And similarly sine is positive on 1st and 2nd
#geometry-and-trigonometry
spiral lodge
slim plinth
What are some tips on trying to locate trig functions
spiral lodge
Radius and hypothenuse refer to lengths, hence they can't be negative indeed
spiral lodge
Like this example
Yeah what about that?
spiral lodge
Ohh I see
slim plinth
Like I’m confused which quadrants are they in
spiral lodge
Honestly I don't know which triangle they are talking about
spiral lodge
Like I’m confused which quadrants are they in
Well, you are given that cosine is negative, so which quadrant can it be?
slim plinth
3rd
Oh btw their coordinates are (cos(theta), sin(theta))
1: (+,+), 2:(-,+), 3:(-,-), 4:(+,-)
spiral lodge
1: (+,+), 2:(-,+), 3:(-,-), 4:(+,-)
Awesome, that's the only thing you need to remember (not strictly by heart of course)
slim plinth
cos is negative, sin is positive
slim plinth
Awesome, that's the only thing you need to remember (not strictly by heart of co...
Will it apply on reciprocal?
spiral lodge
Huh?
slim plinth
Csc, sec, cot
spiral lodge
The reciprocal of a negative is negative and the reciprocal of a positive is positive
slim plinth
Will it still imply the rule
spiral lodge
The reciprocal of a negative is negative and the reciprocal of a positive is pos...
Don't you know this? 😅
slim plinth
I do
spiral lodge
Then what's the issue? Sorry I'm not getting you
slim plinth
Oh btw their coordinates are (cos(theta), sin(theta))
Will it look like (sec(theta), csc(theta))
spiral lodge
What is it?
spiral lodge
I really don't understand what you're talking about
spiral lodge
The coordinate
On the Cartesian plane? Then no,
slim plinth
On the Cartesian plane? Then no,
I mean that
spiral lodge
(cosθ, sinθ) is not at all equal to (secθ, cscθ)
slim plinth
What will it equal to
slim plinth
(cosθ, sinθ) is not at all equal to (secθ, cscθ)
Is it (1/x, 1/y)
spiral lodge
Sure
spiral lodge
Like cot can I first use tan(theta) then flip it
I don't know, I've never done such exercises honestly
slim plinth
I don't know, I've never done such exercises honestly
Is it normal to be confused on it
spiral lodge
I guess so
I mean, it is much more common to be confused in trigonometry than in, let's say, log and exp
slim plinth
Ik that
spiral lodge
At least form my experience here and in my real life
slim plinth
And got 100 and master it
spiral lodge
On the other hand, I personally was way more confused in probability and combinatorics than in trigonometry, but I believe it depends a lot on the person itself and especially on how the teacher explains the topic
slim plinth
Now what happens if I want to see which quadrant are sinθ=.5 and cosθ=-4.1 in
shrewd obsidian
I love math
shrewd obsidian
Why
glacial pelican
dms
tidal anvil
dry cave
Prove that sum of 2 sides of a triangle is larger than half the median PLS HELP
opal raptor
Prove that sum of 2 sides of a triangle is larger than half the median PLS HELP
Could you do a contradictive proof?
Suppose that half the median is larger than the sum of 2 sides of a triangle
Do the working until it contradicts?
Hmm
dry cave
oh lemmetry
exotic yarrow
Prove that sum of 2 sides of a triangle is larger than half the median PLS HELP
Reposted here: #help-14 message
opal raptor
Ah kk
half totem
ok time to derive half tan identity
tan(2x)=2tan(x)/(1-tan^2(x))
=> tan(2x)(1-tan^2(x))-2tan(x)=0
=> -tan(2x)tan^2(x)-2tan(x)+tan(2x)=0
i dont like negative coefficient so
tan(2x)tan^2(x)+2tan(x)-tan(2x)=0
tan(x)=(-2 +/- sqrt(2^2-4(tan(2x))(-tan(2x)) ) / (2tan(2x))
= ( -2 +/- sqrt(4+4tan^2(2x)) ) / (2tan(2x))
= ( -2 +/- 2sqrt(1+tan^2(2x)) ) / (2tan(2x))
= ( -1 +/- sqrt(1+tan^2(2x)) )/tan(2x)
=(-1 +/- sqrt(sec^2(2x)) )/tan(2x)
now since theres a +/- i think the absolute value isnt necessary
= ( -1 +/- sec(2x) )/tan(2x)
=-cot(2x) +/- csc(2x)
so im assuming youre supposed to use the positive root maybe?
so
csc(2x)-cot(2x)=tan(x)
therefore
tan(x/2)=csc(x)-cot(x)
why is there a frowny face
ok anyway lets check now
YESS
i wonder why it cant be the second root though
ok now cot(x/2)=1/(csc(x)-cot(x))=(csc(x)+cot(x))/(csc^2(x)-cot^2(x))=csc(x)+cot(x)
so cot(x/2)=csc(x)+cot(x)
wait a second if theres a half angle identity does that mean theres a one third angle identity
(cosx+isinx)^3=cos^3(x)+3icos^2(x)sin(x)-3cos(x)sin^2(x)-isin^3(x)
=> sin(3x)=3cos^2(x)sin(x)-sin^3(x)=3sin(x)-3sin^3(x)-sin^3(x)=3sin(x)-4sin^3(x)
=>4sin^3(x)-3sin(x)+sin(3x)=0
cardanos formula would be perfect but damn it i havent learnt it yet
dry cave
Oh btw does it specify what median?
i does its the median formed by the 2 summed sides to the third side
opal raptor
i does its the median formed by the 2 summed sides to the third side
Ah kk
royal citrus
\text{ If two tangential lines TP (t being the point of intersection} \\
\text{ between x-axis and the line)} \\
\text{ and LQ (l being the point of intersection between x-axis and the line) of} \\
\text{ a circle make points P and Q such that PQ is an arc, and TP makes an} \\
\text{ angle of $\psi$ and LQ makes an angle of $\psi + \triangle \psi$. Here, angle } \\
\text{TPL would be $\triangle \psi$. If we make enough lines, then a Kite would } \\
\text{ be formed with unequal angles x and $180 - \Delta \psi$. If someone could} \\
\text{ please explain how x would = $\Delta \psi$, it'd be huge.}
somber coyoteBOT
inheritance.
edgy shell
enjoy
crimson wasp
what are those
hexed plank
cunning lion
presumably because they want you to pull all perfect squares out
glacial pelican
can anyone help
lime crownBOT
can anyone help
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.
glacial pelican
sharp girder
Why is 3 square root 8 not the answer?
