting a decimal.
lime dune
BREAKING NEWS: not all your answers will be integers
in real life the numbers rarely come out that nicely
quaint sequoia
But I was told there are no decimals
The question doesn’t say anything about rounding
Idk how to get x I’ve tried everything
lime dune
(17x-(360-17x))/2=75
quaint sequoia
Ur subtracting 17x from 360?
lime dune
(17x-(360-17x))/2=75
that 75 degree angle
is half the difference of the intercepted arcs
lime dune
the big one is 17x, so the smaller one is 360-17x
quaint sequoia
Yes yes but I’m not trying to find the angle I’m trying to find what x is
The angle is already given
lime dune
when did I say I was trying to find the angle
I am finding another EXPRESSION for that angle
setting it EQUAL to that angle
quaint sequoia
U just gave me the angle for “x”?
lime dune
and solving the resulting equation for x
lime dune
U just gave me the angle for “x”?
what the hell does this even mean
quaint sequoia
Ok ok I think I’m miss understanding. I’m trying to find X. The ANGLE has already been given to me. I tried using the “two tangent” formulas which is 1/2( FGH-FH) but that’s to find the ANGLE. But it’s already been given to me
Idk where you got 180 from
quaint sequoia
Yes.
lime dune
and the major arc FG is 17x
so now angle FGH
is (major arc FH - minor arc FH)/2
that is,
(17x-(360-17x))/2
=(34x-360)/2
=17x-180
but we are also given angle FGH = 75
so, 17x-180=75, which gives us x=15
quaint sequoia
I just don’t understand where ur getting 180 from
quaint sequoia
I get how ur getting 15 but I don’t understand how u got there. Ik u explained it but I still don’t understand
Ur subtracting 17x from 360???
quaint sequoia
But then ur also multiplying 17x with its self
lime dune
the two arcs add to 360
quaint sequoia
Yes
quaint sequoia
THATS WHT UR SAYING 😭
lime dune
no?
quaint sequoia
Im using X for the minor arc and 17x for the major arc
crystal ginkgo
this. is Ice-creame! 🙂
lime dune
y+17x=360
quaint sequoia
BC what ur saying is x which is the smaller arc plus 17x ends up equaling 360
lime dune
so y=360-17x, yes
quaint sequoia
Ok so how do u end up getting the y?
crystal ginkgo
catet X/L f
lime dune
bc if you denote it by x
quaint sequoia
Ok
lime dune
that’s very ambiguous as to what it means
quaint sequoia
So how did u end up finding y?
lime dune
that’s very ambiguous as to what it means
(in this case completely incorrect)
basic algebra.
quaint sequoia
But HOW
quaint sequoia
Y=17x-360?
lime dune
no
quaint sequoia
I’ll end up with two variables
lime dune
you now have an expression for y in terms of x
lime dune
Y=17x-360?
y=360-17x
quaint sequoia
Yes so what’s the next step ?
How do I find y?
Or how do I end up getting x?
For 17x?
lime dune
How do I find y?
that’s the neat part, you don’t
now we know that our 75 degree angle
is equal to (17x-y)/2
big arc minus small arc, all divided by 2
quaint sequoia
is equal to (17x-y)/2
divided by two?
lime dune
…yes, that’s what it says
quaint sequoia
Oh ok
quaint sequoia
What are we plugging in?
lime dune
75=(17x-(360-17x))/2=(34x-360)/2=17x-180
lime dune
but we also know y=360-17x
^
you seem to be massively struggling with basic algebra, recommend brushing up on that
lime dune
hmm
quaint sequoia
Like the whole “17x-(360-17x)” makes no sense
lime dune
75=(17x-(360-17x))/2=(34x-360)/2=17x-180
so we have 17x-180=75, which we can now solve for x
quaint sequoia
Im having a hard time invisioning what that looks like
lime dune
Like the whole “17x-(360-17x)” makes no sense
and why doesn’t it?
