yeah the lines are parallel, thats the key
#geometry-and-trigonometry
vivid igloo
foggy heron
From alternating angles, you get that 30 + x = 75. x=45. From alternating axles again, we get that 45 + 55 =100. Therefore, the angle that is left is 80. From linear pair, n=100. From vertical angles, we get that n+m+30=180, since n = 100, then 100 + m + 30 = 180, m = 50. therefore, n=100 and m = 50
trim stump
But m=50
vivid igloo
@dim aurora
slim plinth
How about this
dim aurora
Can 55 and 75 alternate?
dim aurora
M+55=90
M=35
trim stump
180-75=105
dim aurora
I thought we have a 90 degree rt triangle
Yh
vivid igloo
Can 55 and 75 alternate?
nope, in this 75 can only alternate in the bottom right side of the parallelogram
cerulean cipher
Js making sure it is the measure of just Z as well? The teacher put a ? On it and marked it wrong
trim stump
Js making sure it is the measure of just Z as well? The teacher put a ? On it an...
It is
dim aurora
nope, in this 75 can only alternate in the bottom right side of the parallelogra...
55 alternates to TQS, right?
trim stump
Maybe u forgot to add °? Idk but Z= arccos 45/53
trim stump
55 alternates to TQS, right?
Yup
30 can also alternate at SRQ since they're both a parallel line intersection
vivid igloo
55 alternates to TQS, right?
it doesnt dear, 55 alternates the angle on just the left of th 75
TQS
55 = angle TQS
dim aurora
30 can also alternate at SRQ since they're both a parallel line intersection
Yh, SRQ=30
TQR+75+55=180
TQR=180-130
TQR=50
alpine garnet
How is JZ 28
vivid igloo
Yh, SRQ=30
TQR+75+55=180
TQR=180-130
TQR=50
TQR is alternate of m, thus m = 50
trim stump
ABHH NO TQR is the alternate of 55
vivid igloo
ABHH NO TQR is the alternate of 55
bro what are you trying to prove since so long 😭
vivid igloo
ABHH NO TQR is the alternate of 55
and no TQS is the alternate of 55, not TQR
dim aurora
and no TQS is the alternate of 55, not TQR
Parallel Z alternates
vivid igloo
Parallel Z alternates
mhm, RTQ is alternate of TQS not TQR
trim stump
How is JZ 28
I saw those lines | | and lokked at the RMV
JZ= RV
MV=PV
PV= Cos(36)×45
Then cos36×45 + 45 +RV= 180
trim stump
and no TQS is the alternate of 55, not TQR
OH I SAW IT DIFF AGAIN, my first take is TQR=m
And 30= SQR
trim stump
I saw those lines | | and lokked at the RMV
JZ= RV
MV=PV
PV= Cos(36)×45
Then co...
Wait I might be wrong
JZ=ZP=RV right?
dim aurora
mhm, RTQ is alternate of TQS not TQR
Guess so, but same applies to TQR and QTS
dim aurora
OH I SAW IT DIFF AGAIN, my first take is TQR=m
And 30= SQR
Yh
alpine garnet
I saw those lines | | and lokked at the RMV
JZ= RV
MV=PV
PV= Cos(36)×45
Then co...
For JZ =RV you need VZ // RJ and JZ//RV or MJP=VZP =90
vivid igloo
Guess so, but same applies to TQR and QTS
easy to remember, see if those 3 lines make a Z shape
like this:
thats alternate interior
hope it helps
trim stump
For JZ =RV you need VZ // RJ and JZ//RV or MJP=VZP =90
Isn't JRZ=ZVP=RMV?
alpine garnet
Isn't JRZ=ZVP=RMV?
Is it ? When did they say
dim aurora
Yh it did,
RQT=QTS
TSR=QRS
RIGHT?
trim stump
Is it ? When did they say
The lines shows congruency I think, so I assumed since ZV is 45
RV= JZ
alpine garnet
I see
cerulean cipher
JZ=ZP=RV right?
Ye
Assuming its a right triangle itd be 28
Which, arccos 45/53 is still right
trim stump
We were trying to know if JMP is a right angle
cerulean cipher
I js want the full mark idk why he marked it wrong
trim stump
I js want the full mark idk why he marked it wrong
Email your answer and ask why it was wrong
Maybe he didn't notice and marked it wrong
cerulean cipher
Some students got the full mark i dont see any other way of solving but ok
vivid igloo
Yh it did,
RQT=QTS
TSR=QRS
RIGHT?
yes thats correct
trim stump
I was at some point stuck at getting point slope because I was bugging with the signs
marsh marlin
I was at some point stuck at getting point slope because I was bugging with the ...
what
what point slope
trim stump
The (10√5,0) and (0,10√5)
marsh marlin
bruh
you didnt need allat
why does every high level mathematician like chucking things on cooridinate grids
trim stump
why does every high level mathematician like chucking things on cooridinate grid...
DUDE IDK I HAD NO WAY
I think the only time I didn't use coords was when I solved for the radius
trim stump
I think the only time I didn't use coords was when I solved for the radius
Remembered the pythag, then after that it's all coordinates
marsh marlin
or u could subtract radius from the two square length to get mini triangle length
trim stump
or u could subtract radius from the two square length to get mini triangle lengt...
What I did is get 2 of the square and cut them, so 20 ²+10²=r²
marsh marlin
What I did is get 2 of the square and cut them, so 20 ²+10²=r²
yeah
for radius
and then with radius u can directly find each of the shaded areas
no chucking on coord grid
trim stump
and then with radius u can directly find each of the shaded areas
I TOTALLY forgot about that
I went in to solve the slope of the diagonal line
marsh marlin
I went in to solve the slope of the diagonal line
somber coyoteBOT
pebble
trim stump
I got E
I did 2²+2² no?