Try simplifying
(8 = 2 * 4 & 4 = 2*2)
so instead of 3√8 its (3*2)√2
so 6√2
and approx 6√2 via Newton's method (A friend taught me)
cunning lion
pretty sure they are asking just for the radical and not a decimal
fervent depot
and approx 6√2 via Newton's method (A friend taught me)
yea its right thx bro
sharp girder
Or you could ust use a calc and understand, somehow
Yeah, so i in Algebra II, we learned about the 6 (We learned about really 9) of the trig functions. What are all of them???
I know of:
sin(
cos
tan
asin
acos
atan
sec
csc
cot
sinh
cosh
tanh
sech
csch
coth
asinh
acosh
atanh
and exsec
excsc
versin
haversin
and chord
what are the others??
fervent depot
alr bro ima add u
fervent depot
nah like as a dm
glacial pelican
@everyone
sharp girder
@glacial pelican
so, my pfp has a unit circle with tan, cot, etc. on it
I just don't understand their relationships
rough bronze
this is a 45-45-90 triangle
if each side is x, the hypotenuse should be x sqrt 2
that means 100 = x sqrt 2, if you can solve for x, you've got the answer
limber dagger
Yes….
sharp girder
so the answer is 50 sqrt 2 as
45-45-90 triangles use
x to x to x sqrt 2
as the ratio of their sides
Trig question!
(Trivia)
sharp girder
Ill check
limber dagger
as the ratio of their sides
I’m a little confused
I may need
Simpler terms
I have the flu rn so my head is spinning
What is 45-45-90
sharp girder
What is 45-45-90
A right triangle with angles of degree measure 45
so 180-90
-45
= 45
so the 3 angles are 45, 45, 90
the name is 45-45-90 triangles
this is one of the special right triangles
so it maintains a consistent side-to-side-to-side ratio
which is:
x to x to x * sqrt 2
given that the hypotenuse (longest side) is the x*sqrt 2 side
limber dagger
the name is 45-45-90 triangles
oh ok
rough bronze
A right triangle with angles of degree measure 45
dang i just realized you have a unit circle pfp
must really like trig
ornate rampart
wowzers I could actually learn using ths
rough bronze
wowzers I could actually learn using ths
trig is not fun once it gets advanced
also everything connects to the unit circle which is also not fun
marsh stratus
I have to turn stuff like (1+cos(x))(csc(x)-cot(x)) into one trig function or constants like sin(x) for this specific problem
ornate rampart
trig is not fun once it gets advanced
i havent gone to learning trig yet
so im probably fine for a few months
shut thorn
The hell could something like sin^(-1)(B) mean. Will it be the same as 1/sinB?
Got curious about trigonometric functions and wanted to put a negative power on one of them
Because like. Sin^2(B) => (sinB)² so shouldnt it be the same with sin^-1(B)?
cunning lion
the notation is not consistent
the exponent in sin^2 refers to multiplication, whereas the exponent in sin^(-1) refers to function composition
shut thorn
the exponent in sin^2 refers to multiplication, whereas the exponent in sin^(-1)...
uh huh 😭. So what does sin^(-2)(B) mean
or is that even real
at all
gray blade
the exponent in sin^2 refers to multiplication, whereas the exponent in sin^(-1)...
wdym function composition ?
cunning lion
calling $f^2 = f \circ f$ and so on
somber coyoteBOT
cloud ☁
shut thorn
and should not be used
so just to be clear. 1/sinB = (sinB)^(-1) and not sin^(-1)(B)?
cunning lion
yes
shut thorn
kk 👍
wanton yacht
so just to be clear. 1/sinB = (sinB)^(-1) and not sin^(-1)(B)?
Really I think we should just use arcsin or asin to denote the inverse functions to avoid ambiguity
trim hazel
these are trigonomertical functions made for 1/sinx, 1/cosx, 1/tgx, 1/ctgx
for 1/sin is arcsin, 1/cos is arccos, 1/tan is arctan and 1/cot is arccot
but you'll barely use it in school
because in most cases you'll need a calculator, which is mostly forbidden when learning math
and while doing an exam
shut thorn
for 1/sin is arcsin, 1/cos is arccos, 1/tan is arctan and 1/cot is arccot
Isnt 1/sinx = cscx?
nocturne breach
for 1/sin is arcsin, 1/cos is arccos, 1/tan is arctan and 1/cot is arccot
Yo this is straight cap bruh
1/sin is csc
1/cos is sec
1/tan is cot
trim hazel
i said i made a mistake
shut thorn
i didn't do trigonometry for a while
I mean w8th how much trig traumatizes people. You really can't forget something like this can you 😭
violet sluice
the hell is a arc
arcsin is the same thing as inverse sin, arccos is the same as inverse cos, etc
just different names
shut thorn
arcsin is the same thing as inverse sin, arccos is the same as inverse cos, etc
isnt
1/sinx the inverse of sinx
violet sluice
im talking about the function inverse
shut thorn
oh
violet sluice
1/sinx is called the "multiplicative inverse" of sinx
but if you have $f(x) = y$, the inverse function $f^{-1}$ satisfies $x = f^{-1}(y)$
you'll learn about this in algebra
somber coyoteBOT
Altanis
violet sluice
so for example sin(pi/2) = 1. inverse sine should take 1 and give pi/2
i.e., it should undo what sine does
shut thorn
oh
somber coyoteBOT
shut thorn
ok so it just gives you the radians and their measurments
violet sluice
arcsine takes a value and tells you what angle, when you take the sine of it, gives you that value
slim plinth
arcsin(sin(theta))=1
limber dagger
How does sin^-1 work
"(sine) calculates a ratio of triangle sides (opposite/hypotenuse) based on an angle, whereas (inverse sine or arcsin) calculates the angle based on a given side ratio. takes an angle input, while takes a ratio between and to produce an angle (usually in degrees or radians)."
can somebody help me with this?
im on my last try
winged oyster
can somebody help me with this?
i believe y is 7.5 and x is 7.5sqrt(3)
lime crownBOT
i believe y is 7.5 and x is 7.5sqrt(3)
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
shut thorn
can somebody help me with this?
do you know about trigonometric ratios? And what they would be for the angle made between the side 15 and x
limber dagger
do you know about trigonometric ratios? And what they would be for the angle mad...
not really. I've been sick with the flu all week so I don't really know what's going on.
shut thorn
not really. I've been sick with the flu all week so I don't really know what's g...
hope you get well soon.
anyways. a right triangle has some ratios between the non-right angles, these ratios are known as trigonometric ratios. the ratios for an angle theta are as follows -> sin(thetha) = opposite/hypotenuse
cos(thetha) = adjacent/hypotenuse
tan(thetha) = opposite/adjacent.
there are also sec(thetha), cosec(thetha) and cot(thetha) which are 1/cos(thetha), 1/sin(thetha) and 1/cot(thetha) respectively.