lime dune
it’s the part of the circle that’s not in the bigger arc
quaint sequoia
Idk
quaint sequoia
THATS wht im struggling with…
lime dune
it should be automatic to notice that you have linear pairs of angles right there adding to 180 degrees
quaint sequoia
Yes Ik that
lime dune
angle MPL + angle KPL = 180
quaint sequoia
I was trying to find that so I could subtract from 180
lime dune
we are given angle MPL = x
so angle KPL = 180-x
now for a situation like this one where you have two chords intersecting inside a circle
quaint sequoia
Yes how do I find x
lime dune
the angle formed by the chords is the average of the intercepted arcs
quaint sequoia
Wht?
lime dune
angles JPM and KPL intercept that 30 degree arc and the 2x-30 degree arc
quaint sequoia
Yes
lime dune
ok, so what’s the average of those arcs?
quaint sequoia
But isn’t it 1/2 (JM+KL)= to the angle that we are trying to find? Or at least the angle supplementary to it?
I tried that and it didn’t work
lime dune
then you did your computations wrong, that is the intended process
quaint sequoia
Ok ok
lime dune
(JM+KL)/2= angle JPM=angle KPL
quaint sequoia
So I did 1/2( 30+2x-30)
lime dune
So I did 1/2( 30+2x-30)
what does this simplify to
lime dune
/2
lime dune
remember you're dividing that whole thing by 2
for the average of the intercepted arcs
ok now for the other side
quaint sequoia
So 2 divided by 2?
lime dune
the angle JPM and angle KPL
quaint sequoia
I’ll end up with x
lime dune
180-x
quaint sequoia
Wth do I do with that?
lime dune
set it equal to x
quaint sequoia
Why?
lime dune
this is what we were trying to do all along
create an equation that we can then solve for x
x=180-x
quaint sequoia
So 180-x=x?
lime dune
yes
quaint sequoia
💀
lime dune
i am highly skeptical that this is bc of "the way the teacher explains it"
quaint sequoia
So x=180?
lime dune
😭
quaint sequoia
im not dum 😔
lime dune
plug that in and tell me whether that makes any ounce of sense
you have some large mechanical/conceptual gaps that you need to fill in
quaint sequoia
IT DOESNT THATS WHY IM COFUSED
quaint sequoia
how does the x=180?
quaint sequoia
U just said it DIDD😭
lime dune
no i didn't,
quaint sequoia
And why am I setting it equal to 2x?
lime dune
plug that in and tell me whether that makes any ounce of sense
context clues.
quaint sequoia
Oh we are plugging it in?
lime dune
rearrange equation to 180=2x (add x to both sides)
you're done setting things equal to each other at this point, this is JUST ALGEBRA
rearranging a given equation to get x=[something]
quaint sequoia
I NEED VISUAL AIDS
lime dune
you have some large mechanical/conceptual gaps that you need to fill in
^
there is nothing "visual" about this part
quaint sequoia
so is the answer to the question 90?
lime dune
yes
you can't use "visual" "aids" as a crutch for everything, especially when your mechanical foundation is evidently not solid at all
go do some khan academy algebra/geometry exercises until you're comfortable with it
quaint sequoia
So 1/2(30+2x-30) equals x. Then x-180=x which gives me x=180.
lime dune
NO
x=90
actually almost everything you just wrote is wrong
(30+2x-30)/2=180-x
the LHS just becomes x
x=180-x
so x=90
somber coyoteBOT
elrichardo1337
quaint sequoia
IK so where are u getting 2x from ?
quaint sequoia
Im taking alg 2 and geo at the same time. I just don’t know where ur getting these numbers from
dire shadow
i need help pls i can't understand this
lime dune
the actual equations are algebra 1 level bruh 😭
quaint sequoia
the actual equations are algebra 1 level bruh 😭
IK I just don’t know WTH ur talking abt
I need VISUALS
where are u getting these numbers from
lime dune
the visuals are right there
in the diagram
you should not need to visualize solving basic linear equations otherwise your alg1 teacher seriously failed you
quaint sequoia
At this point ur just insulting me 💀
lime dune
did your teacher do a good job?