Wait yea E
2²+2²= √8
To get the 1/2 of diagonal
√8÷2
2√2÷2
√2
Then 2²+√2²
wanton yacht
Yeah
cerulean cipher
Email your answer and ask why it was wrong
The right amswer is 108 and cos doesnt work cuz its not right angle triangle
trim stump
Well that's nuts
jaunty jasper
Can someone tell me how to find the area of a trapezoid if I have the length of the shorter leg and the perimeter??
silent plank
doesn't feel like there's sufficient info
trim stump
How to solve it if it's iso or right angled
grizzled yoke
How to solve it if it's iso or right angled
Mb, it will still won't
jaunty jasper
what does it mean by the shorter diagonal anyway?
trim stump
what does it mean by the shorter diagonal anyway?
Probably sides
What's the full statement
jaunty jasper
What's the full statement
What’s the area of a trapezoid with a perimeter of 20 and a shorter diagonal of 6
(i think i currently do not have the paper with me anymore)
trim stump
What’s the area of a trapezoid with a perimeter of 20 and a shorter diagonal of ...
Yeah I don't think that's enough
silent plank
diagonals are segments formed between non-consecutive vertices
trim stump
Maybe there's some extra infos like
base2 is x as large or smth
wintry stone
Hello, is anyone here?
I just wanted to ask a quick question regarding rotations in 3D.
Can someone help me on that??
grave pond
If you ask your question, someone might.
If you don't, you'll never find out.
wintry stone
ok
can i ask it
question:
basically, can a rotation in a tilted plane centered at the origin be represented as 2 or 3 planar rotations in the planes XY, YZ and XZ. Where, we rotate in a base plane by theta and then in the other 1 or 2 planes by alpha and beta which are tilt angles of the tilted plane in comparison to the X axis and the Z axis?
Plz ping if interested.
stray isle
What’s the area of a trapezoid with a perimeter of 20 and a shorter diagonal of ...
is it isoceles
silent plank
maybe it was supposed to be a rhombus
foggy copper
Is this where to talk about Graphing functions like sin and cos?
west narwhal
Is this where to talk about Graphing functions like sin and cos?
yea sure
or if it's more advanced, you can go to #precalculus
foggy copper
Nah it’s not advanced or really a question at all but I’m having difficulty finding period and frequency does anyone have any tips?
jaunty jasper
is it isoceles
it doesn’t say
stray isle
ok then don't assume anything
exotic yarrow
<@&268886789983436800> spammed across channels
zenith grotto
Nah it’s not advanced or really a question at all but I’m having difficulty find...
what information do u have?
is it using a graph to write the equation of the function?
foggy copper
Using the equation
west narwhal
Using the equation
so what's the equation
foggy copper
I don’t have one on hand I’m just looking for a way to distinguish frequency and period using the equation
west narwhal
I don’t have one on hand I’m just looking for a way to distinguish frequency and...
oh ok, well if you have an equation like $A\sin(B(x-C))+D,$ then the frequency would be $B,$ meaning that the period is $\frac{2\pi}{B}.$
somber coyoteBOT
OGMath_789
foggy copper
Ah ok thanks!
sly urchin
helppp i've been stuck on this forever
Uhm... Angles
shut island
||show that for an incenter I of triangle ABC, /angle BIC = 90 + (/angle BAC)/2|| use cyclicity to finish
bronze dock
ohhhhhh okay i think ik how to solve it now
trim stump
pretty sure thats wrong
Yea I kinda thought all lengths = 2, then read the description again
bronze dock
sorry if my sketch is bad, how would i solve for x?
vocal sentinel
sorry if my sketch is bad, how would i solve for x?
Just draw clearly
weary urchin
||show that for an incenter I of triangle ABC, /angle BIC = 90 + (/angle BAC)/2|...
ahhh alr i got it now
thank you
weary urchin
??
exotic chasm
would 4d geometry be a topic here also?
or would it be more akin to #algebraic-geometry topic unfitting here
exotic chasm
3d rotations "without" fancy nongeometric stuffs? sure
wintry stone
ok so u know that rotations happen in a tilted plane
one that is tilted from one of the existing orthogonal planes(XY, YZ, XZ) by some angle right?
well, my idea was that we could represent this rotation in that tilted plane using rotations in 2 or 3 orthogonal planes by decomposing the tilted plane itself
exotic chasm
ngl had a feeling if instead of using planes we should use the axis instead(?)
exotic chasm
for example rotating with z axis:
get the x1,y1
change to r,θ1
rotate the θ1 until it becomes θ2
change back to x2,y2
and only applicable to a point
exotic chasm
oh z coord still the same
wintry stone
yeah yeah
yeah that makses sense
but you need the radius of that point "on that plane"
you need to find that first and that is slow
exotic chasm
radius from the axis though
wintry stone
cuz it take s 1 sqr root, 2 multiplies and 1 add
exotic chasm
you need to find that first and that is slow
well yeah
wintry stone
i want smth faster
which is what i aimed to do with my method
do u want me to explain it?
ok so tilted planes
its tlted in one or 2 directions
i want u to think that a tilted plane is just a normal base plane like XY, but rotated by some angle alpha in the YZ plane and by some angle Beta in the XZ plane
so
we can represent any rotation on it, as a base rotation in XY and then account for the tilt by rotating it further (in order) in XZ and YZ
so that we account for the extra tilt
all in all here is the important thing - once we do that, all the angles match up, and the point in some sense has basically been rotated in that plane without us needing to project and reproject
u with me?
where
like what do u want me to elaborate on?/
ok
what i meant was that, when u rotate in a base plane right, u aren't accounting for the extra tilt that the point accumulates if it is rotated in a tilted plane
think of it like a book.
the tiltedplane, is what happens when u rotate it around you finger, so like a basketball, but u do it in one or 2 directions
if you move you hand over the original book, it wont be the actual position that u would get if you moved your hand on the tilted book.