But for the question, only the highlighted ones are necessary
let me make a diagram to explain better
lets call it angle A for simplicity. Using the ratios for sin(thetha) and cos(thetha) above. try to find the ratio for sinA and cosA.
This similar method can be used for the question.
shut thorn
lets call it angle A for simplicity. Using the ratios for sin(thetha) and cos(th...
This similar method can be used because sin(30) and cos(30) have some value
1/2 and sqrt(3)/2 respectively
should be enough of a hint?
feel free to ping me if you find any difficulty.
i will try my best to clear that doubt
limber dagger
Uhm
Okay
So
So would I use tan
Then
I’m confused
Like
If I need to find X
What am I trying to find
It’s the hypotenuse right
limber dagger
feel free to ping me if you find any difficulty.
i will try my best to clear th...
I don’t really understand what tan, sin, or cos are
I was there for the introductory lesson
That was it
shut thorn
I don’t really understand what tan, sin, or cos are
theyre the ratios of the side of a right triangle
stray isle
can somebody help me with this?
search up 30 60 90 triangle
shut thorn
So would I use tan
no you cant use tan here. tan(thetha) = opposite/adjacent. the opposite and adjacent of the angle are what we are trying to find.
stray isle
ratio is x, x(sqrt(3)), 2x
stray isle
oh mb
shut thorn
well i aint typing all that so uh
lime crownBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
shut thorn
thats why
shut thorn
nah its good enough
ok how do i explain the core concept of trig to someone more better
shut thorn
It’s the hypotenuse right
youre trying to find the base and perpendicular of the triangle in your question
the hypotenuse and one of the angle is given
which trigonometric ratios use the hypotenuse in them?
try to use that on the 30 deg angle
limber dagger
but the 30 60 90 triangle hint kinds gave it away
No it flipping doesn’t cus idk what the hell that mean chat
Hate to break it to you
shut thorn
No it flipping doesn’t cus idk what the hell that mean chat
they just mean the angles of the triangle. 30-60-90 degree angle triangle
limber dagger
Okay
So
Do I need to apply that to this equation
I googled it
It says like
A ratio
shut thorn
Do I need to apply that to this equation
no you dont need to
limber dagger
youre trying to find the base and perpendicular of the triangle in your question
Okay but
How do I know what I’m solving for
I don’t understand that
If I understood which one I need to use
Id know how to solve from there
But I don’t
shut thorn
What is cos(30)?
30 is the measure of the angle between the side 15 and x right?
if i treat 30 as A.
limber dagger
yes
shut thorn
then what will cosA be?
if
-> sin(thetha) = opposite/hypotenuse
cos(thetha) = adjacent/hypotenuse
limber dagger
So it’d be x
shut thorn
which ISNT the hypotenuse
shut thorn
So it’d be x
yes
now
the trig ratio for cosA is adjacent/hypotenuse
so
what is the hypotenuse?
limber dagger
15
shut thorn
30?
ye
because thats the angle we are working with right
so that measn
cos(30) = x/15 where adjacent and hypotenuse are x and 15 respectively
rearraging to isolate x. we get cos(30) x 15 = x.
now cos(30) has a specific value of sqrt(3)/2
so plugging that in and solving for x
we will get x.
similarly. try to use the sin of the angle
limber dagger
cos(30) = x/15 where adjacent and hypotenuse are x and 15 respectively
Ah okay
I see
spiral lodge
hmm what's 2x2
Don't troll!
acoustic sphinx
Hi, I made this unit circle diagram for my obsidian notes. What do you think is it clear or too complex?
I looked at many examples in google images and tried to make something between table and radial diagram.
exotic marlin
Hi, I made this unit circle diagram for my obsidian notes. What do you think is ...
Not gonna lie, it's amazing. Looking good. And yeah, it's clear for all basic value. Maybe you can also make a diagram with all the trigonometric ratios on the unit circle ? But other than that, great work !
acoustic sphinx
Thanks!
Maybe you can also make a diagram with all the trigonometric ratios on the unit circle ?
Can you elaborate on what you would add? I looked a bit, and notice that tan, cot, sec, csc can be also added, but I am thinking about showing them in a separate table below.
vague geode
hello
exotic marlin
Thanks!
> Maybe you can also make a diagram with all the trigonometric ratios o...
I would add The basic formulas of tan, cot, sec and csc in terms of sin and cos and also I don't know which visualization you watched. But I would prefer the one in which a tangent is drawn from the point (cos(theta),sin(theta)) and let it cut the x axis and y axis and the two segments separated by that point are tan and cot (that's why it's called tan!) Honestly, it looks cool and also neat, another way is to also draw a vertical tangent at the point (1,0) and let it intersect the extended radius but I don't think in that version, cot will look so aligned with tan
In the version I suggested, all the co- ratios like co-sine, co-tangent and co-secant will sit on the complementary angle side of the theta.
limber dagger
Can somebody help me with this problem?
visual trench
Can somebody help me with this problem?