sometimes if they don't teach their students the foundational material well the deficiencies just cascade upward
quaint sequoia
Idek I’m still very confused
quaint sequoia
I got this wrong I put 34
lime dune
$\frac{x}{2}+3=2x-1?$
somber coyoteBOT
elrichardo1337
quaint sequoia
IDEK ANYMORE
quaint sequoia
SHE TOLD ME TO DO THAT
lime dune
well have you considered that maybe she could've been wrong?
that line does nothing, you don't need to draw anything extra in
i'm done here, perhaps someone with more patience than me can help better
quaint sequoia
lime dune
ok
quaint sequoia
Now what
quaint sequoia
Alright so my professor told me if I have the x on the side of the 1/2 to multiply the 34 and the 1/2 by 2
lime dune
you got the order mixed up, it should be
quaint sequoia
To get rid of the fraction
quaint sequoia
Why do I have to put the x+6 in parentheses?
somber coyoteBOT
elrichardo1337
lime dune
this is one of the most common and easily avoidable algebra errors out there
quaint sequoia
So your putting a negative sign in front to avoid ending up with negative numbers?
lime dune
??????
no
this is,
again,
BASIC ALGEBRA.
ie you actually have to distribute the negative sign!
quaint sequoia
So why are u putting a negative sign in front of the (x+6)?
lime dune
nope
lime dune
turn what into a +2?
quaint sequoia
Nvm thanks and sorry, for stressing u out it’s just the way ur explaining it makes so sense and isn’t clicking in my brain
lime dune
34=1/2*(3x-2-(x+6))
go from here
34=1/2(3x-2-x-6) since we have to distribute the negative
rugged shuttle
3.5 is wrong because C is not cos inverse of 6/7 anyways help?
lime dune
3.5 is wrong because C is not cos inverse of 6/7 anyways help?
try Heron’s formula?
quaint sequoia
Yes I got 38 thank you
lime dune
npnp
rugged shuttle
try Heron’s formula?
What’s that
lime dune
Google it
rugged shuttle
K
lime dune
it’s a formula for the area of a triangle given all three of its side lengths
quaint sequoia
X would just be 40 right since it’s a 90 degree angle?
lime dune
yes
rugged shuttle
it’s a formula for the area of a triangle given all three of its side lengths
Thx bro :)
lime dune
np
lime dune
what are we trying to find?
quaint sequoia
The red arc
lime dune
yea that’s right
quaint sequoia
And for this since both TU and UV are 34 degrees would that mean the red arc would also be 5?
lime dune
yes
quaint sequoia
See I’m smart
lime dune
epic
quaint sequoia
Can u help me with this?
quaint sequoia
Like this?
lime dune
not quite
quaint sequoia
Then what do u want me to do?
lime dune
that works too
quaint sequoia
Then?
lime dune
now we have a right triangle, what can we do with right triangles?
you know the length of two of its sides and need the third
so ||pythagorean theorem||
quaint sequoia
You wanna do Pythagorean theorem ?
lime dune
yes.
quaint sequoia
Alright
quaint sequoia
I got a long decimal
lime dune
what lengths did you plug in for the legs
quaint sequoia
6 and 7
quaint sequoia
Um idk bc it said 7 was congruent to the other side
lime dune
||that leg of the right triangle is only half the chord of length 7||
quaint sequoia
So I put 7^2
lime dune
ok the diagram is a bit ambiguous I’ll give you that
quaint sequoia
So 7 •2?
lime dune
I think based on its scaling it’s saying that the entire chord has length 7
so half of that is the leg, 3.5
quaint sequoia
Wait why? Do 7 isn’t his half of the chord?
lime dune
sqrt(3.5^2+6^2) would be your answer