so u move your finger on the base book first and then, you rotate it by the tilt angles, so u move it in line with how much the tilted book is off from the original base book
once u do that, u account for the extra tilt of the tilted book that u woulnt get if u just rotate on the book when u hadn't tilted it.
do u get it now?
i think it would be easier to see it with a demonstration maybe
exotic chasm
it is
wintry stone
so u do understand it?
i don't quite have a video on me rn, but maybe i can search for one
exotic chasm
so say, if a tilt angle with m_x=1/2 and m_y=1/3
wintry stone
whats m_x and m_y here
exotic chasm
slopes
wintry stone
oh
exotic chasm
bcos planes has "two" slopes right
exotic chasm
or one if you consider the direction
wintry stone
ahh i guess
exotic chasm
like it is m = y/x
this one if in 2d
wintry stone
yeah
exotic chasm
cos in this case we have an extra dimension, namely z
exotic chasm
eh, we only need 2 ig, m_x=Δz/Δx and m_y=Δz/Δy
though technically you can calculate slope of x and y
wintry stone
yeah, i guess
you would get the ratios of x, y and z from 2
slopes
not to be condescending, but may i ask how slopes are related to rotations here, i mean if u want to represent points with slopes, then i can try my best
like if u want, i can try to explain rotations with how the slopes change
exotic chasm
i'll use the slopes to determine z values of known x and y points i guess
wintry stone
i think it would be more intuitive for you
that's great but there is a slight issue
exotic chasm
for (x,y) values of (-1,-1), (-1,0), (-1,1) ... determine z from the given slope
wintry stone
wait, are we still talking about 3d rotations
exotic chasm
eh nevermind
wintry stone
or about planar ones
i think this is for planar right
like in the XY, YZ OR XZ planes seperately
exotic chasm
eh it was kinda both though
cos the initial plan was to calculate 3d rotation using the tilted plane thiingy right
wintry stone
ok well, i gotta say smth
when we rotate in a tilted plane, x, y and z all change so you would kind of need a universal slope so liek maybe y/x/z or smth, But that does not work
so
..
instead, you might want to calculate the slope of the point on that tilted plane right
but the thing is, to do that, u would need to project the point on to that plane and then reproject back to our space
and u can definitely do that, but its a bit slow
exotic chasm
now i wonder,
how would 8 points at $(\pm 1,\pm 1,\pm 1)$ if rotated to any directions you like, with your way
somber coyoteBOT
tsuitachi (tuitati)
exotic chasm
as in, the process
wintry stone
the plane is tited - it is not aligned with our orthogonal axes or space, so you need to first move it so that is does align, then rotate using slopes and then move it back as to not distort the space
wintry stone
**tsuitachi (tuitati)**
??
you mean u want me to explain my way
well i would be delighted to do so
yes
ok now that u get the idea of what tilted planes are (better than me cuz i am a nebie here)
we can move on to how u actually rotate
ok
so lets say we have a 2d point
with an angle of theta
and i rotate it by some angle alpha
what will be the new angle??
any guesses
origin
in 2d
2d
srry 2d
like a line from the origin like u would have in cartesian coordinates
like some point(x, y)
its angle is theta, you rotate it counterclockwise by alpha, whats the new angle?
?
yes
ok
now what did we learn
that when we rotate...
angles..
?
go on
uhh, we are just rotating points, by adding the current angle plus the rotation angle
dont think of a specific method, just think generally
when we rotate, what happens to the angle
yeah
that is true
yes
but just be general with it
think about a vector in space
when you rotate it counterclockwise
what happens to the existing angle theta
it adds right??
so theta + alpha = new_angle
quick question, have u learnt about multiplying 2Dvectors?
ok
what happens to the radii
no no
just liek normal 2d vector multiplication
using imaginary coordinates
so lije: (a+bi)*(a+bi)
i am specifically talkingabout imaginary multiplication
cuz that fits the purpose here
have u learnt about it?
like how to multiply 2 complex numbers.
?
ok
ping me when free
marsh marlin
Yea I kinda thought all lengths = 2, then read the description again
yay correction is good
slim plinth
trim stump
-3
pulsar dome
That’s the two imaginary solutions
Oh yh I see that now but how did you got to (2x+1)^2 +(3x+4)^2?
trim stump
Oh yh I see that now but how did you got to (2x+1)^2 +(3x+4)^2?
Probably √ both terms
slim plinth
It’s 4th root
slim plinth
Oh yh I see that now but how did you got to (2x+1)^2 +(3x+4)^2?
Do u guys what’s this equation called
Is that exponential
I’m interested solving these
sick palm
is there a shorthand for trigonometric identities
silent plank
wdym by shorthand
sick palm
like sin cos and tan have a shorthand soh cah toa but do identities also?
silent plank
no
sick palm
telling me i have to memorize it!?!
silent plank
yes
sick palm
do u have any tips to memorize them
vestal basin
i think you should understand why things are true instead of memorising formulas
thats the breakthrough for me in trig
sick palm
i think you should understand why things are true instead of memorising formulas
thats lowk what i want to do but i can barely understand it
i just know soh cah toa (sin, opposite side, hypotenuse,cos, adjacent side, hypotenuse, tangent, opposite side, and adjacent side)
sharp stag
Angle-Side-Angle is a theorem and Side-Angle-Side is an axiom right?
west narwhal
Angle-Side-Angle is a theorem and Side-Angle-Side is an axiom right?
yeah
west narwhal
yes, you just need the SAS and prove it by contradiction
sharp stag
How?
silent plank
wdym by prove ASA
as in prove the theorem works
or apply the theorem to show that two triangles are congruent
sharp stag
What is the method of proving ASA through SAS?