Your side a=4 and angle A=30 degrees, whilst side b=x and angle B=60 degrees. Both sides are opposite to the angles, so you can apply Law of Sines to this problem
Did you try using Law of Sines?
somber coyoteBOT
limber dagger
Your side a=4 and angle A=30 degrees, whilst side b=x and angle B=60 degrees. Bo...
ah oka
limber dagger
Did you try using Law of Sines?
i did not
exotic yarrow
visual trench
Oh wait
exotic yarrow
it's essentially a pattern matching exercise
visual trench
I didn't notice it was 30-60-90
Yeah your point makes more sense than mine
My bad
limber dagger
it's essentially a pattern matching exercise
im just confused like
what i do
after i know that
though
like
im a bit overwhelmed beecause i missed almost all this week of class so i know very little about whats going on
visual trench
im a bit overwhelmed beecause i missed almost all this week of class so i know v...
Rules for 30-60-90 triangle are, that Short leg (opposite to the 30 degree angle) = s, Long leg (opposite to the 60 degree angle) = s√3 and Hypothenuse = 2s. You can apply this rules to any 30-60-90 triangle and they will work for each of them.
In your situation s=4
silent plank
use a different variable
dull venture
Can anyone help me with sorting triangle congruence theorem examples?
These four examples i categorized it as not enough information
real sentinel
Can anyone help me with sorting triangle congruence theorem examples?
These fou...
ok
dull venture
which triangles do u have to show the congruence?
You have to prove if each triangle is congruent or not and i selected all of this as not enough info for congruence theorem but i dont know if its right
real sentinel
You have to prove if each triangle is congruent or not and i selected all of thi...
Come in forum
dull venture
Ok
radiant rivet
does anyone know how to use eulers spiral to optimise racing line
candid plank
can somebody help me with this?
15 times sin(30) then that's y then do a^2 plus b^2 = c^2 for x
real sentinel
can somebody help me with this?
use sine and cosine
burnt crystal
Hi! I am new here.
Could you help out with some trigonometrical sums I have some difficulty in?
I am in Grade 9.
The 16th and 17th.
rustic spruce
The 16th and 17th.
no way this is 9th
cerulean tundra
I am in Grade 9.
9th?
cerulean tundra
Could you help out with some trigonometrical sums I have some difficulty in?
Sure
cerulean tundra
no way this is 9th
Maybe she's preparing for some olympiads
burnt crystal
Maybe she's preparing for some olympiads
.... No.
Its school
burnt crystal
https://tenor.com/view/fahhh-fah-skeleton-vonoffe-meme-gif-17918076419074819351
Lmaooo
cerulean tundra
Where are you from?
burnt crystal
Where are you from?
India
cerulean tundra
Wth
burnt crystal
Yep
burnt crystal
There are worse sums-
cerulean tundra
Makes sense
cerulean tundra
In state boards this level aint even in 10th
burnt crystal
I will solve it for you
thanks♥️
Uhh... Suppose i need help with Theorems on Area and Mensuration.
Where am I supposed to write?
summer cradle
The 16th and 17th.
for 16:
cos²(45+theta)
= ½(1+cos(2(45+theta))
= ½(1+cos(90+2theta))
= ½(1-sin(2theta))
cos²(45-theta)
= ½(1+cos(2(45-theta))
= ½(1+cos(90-2theta))
= ½(1+sin(2theta))
tan(60+theta)tan(30-theta)
= (sin(60+theta)/cos(60+theta))
(sin(30-theta)/cos(30-theta))
= (2sin(60+theta)sin(30-theta))/(2cos(60+theta)cos(30-theta))
= (cos((60+theta)-(30-theta))-cos((60+theta)+(30-theta)))/(cos((60+theta)-(30-theta))+cos((60+theta)+(30-theta)))
= (cos(30+2theta)-cos(90))/(cos(30+2theta)+cos(90))
= (cos(30+2theta)-0)/(cos(30+2theta)+0)
= cos(30+2theta)/cos(30+2theta)
= 1
so the denominator evaluates to 1 thus we now only need to care about the numerator
cos²(45+theta)+cos²(45-theta)
= ½(1-sin(2theta))+½(1+sin(2theta))
= ½(1-sin(2theta)+1+sin(2theta))
= ½ • 2
= 1
burnt crystal
for 16:
cos²(45+theta)
= ½(1+cos(2(45+theta))
= ½(1+cos(90+2theta))
= ½(1-sin(2t...
Thanks♥️
summer cradle
you're welcome
rustic spruce
Even though im also icse I never had these
olive dagger
for 16:
cos²(45+theta)
= ½(1+cos(2(45+theta))
= ½(1+cos(90+2theta))
= ½(1-sin(2t...
HOLY
This makes me feel dumb
and I finished my unit on geo trig..
😭
burnt crystal
Even though im also icse I never had these
........how.
cerulean tundra
The 16th and 17th.
If you want to know the explanation for denominator step
cerulean tundra
If you want to know the explanation for denominator step
Go ahead
burnt crystal
thanks i got it
cerulean tundra
thanks i got it
There's misprint in Q17's first part
I'll do the other two
cerulean tundra
The SAT identity is this
SAT identity?
slim plinth
For trig
slim plinth
I’m just did that
Just by drawing triangle
And subtract by 0,90,180, or 360
To get to 30-60-90 or 45-45-90
cerulean tundra
Nah I remember it by even and odd multiple of 90 and for sign conventions take help from STSC rule
If it's odd then the function will turn into the opposite one
If even it will remain same
minor heron
i just remember bcs the sine and cosine functions are pi/2 from each other
tho i haven't taken the sat yet igs so idk how important most identities are
burnt crystal
There's misprint in Q17's first part
I'll do the other two
yeah that will be 2A
sorry i forgot to mention it-
cerulean tundra
The 16th and 17th.
Q17:
There are many methods by which I solved but I'd go with easier.
B) tan(2A)= cot(A-18)
WE CAN USE THE IDENTITY tan(90-A)=CotA
=> tan(90-(A-18)
=> tan (108-A)
Now, tan(2A)=tan (108-A)
2A= 108 - A
3A= 108
A= 36
C)Sec(2A) = Cosec(A-27l
Cosec(90-2A)= Cosec( A- 27)
90-2A= A -27
117= 3A
A=39
Eww it's soo hard to type
lime crownBOT
Q17:
There are many methods by which I solved but I'd go with easier.
B) tan(2A)...
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
cerulean tundra
As a helper, please do not give out answers that could be copied as a homework s...
Oh okay
cerulean tundra
yeah that will be 2A
Just use trigonometric functions of allied angles
burnt crystal
thanks i appreciate it
and...my earlier question. where do i ask if i want help in Theorems on area and Rectilinear figures?
cerulean tundra
and...my earlier question. where do i ask if i want help in Theorems on area and...
You can ask here?
cerulean tundra
But it's better if you ask about the method or idea
cerulean tundra
its a lil confusing-
Go ahead
burnt crystal
yeah yeah'
that only
im capable of finding the answer
some sums are a lil tricky
a sum of money placed at compound interest doubles itself in 5 years. It will amount to 8 times in -------- years.
how to find this out-😭
what sums are these😭
minor heron
a sum of money placed at compound interest doubles itself in 5 years. It will am...
(one problem i did by college board had like a 30% interest rate or something... anyway)
so, lets make the sum of money a, and if it doubles itself every 5 years.. a(2)^x would be if it doubles every year, so to make it five years, at five you want the exponent to be 1. so x/5 for the exponent
and, you want it to be equal to 8a in some x amount of years
so divide out the a. does that make sense? i think thats what the probem is asking... if it is what the problem is asking i think you can figure it out from here
minor heron
So.... 15?
yup
burnt crystal
One angle and side are given... But the other is not.
So
Ig this is ASA
I am not sure tho
dull venture
One angle and side are given... But the other is not.
So
Ig this is ASA
Which example?
burnt crystal
The first one
burnt crystal
I think its the first.... SSS
dull venture
I think its the first.... SSS
How come
dull venture
I’ll recheck the first one
burnt crystal
Yes
It is the first one in SSS
dull venture
This is what i got from it
It tels us UX And VW are congruent
Y is midpoint of UW and VX so those two sides bisect
burnt crystal
Hmm..
Its confusing
All of them seem to be correct-
I have to do this ig
Can u wait?
minor heron
is there a wrong one in all categories all the sss one look right to me
burnt crystal
I am currently doing a sample, so i may not reply so quickly
burnt crystal
is there a wrong one in all categories all the sss one look right to me
Ik... Thats why...
I thought it was the first one as per the instructions but it cant be-
burnt crystal
It has 7 examples which is odd
Yea
dull venture
is there a wrong one in all categories all the sss one look right to me
Wdym?
burnt crystal
Wait
dull venture
May I ask, which standard is this?
Standard?
burnt crystal
Which grade?
dull venture
10th
dull venture
SSA is not a congruence theorem
minor heron
nvm oops (srry i haven't done ts in a while)
dull venture
It’s fine this stuff is weird
minor heron
yeah lol
burnt crystal
It’s fine this stuff is weird
100%
I am doing a maths sample
I may have to ask questions too-
Its a little confusing
minor heron
I am doing a maths sample
I may have to ask questions too-
Its a little confus...
whats a sample if you dont mind me asking?
like... a practice test, or something?
minor heron
Its my school's previous year paper
I am practicing those
ooh i see! depending on what grade level type stuff i can try to help... good luck~
burnt crystal
i am ninth
burnt crystal
ooh i see! depending on what grade level type stuff i can try to help... good lu...
and i have doubt
the question is
if x=7-4root3, find the value of root x + 1/root x
minor heron
if x=7-4root3, find the value of root x + 1/root x
like uh
this?
or is 1 not under the root
burnt crystal
yea
minor heron
yea
so, first step i'll give you is 7-4root3 isn't an easy number to work with...
...so, try to express it as a square of an expression
then, you can easily write it and square root it to that expression...
make sense?
minor heron
Like ah
burnt crystal
burnt crystal
yeah?
minor heron
how can you make x into that form
burnt crystal
.....
minor heron
the expanded form is a^2+b^2-2ab, so lets say 2ab is 4sqrt3
and a^2+b^2 would be the 7... so how could you simplify it
stone carbon
hi there.
burnt crystal
then sqrt x would be a-b
hm yes
minor heron
so what would a-b be hmm
stone carbon
minor heron
yupppp
minor heron
after you plug it in its just one more "big" step (to simplify 1/sqrtx) and it should come out as a nice clean number
burnt crystal
I FEEL LIKE EINSTEIN-
stone carbon
you guys look like a couple of Einstein brains.
minor heron
yayyy
burnt crystal
thanks evelyn!
minor heron
phew i wasn't sure what grade you were so i was hoping i wasn't overcomplicating it lmao
burnt crystal
phew i wasn't sure what grade you were so i was hoping i wasn't overcomplicating...
nope i understood
minor heron
yey xd glgl with the rest of the.. sample
burnt crystal
you guys look like a couple of Einstein brains.
lol
burnt crystal
yey xd glgl with the rest of the.. sample
yeah
stone carbon
may i share my question.. uh 
?
burnt crystal
ok
minor heron
may i share my question.. uh <:eeveekawaii:556858499930259471>?
yup~ for sure
burnt crystal
me will try to solve-
stone carbon
yay!
minor heron
me will try to solve too~
stone carbon
burnt crystal
CIRCLES!
stone carbon
Angle BAC=90° btw.
minor heron
alr
burnt crystal
radius not given right?
minor heron
so to clarify, between o and c is 5, c and f is 4? and is that other value up there...8?
stone carbon
radius not given right?
we can find it actually, 5+4.
burnt crystal
we can find it actually, 5+4.
yeah
stone carbon
OC=5, CF=4.
minor heron
is o the center
stone carbon
original question is this, if you wanna take a glance.
burnt crystal
ah thanks\
minor heron
oh, so i guess o is the center
stone carbon
yup.
stone carbon
bon aphetit!
stone carbon
ummm im pretty sure its 5.6 but im not sure
genius.
dull venture
@burnt crystal @minor heron
burnt crystal
Yeah?
dull venture
Heres the forum for my question btw
I explained pretty much every example
So if you find something wrong you can tell me
burnt crystal
Thanks
stone carbon
burnt crystal
Guys i have my maths exam tmrw and im freaking out
minor heron
hmm ah this problem might be a bit… above my level 😅
burnt crystal
19 chapters.... 19 CHAPTERS😭
minor heron
Guys i have my maths exam tmrw and im freaking out
Noooo its okay 😭
burnt crystal
hmm ah this problem might be a bit… above my level 😅
it is for me too-
minor heron
what are the chapters focused on
burnt crystal
what are the chapters focused on
EVERYTHING MATHS HOLD
EVERYTHING
WHAT IS NOT THERE?