silent plank
angle sum and sine rule
silent plank
proof of what
vast raptor
huh
marsh marlin
huh
cobalt scarab
huh
west narwhal
umm
slim plinth
proof of what
Of two parallel lines
:((
slim plinth
proof of what about parallel lines
I meant to say one parallel lines and has a line crossed between
And that formed transversal
minor heron
I got a 69% on my unit test <:blobcry:971797574916907028> :((
what do you need help with
silent plank
I meant to say one parallel lines and has a line crossed between
can you write the full thing you want to prove
slim plinth
Not good at describing
silent plank
draw it out
slim plinth
hazy harbor
usually one of the parallel line angle theorems is taken as an axiom
silent plank
ok, so you want to prove that alternate angles on paralle lines are congruent
slim plinth
ok, so you want to prove that alternate angles on paralle lines are congruent
Yess that’s what my teacher said about bearing
silent plank
usually you'd take corresponding angles as the axiom
since vertical translation doesn't change the angle
hazy harbor
yeah any one of the parallel line angle theorems can be taken as an axiom to prove the others
minor heron
yup dont rlly think u can prove it without using another parallel line angle theorem
slim plinth
Okay
marsh marlin
first
dire jackal
nice q
native gull
dire jackal
yes!
dire jackal
Can you provide a solution or hints for this?
hint1: ||sum of focal distances of a point on the ellipse is equal to length of major axis ||
another hint: ||the length of diagonals is same and equal to distance b/w foci ||
rain scaffold
Yes, I think I got it now.
drowsy garnet
guys can someone tell me what are modulus and conjugates
rain scaffold
My geometry is pretty rusty.
drowsy garnet
ok thanks
sharp stag
Guys how is Angle-Side-Angle proven?
grave pond
Euclid (http://aleph0.clarku.edu/~djoyce/elements/bookI/propI26.html) gives a somewhat involved indirect proof that ultimately rests on the SAS theorem. But he could also have used "superposition" directly, as he does in his proof of SAS.
See http://aleph0.clarku.edu/~djoyce/elements/bookI/propI4.html for a discussion of the somewhat murky status of "superposition" as a proof technique.
winged oyster
liwkllgx
sharp stag
Euclid (http://aleph0.clarku.edu/~djoyce/elements/bookI/propI26.html) gives a so...
Does anyone know how this would be proven using Lean?
grave pond
It would depend critically about which particular theory you're trying to prove it in, and not so much about Lean details.
I'm not familiar with any common development of basic geometry in Lean.
sharp stag
It would depend critically about which particular theory you're trying to prove ...
euclidean geometry?
grave pond
I mean, a Lean library for that might very well exist, I'm just not personally familiar with it.
cosmic lagoon
hey, I have a question I hope can be answered
lime crownBOT
hey, I have a question I hope can be answered
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
cosmic lagoon
There's an AI called TeXit, and does it ues LaTeX?
it's an AI in the discord server
I've seen people use it and I've tried to use it myself and kinda failed?
and I'm just wondering if I can use LaTeX on it and it'll work
\phi=\frac{1+\sqrt{5}}{2}
$\phi=\frac{1+\sqrt{5}}{2}
$\phi=\frac{1+\sqrt{5}}{2}$
somber coyoteBOT
John zen
minor heron
it's an AI in the discord server
it is not an AI err
its just like a bot
which translates like latex code....
opal dawn
how do u use it
cosmic lagoon
oh
I think I somewhat****** know how it works
with multiple asterisks
you just put your LaTeX code, and put it around doller signs
opal dawn
how do u use latex
opal dawn
how do i use it tho
cosmic lagoon
so look
minor heron
how do u use latex
latex is like a formatting
cosmic lagoon
let's say I wanna say phi is equal to the square root of five plus one over two
opal dawn
x^{2}+3x+5
minor heron
cosmic lagoon
you type what you want in desmos, copy that, paste it here, and then boom.
opal dawn
i did that
minor heron
cus desmos uses latex to render too (i think)
opal dawn
$x^{2}+3x+5$
somber coyoteBOT
🌪️∑ Nova☃️
minor heron
yay
opal dawn
oh
cosmic lagoon
Like this: $\phi=\frac{1+\sqrt{5}}{2}$
somber coyoteBOT
John zen
cosmic lagoon
see?
so if you just don't use LaTeX or don't know how, just use desmos
because it works for some reason
opal dawn
$how\ do\ i\ solve\ \operatorname{for}\ \log s?$
somber coyoteBOT
🌪️∑ Nova☃️
cosmic lagoon
and you can properly decypher what people are saying instead of trying to read the hyroglyphics
minor heron
$how\ do\ i\ solve\ \operatorname{for}\ \log s?$
do you actually want help with logs or was this just testing
cosmic lagoon
it's still hyroglyphics but somewhat easier to read
opal dawn
do you actually want help with logs or was this just testing
addition and subtraction of logs
minor heron
addition and subtraction of logs
Can you provide an example?
oak anchor
bro its so weird using forward slash
cosmic lagoon
ik
also guys
not LaTeX focused question
but how tf is $\sin\left(18\right)=\frac{\sqrt{5}-1}{4}$
minor heron
$how\ do\ i\ solve\ \operatorname{for}\ \log s?$
So like if you have log(a)+log(b) this is equal to log(a*b) and vice versa
somber coyoteBOT
John zen
minor heron
18 degrees?
minor heron
if you want radians, then that's pi/12
*pi/10
cosmic lagoon
oh, really?
minor heron
... yes?