Ok imma sleep now
Its 4:25 am
My parents will kill me
Gn
potent hollow
Anyone know a good source of practice question for high school vectors? (scalar/vector proj. dot product, parallel perpendicular components, relative vectors, applications) stuff like that
minor heron
mmhm khan academy was my goat in the past
had to be a bit picky thru lessons to find what i wanted but yeah
burnt crystal
NCERT MATHS TEXTBOOK OF CLASS 11
burnt crystal
had to be a bit picky thru lessons to find what i wanted but yeah
yeahh
minor heron
tho it doesn't go the most in depth iirc
haven't learned some of the stuff u listed so not sure if that'l cover, but i guess just look around
potent hollow
NCERT MATHS TEXTBOOK OF CLASS 11
Thanks
real sentinel
<@876764342111072297>
Heyy a friend helped me to do ur sum
Here
no direct solutions please!
stone carbon
<@876764342111072297>
Heyy a friend helped me to do ur sum
Here
how did you know the angle DOC is 90°?
?
seriously?
stone carbon
blissful pivot
please speed i need this
dull venture
Can anyone help me with my question? https://discord.com/channels/268882317391429632/1477193085623599134
devout summit
Does this cover college mathematics?
If so, I did not take additional mathematics in school and I am currently spending 3 hours on an addmath homework. Is there any channel to ask questions?
cerulean tundra
Can anyone help me with my question? https://discord.com/channels/26888231739142...
Sure
viral obsidian
Help me explain proof for volume of sphere
bright crater
slice a sphere horizontally into slices
each slice approximates a cylinder
calculate volume of cylinder and then take integral
dull venture
Are all of these ASA?
dull venture
at least i think they're not
Which ones arent
spiral lodge
Are all of these ASA?
Yes, all of them 👍
quasi remnant
Are you trying to prove it?
patent crane
looking for team mate to study geometry (i am russian but small speak eglish)
dull venture
Are you trying to prove it?
I have to put the examples in the right categories
Not Enough Information
SAS
SSS
HL
ASA
AAS
quasi remnant
Ok
patent crane
looking for bro to study geometry together ( i am russian)
distant geyser
I am also in Geometry
minor heron
looking for bro to study geometry together ( i am russian)
mm im not in geo im in precalc but i can help (tho i dont know russian)
royal bluff
Hello! I am trying to help my friend on inscribed angles, is there anywhere where I could find some practice problems
rough bronze
[Here is one](https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_10B_...
aops mentioned
i love aops for practice problems too
waxen ferry
[Here is one](https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_10B_...
130
fathom helm
@exotic yarrow how often do u deliver mails
shrewd osprey
Am I wrong on this one?
silent plank
20/360 isn't 18
mild salmon
Does anyone know how to solve theses sort of questions?
shrewd osprey
Oh
mild salmon
huh
spiral lodge
Does anyone know how to solve theses sort of questions?
I guess so, but you should provide a translation, at least for the exercise you have doubts on
mild salmon
I guess so, but you should provide a translation, at least for the exercise you ...
ok tysm i will translate them
exotic yarrow
i love aops for practice problems too
That’s good
But please don’t ping me unless you have a comment with actual substance
exotic yarrow
130
Yes that’s in the link
please don’t ping me unless you have a question or smt that’s not already answered by what I sent
exotic yarrow
<@560122149126275093> how often do u deliver mails
What
burnt crystal
well...my maths exam was today.
THE PAPER WAS HELL-
LIKE
SOME THEM ARE NOT EVEN IN OUR BOOK-
icy hamlet
I want it
dull violet
Can someone help me solve this i have a test in 2 hours
How do you know which angle you’re supposed to find
coarse lance
i'm not good at geometry, and this problem that I need to solve has come up.
Say the blue arch represents the path of a ball, the ball bouncing around this circle forever. How do I figure out which way the ball should bounce/reflect off the circle?
karmic hamlet
theres this one problem I have where its a 30-60-90 triangle with the shortest side being x-1 and the middle side being x, when I solve for x I get x=1 which would make the shortest side 0, how would I solve this
potent hollow
theres this one problem I have where its a 30-60-90 triangle with the shortest s...
Whats your diagram?
potent hollow
Oh i see
The middle angle has the middle length send
And the hypotenuse is the longest
Oh waitp💀
I cant read
That kinda feels like giving the answer
surreal iron
foggy heron
That kinda feels like giving the answer
Hello! can you answer one of my questions in precalculus chat?
potent hollow
Hello! can you answer one of my questions in precalculus chat?
im not really sure what counts as precalc cus i think thats more of a US thing and i live in australia, but if youve done college algebra i would assume they covered that sorta stuff?
foggy heron
kk, thank you!
weak hatch
Hey guys, please I need help on the question:
"Four angles of a pentagon are equal and the fifth is 60°. Find the equal angles and show that two sides of the pentagon are parallel."
How is it possible that 2 sides would be parallel?
rough bronze
Hey guys, please I need help on the question:
"Four angles of a pentagon are eq...
kinda looks like that though i drew it horribly
you solve for internal angles to find the 4 congruent angles then use alternate interior to prove that the 2 sides shown are parallel
weak hatch
kinda looks like that though i drew it horribly
Thank you
marsh dune
How do I solve for x? b*b(x-d)=-1/b (x-1)
exotic yarrow
How do I solve for x? b*b(x-d)=-1/b (x-1)
This is a glorified linear equation. Using the distributive property yields
$$b^2 x-b^2 d=-\frac{1}{b}x+\frac{1}{b}$$
Now, get your terms with $x$ on one side and the terms without $x$ on the other. Then divide by the coefficient of $x$.
somber coyoteBOT
Civil Service Pigeon
young elm
anybody have some cool / interesting 3d vector planes or complex numbers questions?
exotic yarrow
anybody have some cool / interesting 3d vector planes or complex numbers questio...