opal dawn
$$how\ do\ i\ graph\ \log s\ on\ a\ graph?\left(seriosus\ question\right)$
somber coyoteBOT
🌪️∑ Nova☃️
opal dawn
like the VA, domain, range etc
minor heron
180/18=10
minor heron
like the VA, domain, range etc
Well, the inside of a log cannot be 0
cosmic lagoon
sorry
opal dawn
can i just use a graphing calculator
minor heron
domain is dependent on what side of the vertical asymptote the log is on
minor heron
can i just use a graphing calculator
u can if u have one
weary urchin
can i just use a graphing calculator
or just use desmos
ig desmos is a graphing calculator
minor heron
**John zen**
so i would use sum and difference formulas in addition to like multi angle formula
opal dawn
$\sqrt{3x+5}=81^{\frac{1}{2}} (to solve do you just equal them? for radical equations)$
somber coyoteBOT
🌪️∑ Nova☃️
opal dawn
like 3x+5=81
winter shuttle
vocal sentinel
ye like this
number 1 is not in the squareroot 
minor heron
number 1 is not in the squareroot <:catgiggle:912459497954500659>
ack excuse my handwriting
vocal sentinel
looks good btw if its written by mouse
dusky nexus
tiny acorn
how the frick do i construct this
Draw 2 tangents AB,AC from A to the circle (O;R) [center O with radius R] (B,C are the intersections). Let BD be the diameter of circle (O). Let K be the projection(?) of C over BD, CK intersects AD at I.
i have no idea what projection means in this problem
tiny acorn
how the frick do i construct this
Draw 2 tangents AB,AC from A to the circle (O;...
how do i prove I is the midpoint of CK
vocal sentinel
Thales Theorem in triangle ABD with ratio IK/AD?
gentle jewel
Hi can smn help w this it’s noncalc. Also angle CDA is 154
vocal sentinel
Then use assumptions if I is midpoint of CK
vocal sentinel
Hi can smn help w this it’s noncalc. Also angle CDA is 154
B?
gentle jewel
The diagram drew it wrong n said this og:
vocal sentinel
If it is OBD it would make sense
gentle jewel
The text might b wrong instead then
vocal sentinel
Holy shit why the printing says OBD = 26 (like what i guessed) and ABC is 26 there lol
Anyways OBD is isoceles triangle
gentle jewel
Yea I think angle abc’s not 26
vocal sentinel
Then you can find BOD
gentle jewel
Anyways OBD is isoceles triangle
Is it cz it touches the tip of the circle
vocal sentinel
Yup the sides are radii
If you find BOD you will quickly realise this angle and x also subtend same arc
vocal sentinel
Is it cz it touches the tip of the circle
Can you find x from here?
vocal sentinel
Is it x + 26=180? But they’re not opposing each other
No
gentle jewel
If you find BOD you will quickly realise this angle and x also subtend same arc
How do I get bod if I only k that abc=154 and obd=26
vocal sentinel
You see triangle BOD right
gentle jewel
Ya
gentle jewel
Ohh do I use Pythagoras
vocal sentinel
No...
gentle jewel
Cz it touches the tip from the center
vocal sentinel
Look again, OB and OD are ??? Of the circle?
gentle jewel
Radii
vocal sentinel
Then, OB and OD are?
vocal sentinel
😑
gentle jewel
Oh.
vocal sentinel
Yet you still get it wrong :v
gentle jewel
26
vocal sentinel
Then can you find BOD now?
gentle jewel
Yes
vocal sentinel
If you find BOD you will quickly realise this angle and x also subtend same arc
Then read this message, that should give you hints
gentle jewel
Bod=28degrees
vocal sentinel
My bro
gentle jewel
vocal sentinel
180-52=28?
vocal sentinel
How did you get to this grade genuine question 😭
vocal sentinel
Then is angle x and BOD subtending same arc?
gentle jewel
What does that mean
vocal sentinel
I understand better when I talk lol
Yeah no vc in this server anyways
You have not studied subtended angle theorem?
gentle jewel
Yeah it’s alr idc
gentle jewel
You have not studied *subtended angle theorem*?
What does that mean like can u explain it
Idr the names of the stuff
vocal sentinel
It have many stuffs, if two angles covering same arc then it is equal
But for this case angle BOD is centre of circle so it is twice of x
Read pls
gentle jewel
Ohh
I remember the arrow head
R they all the same type of thingy thing theory
Name
vocal sentinel
Yes
vocal sentinel
Have you found x
vocal sentinel
Then find y
gentle jewel
116
grave mica
Wait why is y not 116 degrees?
vocal sentinel
Ah nevermind
tiny acorn
Thales Theorem in triangle ABD with ratio IK/AD?
how about CI? you cant prove CI = IK like that or am i tripping
grave mica
Isn't the opposite angle in a cyclic quadrilateral supplementary
vocal sentinel
I looked at x
grave mica
ohh okay
vocal sentinel
how about CI? you cant prove CI = IK like that or am i tripping
IK/AB = KD/BD using talet
vocal sentinel
Like y=116 degrees
yes you are correct i mis looked and thought they refer to x
vocal sentinel
IK/AB = KD/BD using talet
Then use similar triangle ratios in BCD
severe ether
The diagram drew it wrong n said this og:
Which class question is this
I tried to solve this but
Angle 154°
No 180 there or no straight line for 180°
How she take out angle x and y 😵💫😵💫😵💫
tight lichen
I have a question is this correct To Prove that sec³θ/sec²θ-1 + csc³θ/csc²θ-1 = secθ×cscθ×[secθ+cscθ] ?
exotic yarrow
I have a question is this correct To Prove that sec³θ/sec²θ-1 + csc³θ/csc²θ-1 = ...
your math is fine, the notation is a bit of a mess
ex. why are you using implication arrows? equal signs are fine
tight lichen
ex. why are you using implication arrows? equal signs are fine
idk they told us to write it
tight lichen
your math is fine, the notation is a bit of a mess
thanks, yh I know
slim plinth
Which one is easy to derive
cinder spear
Which one is easy to derive
The area for the equilateral triangle is wrong. It should be (sqrt3 * s^2)/4
Try to derive it
slim plinth
The area for the equilateral triangle is wrong. It should be (sqrt3 * s^2)/4
Do we use trig
cinder spear
No. It doesn’t require trig
slim plinth
Ok
slim plinth
No. It doesn’t require trig
Is it x:xsqrt(3):2x
thorny venture
Someone tryna help me prove the ns^2/4tan(pi/n) method
For area of a polygon
My teacher said she’ll only accept me using that method if I can prove it
queen juniper
split the polygon into isoceles triangles from the center
and split each of those triangles into 2 right triangles
then derive it from there
slim plinth
split the polygon into isoceles triangles from the center
We use 1/2 bh
Is this right
thorny venture
then derive it from there
I got till here
But like idk where to go after
Wait
Dont tell me
Lemme think for a bit
queen juniper
ok
queen juniper
use the properties of the 30 60 90 triangle
slim plinth
slim plinth
since u know the 2 legs of the right triangle
Pythagorean theorem
winged oyster
nw jv1n
grave pond
Do you have any thoughts?
winged oyster
look
thorny venture
How doni spoiler
winged oyster
5(45) > 180
winged oyster
i got ||x = 20||
winged oyster
do you see
slim plinth
||180/7 ||
Why is 7
thorny venture
do you see
Wait gimme a sec I’m doing smth
winged oyster
ok
slim plinth
What’s y for
stray isle
one of the base angles in the isoceles triangle
stray isle
5x + y = 180 - 2x
you can make this y = 180 - 7x
then substitute it in for y
5x + 2(180-7x) = 180
5x + 360 - 14x = 180
-9x = -180
||x = 20||
slim plinth
Ok
wraith pilot
I’m having trouble getting this problem started
silent plank
apply cosine rule
wraith pilot
apply cosine rule
silent plank
continue
also in the previous question you've incorrectly written
sinBeta = 43.8
(assuming the calculation was correct)
after using inverse trig to get the angle, you'll no longer have the sin there, i.e just Beta = 43.8
wraith pilot
I’m not sure what to do after I get 0.72
Just find gamma and I leave it like that?
Or do I use the inverse of sin beta and then find gamma
silent plank
inverse trig to get your angle
and since Beta isn't opposite the longest side, you don't need to worry about ambiguous case
and then you can use angle and m to get gamma
wraith pilot
ChatGPT is also getting different angles but I’m not sure if their trig answers are super accurate
silent plank
don't trust chatgpt/ai with math
you have some rounding errors,
(and notation issue above)
other than that it's fine
wraith pilot
Okayy tysm
gloomy wraith
one icosceles and a right triangle maybe
loud sphinx
nova sentinel
its hard right?
grave pond
Looks like an "adventitious angles"-type problem; those are quite tricky.
You can fill in a lot of the angles by angle sums and isosceles triangles -- in fact every angle that doesn't include the line DE as one of the legs. But typically to get the last step of the way will require either some trig functions that miraculously work together to produce an integer for alpha, or a really inspired argument that depends on "accidental" facts such as 20° being exactly 1/18 of a circle, and putting 18 of these triangles together in a wheel or something like that.
grave pond
Sure, if trig bashing is acceptable, then after deriving the easy angles you can put everything into a coordinate system, say, with B=(0,0) and C=(1,0), and calculate away. That's not even conceptually difficult. But (given that the teacher asked about this configuration in particular) it is pretty likely that alpha will end up as some multiple of 10° exactly, and the trigonometry will be useless for understanding why.
upper echo
Hint: ||Let H be a point on AB such than CH=BC, then CHE is equilateral, the triangles DHC and DHE are isosceles. So, by angle chasing you find alpha=80.||
nova sentinel
Hint: ||Let H be a point on AB such than CH=BC, then CHE is equilateral, the tri...
can you draw it?
i didnt get it
upper echo
i didnt get it
What exactly is unclear? ||Just draw CH first, such that CH=CB.||
nova sentinel
and?
upper echo
bro just dont give hints i need the solution
I'm not supposed to give ready made solutions here. If something is unclear just ask.
nova sentinel
would that work
upper echo
would that work
probably not, at least I don't see any proof of similarity for those triangles here
nova sentinel
if the answer is 80 they should be similar
upper echo
if the answer is 80 they should be similar
yep, they are similar. That's correct
nova sentinel
can i prove it though?
upper echo
can i prove it though?
Yes, I have shown a solution above. The similarity follows from it
upper echo
can i prove it though?
If you still want a geometric solution to the problem, I recommend working through those hints above, as it’s one of the shortest approaches. You’re unlikely to find a significantly simpler or shorter geometric solution. That said, a trigonometric approach is quite straightforward here too. But I’d suggest first drawing a more accurate diagram where the angles are represented correctly. Your current diagram is a bit misleading, as the visual angles are far from accurate.
nova sentinel
i have found the solution on youtube
was that what you were trying to explain?
also thanks
silent plank
can you show the full original problem
upper echo
was that what you were trying to explain?
yeah, that's essentially the same solution
silent plank
On-topic channels aren't the place to crack jokes.
Many people go out of their way to help people in need. Don't waste their time.
If you want to crack jokes, go to #chill
mystic cedar
Can anyone help me in trigonometry
grave pond
Perhaps someone can, but only if you actually ask a question about something that stumps you.
tiny acorn
Can anyone help me in trigonometry
!da2a
lime crownBOT
Can anyone help me in trigonometry
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
mystic cedar
I am in class 10th and this year trigonometry is started and I am doing them easily but these formulas like
sin theta +cos theta =1 ( this one is the simple
But the others like here you can see written in blue colours
They are going over my head
I am gonna sleep now
shy flower
vocal sentinel
But the others like here you can see written in blue colours
it just a derive of the original pythagorean identity
jaunty jasper
can someone tell me what this S means??
vocal sentinel
can someone tell me what this S means??