Consider a tetrahedron with two isosceles triangle faces with side lengths $5\sqrt{10}, ,5\sqrt{10},$ and $10$ and two isosceles triangle faces with side lengths $5\sqrt{10},, 5\sqrt{10},$ and $18.$ The four vertices of the tetrahedron lie on a sphere with center $S,$ and the four faces of the tetrahedron are tangent to a sphere with center $R.$ Compute $RS$.
young elm
thank you!
somber coyoteBOT
Civil Service Pigeon
exotic yarrow
wait no this is the shit one
young elm
oh like too easy?
exotic yarrow
it's just boring
young elm
oh alr alr
exotic yarrow
I mean feel free to do it if you want
young elm
u got any interesting ones?
young elm
[Perhaps this is a bit of a troll choice since the vector method isn't terribly ...
thanks!
lwk preparing for my yr 12 vectors and complex numbers test lol
it's just standard vector lines and planes
and some supplementary links to complex numbers, simple trig and sequences/series
neat kite
i lwk need help w this
Given a pyramid S.ABCD where the base ABCD is a rhombus with side length a and angle ABC equal to 60 degrees. The orthogonal projection of point S onto the plane ABCD coincides with the centroid of triangle ABC. (Let H be the centroid). Let P be the angle between the line SB and the plane SCD, Calculate the sine of angle P, knowing that SB = a.
i dont understand the 2/3 HK part much
green yew
,rotate
somber coyoteBOT
spice oar
shouldn't H be inside the triangle ABC if its the centroid? isn't it like the intersection of its medians?
green yew
yeah thats what i was wondering
spice oar
Which one here is correct???
none?
green yew
gang?
spice oar
if theres addision in a square root, you need to calculate it
shrewd osprey
I was trying to solve for the hypotenuse but i've gone with something simpler instead
a^2 + b^2 = c^2
literally just the Pythagorean theorem
green yew
yes thats what this is too...
shrewd osprey
welp my bad
green yew
hypotenuse is c
shrewd osprey
yeah
green yew
u have rearranged the pythagorean theorem here
shrewd osprey
maths server
wizard hangout
warm gulch
wizard hangout
Lol
surreal moth
I am right, rigth ?
humble granite
I am right, rigth ?
yes
surreal moth
Thank you sir
Just started doing these I. Trig they go from that’s pretty easy to fuuu that
humble granite
Thank you sir
no need to call sir bro lol
humble granite
Just started doing these I. Trig they go from that’s pretty easy to fuuu that
yes this probably is level 1
surreal moth
Heyy this was in my exam!
Some of these are easier than others. XD
Like WAY easieer.
glacial pelican
can anyone help
burnt crystal
Like WAY easieer.
ikr
burnt crystal
can anyone help
what do u need help for?
glacial pelican
pythagorean triple]
quiet sequoia
a very neat triangle I came across when messing around with geometry
nocturne breach
a very neat triangle I came across when messing around with geometry
Yo that’s tuff bro
quiet sequoia
I would definitely recommend just sitting down with graph paper and messing with geometry. things like this seem to come up out of nowhere when you do that
sonic ermine
can anyone tell me how to know if there are one or two or non ssa triagnels
this is gonna be on my precal test
also hwo do i do angular momentum
minor heron
can anyone tell me how to know if there are one or two or non ssa triagnels
dyk the law of sines
heres a pdf if u wanna look thru this https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/T7_AmbiguousTriangles_BP_8_17_18.pdf
its based on the angles and stuff
vocal pollen
minor heron
lwk idk its not on my precalc test i haven't done this since last year where i used ai to help.... guide my ah
idk what angular momentum is so glgl with that igs
sonic ermine
dyk the law of sines
yea its like sinA/a = sinB/b=sinC/c right
quasi remnant
Angular momentum is the same as linear momentum but for angles
quasi remnant
use this
quasi remnant
Np
minor heron
yea its like sinA/a = sinB/b=sinC/c right
yeah
fleet light
may I have help on this?
sonic ermine
there should be a formula or smth right
sly slate
may I have help on this?
I got 85and a half degree
sonic ermine
howd u do it
fervent depot
How does line DC correspond with line BC
sly slate
howd u do it
I checked once again I think I did wrong first time so i reattempted it and got 81° this time I dont know it's correct or not I solved this as shown in img I don't know weather this is the right method or not😅
sly slate
How does line DC correspond with line BC
Since ABC triangle and BDC triangle are similar triangle due to ASA criteria AC/BC i.e hypotenuse of triangle ABC and BCD is equal to DC upon BC i.e DC short side of triangle BDC upon BD short side of triangle ABC
Here you are getting confused because You have fixated that BC is hypotenuse of triangle BDC but you should also keep in mind that it is also short side of triangle ABC
sly slate
may I have help on this?
Yo bro give answer I am curious
sinful hatch
`
vivid ice
@fleet light here is another simple solution of ur problem
vivid ice
How does line DC correspond with line BC
i guess it does coressponds bcz triangle DBC and triangle BAC are similar
by AA similarity
fierce karma
Any ideas why this is wrong?
Part ii where you have to find f(x) =0 is the problem
Because pi/2 doesn't work
exotic yarrow
Any ideas why this is wrong?
,w true or false cos(2x+ pi /3) = -sin(2x+pi/3+pi/2)
somber coyoteBOT
exotic yarrow
,texsp ||Note that your $\theta+\frac{\pi}{2}$ is $2x+\frac{\pi}{3}$, so it should be
$$\cos \left(2x+\frac{\pi}{3} \right)=-\sin \left(2x+\frac{\pi}{3}-\frac{\pi}{2} \right)$$||
somber coyoteBOT
Civil Service Pigeon
quiet sequoia
another geometry thing
exotic yarrow
another geometry thing
low cosmos
Anyone understand the law of cosines?
lime crownBOT
Anyone understand the law of cosines?
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.
quasi remnant
Anyone understand the law of cosines?
You can use laws of cosines when there is a SAS or SSS
sharp void
Anyone understand the law of cosines?
lots of people yes
low cosmos
…
low cosmos
Not wrong
spiral lodge
But yeah it's easier if you share a problem you can't do, or a question about it
quasi remnant
What’s going on?
sharp void
math
slim plinth
Hey I wonder what is borrowing in trig
sonic ermine
my precal test went good
surreal moth
My math correct or I got to go back and relearn mathematical properties.
violet oasis
My math correct or I got to go back and relearn mathematical properties.
Well the process is rough...