Area
silent plank
the question should tell you
or look in the previous section for how the book uses S
hasty juniper
Does anyone have any tips for unit 10 in geometry? Covering 10-1, 10-2, 10-4 and 10-5? I’m having trouble understanding 10-5…
silent plank
post specific questions
we don't know what resource you're using or even have it
hasty juniper
it’s mostly about Inscribed angles, Arc measurements, Arc lengths, Theta, “How to find arc __ using degrees” and stuff. I’ll send a couple images
I don’t have much with theta since my professor says I won’t need it for my final exam
silent plank
theta is just a variable/symbol like x
did you make attempts, where did you get stuck
hasty juniper
did you make attempts, where did you get stuck
Yes I have attempted, I’ve messed up around how to find the relations to the measurements (as in the degrees and arcs, such as the first image up there) so I couldn’t really finish the rest of the problem. I mostly need help with figuring how the information given relates to the diagram and how to find the information needed from there.
silent plank
do you know and/or have access to a list of circle theorems
hasty juniper
yes, I have access to circle theorems.
it’s just that the way my professor explains it makes it difficult to understand.
silent plank
do you know what angle the tangent makes with the radius?
hasty juniper
I believe it’s a right angle
hasty juniper
oh
so what would I apply for the rest? Because it won’t always be in these same conditions
would I just use the theorems to help move on?
silent plank
yes, identify what theorems are applicable
set up your equation and solve
marking info on your diagram also helps
solid pivot
hey guys
im a 8th grader, 13 doing 10th grade math
and i need help with a certain problem
i dont understand it
i could use some help please and thanks
wanton hawk
im a 8th grader, 13 doing 10th grade math
I did that too!
wanton hawk
Ok do yk what ce || ab means?
wanton hawk
What’s the equation for the area of a triangle?
solid pivot
(l * w)/2
solid pivot
yea
wanton hawk
So h doesn’t have to be an actual side, just how tall it is
wanton hawk
All the triangles have ab in their name, so they all have the line ab
solid pivot
yup
wanton hawk
Since ce || ab, that means that the distance between them is constant
solid pivot
yeathat makes sense
wanton hawk
If you take ab to be the base, you know h is constant (since distance is constant)
solid pivot
oh ok so like the height of all the triangles r the same then right?
wanton hawk
Don’t be bro
wanton hawk
Nah ts took me a sec to think through
solid pivot
i was lowk so confused
wanton hawk
Yep!
solid pivot
its just confusing cus of all the lines
wanton hawk
Now idk what the keywords are lol
wanton hawk
its just confusing cus of all the lines
Yeah, what I do is I trace each triangle in my head and isolate it
solid pivot
cya
i also need help to understand circles too...
not any certain principle but circles in general
solid pivot
did yk that a circle is actually only the circumfrence
and it doesn't include the inside
wanton hawk
Yeah
solid pivot
like bike tire is a circle but the stuff inside isn't
wanton hawk
Well a bike tire is a hollow cylinder if you don’t wanna be technical, and if you do it’s a torus
solid pivot
😭
wanton hawk
Ok bye fr fr I gotta get up early
wanton hawk
i don't even know what a torus is 😭
Doughnut
candid yacht
solid pivot
bru
hasty juniper
marking info on your diagram also helps
okay, thank you!
shut thistle
the representation is right ig
slate needle
can somebody explain why cos(-theta)=cos theta it might be simple to some but i dont understand
exotic yarrow
can somebody explain why cos(-theta)=cos theta it might be simple to some but i ...
$\cos(-x)=\cos(0-x)=\cos(0)\cos(x)+\sin(0)\sin(x)=1\cos(x)+0\sin(x)=\cos(x)$
somber coyoteBOT
Civil Service Pigeon
astral stream
Hi
wanton hawk
can somebody explain why cos(-theta)=cos theta it might be simple to some but i ...
Because a cosine wave starts at one. If you go right (positive) 1, or if you go left (negative) 1, you get the same value either way
slate needle
Because a cosine wave starts at one. If you go right (positive) 1, or if you go ...
-1.05... and 1.05... ?
wanton hawk
-1.05... and 1.05... ?
What?
wanton hawk
-1.05... and 1.05... ? isnt same
That’s an (x,y), where x is the angle
Y is the cosine of that angle
minor heron
can somebody explain why cos(-theta)=cos theta it might be simple to some but i ...
So negative theta is like going across the x axis right?
On the unit circle
And cosine is the x value on the unit circle
So the x value on the top and bottom of the x axis is the same
vestal basin
can somebody explain why cos(-theta)=cos theta it might be simple to some but i ...
cosine is an even function 👍
winged plinth
https://en.wikipedia.org/wiki/Even_and_odd_functions
"Why is my soup cold?"
"Because it was cooled 👍 "
runic pasture
cosine is an even function 👍
👍🏻
violet sluice
"Why is my soup cold?"
"Because it was cooled 👍 "
that's a perfectly fine explanation i'm not sure what you mean
f(x) is even <=> f(x) is symmetric about the y axis <=> f(-x) = f(x)
winged plinth
that's a perfectly fine explanation i'm not sure what you mean
It's equivanlent to: "x is x because x is x"
violet sluice
no it's not
winged plinth
"cos(x) fulfills the definition of an even function because cos(x) is even"
violet sluice
f(x) is even <=> f(x) is symmetric about the y axis <=> f(-x) = f(x)
🙃
you can see from the graph of cos(x) that it is symmetric about the y-axis. thus it is even. thus cos(x) = cos(-x).
cinder spear
can somebody explain why cos(-theta)=cos theta it might be simple to some but i ...
On the unit circle, the cos value is equal to the x value. Do you see why cos(θ) and cos(-θ) are equal?
cinder spear
you can see from the graph of cos(x) that it is symmetric about the y-axis. thus...