And I don't know what you're doing XD.
limber dagger
Hey. Can somebody help me out here? This is on the review guide. When I did it, I got 9, not -680. What have I done wrong?
violet oasis
Hey. Can somebody help me out here? This is on the review guide. When I did it, ...
Umm...
violet oasis
689 - 680cos(x) $\neq$ 9cos(x).
somber coyoteBOT
Restarter
violet oasis
$689\cos(x) - 680\cos(x) = 9\cos(x)$.
somber coyoteBOT
Restarter
limber dagger
shes done 900-689
violet oasis
shes done 900-689
Yeah.
limber dagger
ahh ok
vocal pollen
dense carbon
Find x without using trig I was told 😭
copper dirge
can a 3 dimensional frequecy table be used to display more complex data sets ?
slim plinth
No solution
slim plinth
?
slim plinth
use de moivre
Huh
slim plinth
use de moivre
Is it in Spanish
vocal pollen
formal bane
Hey can someone help me pls
I don’t understand the ambiguous case
<@&286206848099549185>
candid veldt
?
formal bane
Could u explain the ambiguous case pls 💔
fickle plume
Wdym by ambiguous case
formal bane
When ur trying to see how many triangles are possible given 1 angle and 2 sides
inland yarrow
When ur trying to see how many triangles are possible given 1 angle and 2 sides
you could have been more specific and said it from the start
eternal quiver
Find x without using trig I was told 😭
You can use similarity to solve this
formal bane
you could have been more specific and said it from the start
Mb my teacher calls it ambiguous case so I js said that
slim plinth
I am doing sin(theta)=cos(90-theta), cos(theta)=sin(90-theta) and what else also like cot(theta)=tan(90-theta) and tan(theta)=cot(90-theta)
eternal quiver
I am doing sin(theta)=cos(90-theta), cos(theta)=sin(90-theta) and what else also...
Ez
slim plinth
What’s this called
eternal quiver
Take theta = 45
slim plinth
x 2
fickle plume
When ur trying to see how many triangles are possible given 1 angle and 2 sides
if say the angle isn't between the two sides?
it's ambiguous in that case
green yew
pi/6 + 1/2*i?
upper karma
hey guys can anyone help me , and explain to me how to solve it , cuz idk
karmic hull
hey guys can anyone help me , and explain to me how to solve it , cuz idk
idk lol
upper karma
bro wth r u saying i dont understand
karmic hull
bruh wut r u talking about 🤔
karmic hull
like how do i solve it using the pythagoras theorem?
idk lol what do u mean by b_12_7 lol 😁
karmic hull
its my friends initial , and bd date
lol nice
karmic hull
its my friends initial , and bd date
nice, so its like a special birthday initial
upper karma
nice, so its like a special birthday initial
yeah kinda, but were not friends anymore
yk what? idek anything so imma ask chatgpt , ty for helping
bruh
i aint drawing bro
u dont even know my bd , do u ?
elfin saddle
i would give up by now they don't even want to know
upper karma
i would give up by now they don't even want to know
bro i just dont know what hes talking abt
i just know the c^2=a^2+b^2
so?
ohhh okk
okk tysmm
i understand now
wet flower
Anyone any doubts?
inland sonnet
ty
surreal moth
And I don't know what you're doing XD.
Do you think I KNOW ! I am DYING out here MAN!!!! 😭
violet oasis
Do you think I KNOW ! I am DYING out here MAN!!!! 😭
No comment.
Thank you very much.
upper karma
can U guys help me with 4c
regal sedge
can U guys help me with 4c
where are you stuck?
upper karma
where are you stuck?
4c
regal sedge
i hope you know that the locus of this point P is a circle?
Since the radius is greater than the distance from the origin to the center, the origin lies inside the circle, right?
for maximum value of |z|
This is found by starting at the origin, going to the center, and continuing to the far edge of the circle. that is |z| max= d+r = 5+8=18
regal sedge
for maximum value of |z|
This is found by starting at the origin, going to the c...
with a similar logic you can say that for |z|min you can say r-d=3
i hope you got it? @upper karma
upper karma
for maximum value of |z|
This is found by starting at the origin, going to the c...
ohhh yh ofc
upper karma
i hope you got it? <@456226577798135808>
yh bro i did thx a lot
upper karma
for maximum value of |z|
This is found by starting at the origin, going to the c...
though not sure about 5 + 8 = 18
regal sedge
though not sure about 5 + 8 = 18<:blobsatisfied:547119756768182282>
whats your doubt ?
charred meteor
the addition 5+8=13 its nothing much
upper karma
whats your doubt ?
uhh just saying you made a silly with 5 + 8 = 18
regal sedge
uhh just saying you made a silly with 5 + 8 = 18
ooh sorry, its a typo!
upper karma
ooh sorry, its a typo!
btw how do you know that the maximum the minimum value of z is on the straight line that goes through the origin and the center and where the line intersects the circle
like sure it makes sense when you look at the diagram but yk we just cant assume stuff like that
quiet sequoia
2 constants in one circle, pi and root two
slim plinth
2 constants in one circle, pi and root two
Or pi*sqrt(8)
acoustic sphinx
Hi, if anyone needs it, I made an extension to a unit circle diagram with tan,cot,sec,csc. I made it primarily for obsidian notes, so that it's easy to read even without zooming in.
stone drift
2 constants in one circle, pi and root two
Did you draw that circle without a compass?
quiet sequoia
no, I wish I could do that though
slim plinth
Hi, if anyone needs it, I made an extension to a unit circle diagram with tan,co...
Thanks
Is it true that on Pythagorean triple its; Write odd squares consecutively. Add or subtract 1 to even- numbered semi- squares. Double it arbitrarily by three, four, or five
neon iris
I don't need help with this I was just messing around
fleet light
Yo bro give answer I am curious
idk this is my homework for school i lowkey couldn't solve it for so long
How do I solve this
quasi remnant
What are we solving for?
regal sedge
like sure it makes sense when you look at the diagram but yk we just cant assume...
I have a reasoning above for that
regal sedge
Since the radius is greater than the distance from the origin to the center, the...
See this
mint holly
hey so I need help im doing a study guide for similar triangles and need help understanding how to set up and solve problems and maybe find a pattern to use
karmic hull
hey so I need help im doing a study guide for similar triangles and need help u...
same lol we got a study group goin on rn in geom & trig 🤔