This is a good explanation!
violet sluice
thx
but yeah if you look at the unit circle or just a graph of cosx you see that it exhibits symmetry in such a way that cos(x) = cos(-x)
cinder spear
you can see from the graph of cos(x) that it is symmetric about the y-axis. thus...
Exactly. Just to add on for the person originally asking the question: if you change the input value of a function to its negative counterpart (x —> -x), you flip the function about the y-axis. An even function’s definition is ‘a function symmetrical about the y-axis’ soooo f(x) is equal to f(-x) in an even function (for example a cosinusoidal)
limber dagger
Does anybody know how to do these types of questions? 2 of this are vaguely similar and i dont really know how to get the answer. I got these wrong on my quiz. (were allowed to seek outside help for quizzes)
the 3rd one should be the intersecting secant tangent theorem
i believe
should C=38?
well it told me that was wrong
vocal sentinel
well it told me that was wrong
The angle C is half of (AD-BD)
You can find arc AD then calculate
limber dagger
You can find arc AD then calculate
so 49?
vocal sentinel
what is arc AD
vocal sentinel
I think it is 11 +11 + 14 +14
I dont know if they say 2 and 3 implies on which part of the line
Because 2 tangents start from 1 point are equal
limber dagger
oh
limber dagger
I think it is 11 +11 + 14 +14
thats the same thing tho
😦
whats the difference
they both equal 50
limber dagger
ok
limber dagger
yeah
question 3 i got 72 cus 112+32 then divided that answer 144/2 gives me 72 but it says thats wrong
so im
confusedd
oh wait
i see now
i need to do that with the other two arcs
but how do i solve for the other two arcs
vocal sentinel
question 3 i got 72 cus 112+32 then divided that answer 144/2 gives me 72 but it...
find sum of other 2 arcs
then divide all 2
vocal sentinel
yup
limber dagger
also this should be 125 right because 360-110 =250 then 250/2=125
vocal sentinel
also this should be 125 right because 360-110 =250 then 250/2=125
Yes since the line is a tangient
limber dagger
Yes since the line is a tangient
okay
thats the one i really struggle with so i just wanted to be sure
thank you
wraith garden
Yes since the line is a tangient
is it actually a tangent, because it looks like its passing inside the circle
vocal sentinel
is it actually a tangent, because it looks like its passing inside the circle
What?
wraith garden
is the line a tngent?
vocal sentinel
Which line are you referring to?
woeful pelican
so uhh
if i have 2 sides of a triangle with no 90 degree angle, a and b (7 and 10cm both) and i have the angle alpha (30°), why would i have 2 different numbers for beta? and why would 1 of them be "more correct than the other?
beta can be either 45.6 or 135.6 degrees for some reason, and apparently it has to be 135.6 degrees according to chatgpt (yeah i know, bad source but i cant figure out why it would even say beta can only be 135.6 degrees)
i already teated it out, both angles make a functioning triangle but why would chatgpt say 45.6 is wrong?
silent plank
don't trust llm ai for math
there are two possible values due to properties of the sine function
somber coyoteBOT
ραμOmeganato5
silent plank
here there would be two possible triangles
both are valid unless there's some other info
one isn't more correct than the other
chatgpt is just spouting bs here
woeful pelican
here there would be two possible triangles
aight thanks, i was studying this question and it popped in the exam (90 mins and 20 questions and it happened to be one of them :D)
probably not the best idea to start studying 10 mins before an exam
but it went well so it works for me
grave pond
If an LLM bot says something about math that you don't know for sure, then there's a fair chance it's right. (The chance is better if it's at high-school or undergrad level, and especially if it's a general claim rather than something specific to a particular problem).
However, when the LLM bot says something that you have a halfway cogent reason to think is wrong, then it almost certainly is.
golden knot
How would y’all do this? I mean, I’ve done a similar problem but the reciprocal trig is so confusing!! I liked using a triangle visualization but I DON’T know that inverse trig means when trying to draw triangles and whatnot
upper echo
How would y’all do this? I mean, I’ve done a similar problem but the reciprocal ...
You have a sum of two angles. Since all the values 3/4 and 5/13 are nice, you know immediately all the trig functions for both of them. So, just use cos(a+b) formula.
golden knot
Those are nice?? really?? 😭
my first approach was plugging them into the cos(a+b) thingy but it was a MESS
with all the ugly trig functions
upper echo
Those are nice?? really?? 😭
yep, the Pythagorean theorem: 3^2+4^2=5^2 and 5^2+12^2=13^2
upper echo
ok, you know at once that sin(a)=3/5 and cos(a)=4/5
upper echo
and sin(b)=12/13 and cos(b)=5/13
golden knot
how do i know that instantly?
upper echo
ok, that Pythagorean stuff is just the same base identity: cos(a)^2+sin(b)^2=1
golden knot
yaa i'm aware of dat awesome identity
upper echo
it's another form of the Pythagorean theorem
It's easy to check that 3^2+4^2=5^2 (In fact everyone should already know that) and 5^2+12^2=13^2
golden knot
yep yep that's all fine and easy
upper echo
so if you have a right triangle with an angle whose tan(a)=3/4 then you immediately know that its sides have a ratio of 3:4:5, and sin(a)=3/5 and cos(a)=4/5
golden knot
the fact that it's tan^-1 doesn't affect that at all?
upper echo
so, cos(a+b)=cos(a)cos(b)-sin(a)sin(b)=4/5 * 5/13-3/5 * 12/13
tan^-1 is just an angle. You don't need it. You need its cos and sine
golden knot
i don't really understand why tan^-1(3/4) wouldn't be tan(4/3) then you could construct a triangle with those sides tho
upper echo
i don't really understand why tan^-1(3/4) wouldn't be tan(4/3) then you could co...
tan^-1 is an inverse function. Just check what it is
say tan^-1(1/sqrt(3))=pi/6