geometry-and-trigonometry

[signal swallow]

B is also an angle

[celest cloud]

ok interesting

[wise pawn]

cos(A)^2 + sin(A)^2 = 1

[celest cloud]

ahhh

[wise pawn]

you know sin(A), plug in and solve for cos(A)

[celest cloud]

you fellas are smart

you can make it = 1 using pythag?

am i correct in saying that

[celest cloud]

why would you do that tho ?

its not supposed to be cos(a)

its supposed to be sin(a+b)

[wise pawn]

Sin(A+B) = 20/65 + (CosA)(SinB)
this is where im at right now

you need cos(A) and sin(B)

you have sin(A) and cos(B)

[celest cloud]

exactly but you cant get it

hence im confused

[wise pawn]

that's what cos(A)^2 + sin(A)^2 = 1 is for

[celest cloud]

so do i only do a triangle to satisfy (CosA)(SinB)

[wise pawn]

you have sin(A), plug it in and you can solve for cos(A) for your formula

don't need to draw anything

[celest cloud]

Sin(20/65 + B) = 20/65 + (CosA)(SinB)

is this what you mean fella?

[wise pawn]

nope

you're looking at the wrong term

on the right side you have cos(A)

[celest cloud]

ohhh ye

[wise pawn]

don't mess with the left side

[celest cloud]

but how do you know what cos(A) is tho

thats my question

[wise pawn]

you can solve for it

from

cos(A)^2+sin(A)^2=1

we'll do it together

what's sin(A)

you tell me, it's a number you were given

[celest cloud]

hold on

5/13

[wise pawn]

ok perfect so plug it in to this formula

cos(A)^2+sin(A)^2=1

[celest cloud]

cos(A)^2 + (5/13)^2 = 1

[wise pawn]

nice, keep going and rearrange it until you have cos(A)=...

[celest cloud]

cos(A)^2 = 0.86

[wise pawn]

keep it as fractions

it simplifies nicer that way

[celest cloud]

im getting a pretty large fraction do you want me to stick with it

Technically not large but disgusting looking

[wise pawn]

it gets smaller soon

[celest cloud]

cos(A)^2 = 144/169

cos(A) = 12/13

[wise pawn]

yeah, good, well technically could be + or - that when you square root

[celest cloud]

i got told you assume its a + as a mathematician

[wise pawn]

no

[celest cloud]

because when dealing with functions you cant get 2 different outputs

[wise pawn]

the sqrt symbol itself is +

[celest cloud]

so you assume its +

[wise pawn]

but when you square root something to solve it, you have two possibilities that it could have came from

I'll say it again, $\sqrt{x}$ is positive because we define it this way, that's true. But don't confuse this with saying every time you square root in the process of solving something that it's positive. When you're solving things, there are two possible ways to make 144/169 by squaring, you could have squared 12/13 or -12/13

[somber coyote]

Merosity

[celest cloud]

maybe it matters ¯_(ツ)_/¯

[wise pawn]

it definitely matters

[celest cloud]

when does it matter

[wise pawn]

you're gonna have more than one possible solution

any time you square root while solving a problem it matters

[celest cloud]

1 solution is more than enough

[wise pawn]

if you just see sqrt(144/169) written down by someone else, then it means +

[wise pawn]

lol no it's not

[celest cloud]

ofc it is

[wise pawn]

if I ask you where does the parabola x^2 - 1 hit the x-axis and you only give me one solution, it's wrong

[celest cloud]

its not inequalities

thats picky

[wise pawn]

I'm just the messenger

[celest cloud]

alright i think i understand how to solve these now but ive got much tougher questions coming up

they are pretty tough so

i might pop in again

[wise pawn]

ok

are you sure you know how to finish this problem?

[celest cloud]

i think so lemme have a look

nvm I dont know

[celest cloud]

20/65 + 12/13 * sinB

how do i solve for sinB

acc wait

[celest cloud]

ok nah i dont know

[wise pawn]

do the same thing we did to get cos(A)

except since you want to get sin(B), you have to plug in cos(B)

[celest cloud]

ye but that only works with cos(A)^2+sin(A)^2=1

hmm

so like this cos(b)^2+sin(b)^2 = 1

@wise pawn

sinb = 3/5

[celest cloud]

ayy i got it

LETSSS GOO!!

thanks

[woven copper]

ad/ac=sin30=1/2 angle cad=60 cos60=ac/ab and use pythagoras theorem to find cb

[valid sluice]

x^3+4x^2+6x+24

Don't understand it seem correct

@storm portal

i need help

[storm portal]

Don't ping anyone randomly

[valid sluice]

ok'

but is my anwer is correct

[crisp mason]

If the polar distance of the star is 2°30’, what is its declination?

[pliant bramble]

anyone know how to do this

pls im really stuck

u have to prove congruence using theorems like asa

[smoky palm]

Those who are now in calc, does anyone really remember the formulas for the trig stuff?

[clever fable]

Does anyone know how to find the range of this function?

(By hand)

[simple estuary]

B

A=B

Y=X

D=R6

[sturdy oriole]

this correct

or its suppose to be 10, 7, 6

im not sure

[lethal mist]

They can't be equal to length of outer triangle

[sturdy oriole]

oh

so its 10, 7,6?

[sturdy oriole]

?

[lethal mist]

No idea about that

[sturdy oriole]

😭

[lethal mist]

Oh yeah they are half of corresponding parallel sides

But still confirm it with helpers

[onyx iron]

im not sure if what i did is correct can someone help tysm!

the task: construct a Poincaré disk with two distinct hyperbolic triangles. The vertices need not all be distinct, and may not all lie on infinity.

[dark sparrow]

well the marked points do not seem to be the vertices of any triangles

however you did draw a collection of lines that forms two triangles

so it looks like you did what you were asked for

[dense comet]

can anyone help me with this? I don;t know how to do this

[onyx iron]

wait how about this

[dark sparrow]

this works too i suppose

and now the marked points align

which is a good thing

[wise pawn]

,rotate

[upper merlin]

which question are you confused in?

[dapper marlin]

i got it now

[mystic karma]

@dusky surge bro

how

[dusky surge]

?

[loud shard]

can someoe please help me with this questin?

[clever fable]

?

[quiet bramble]

can someone help me with this?

[stuck dragon]

Do you know the relationship between any of those angles?

[simple estuary]

😢 😢

[upper karma]

please help me learn this

[glacial dawn]

Do you know what a transversal is

[bold galleon]

Given: cot38∘=43andsin33∘=47. Find sin104∘.
How do I solve this

[onyx iron]

thanks! @dark sparrow

[upbeat helm]

hint: sin(104) = sin(2 * 33 + 38)

[upper karma]

let me tell you a fun abbreviation u might know

Some Old Hags: sin = opposite/hypotenuse

Cant Always Hide: cos=adjacent/hypotenuse

Their Old Age: tan= opposite/adjacent

these are the 3 trigonomic functions

[lusty abyss]

How do I find x ?

????

[upper merlin]

think about the area of a parallelogram

[upper merlin]

try to express it in the form of $\sin(\frac{\alpha}{2})$ and $\sin(\frac{\beta}{2})$

[somber coyote]

LazyKnight

[ivory path]

If I'm correct, 66 + 6x-6 = 180

and after finding what 6x-6 is

simply do answer of 6x-6 + -10y-4 = 180

and then after having the answer for -10y-4

do -10y-4 + -10z+4 = 180

$$\frac{x^2}{2}

[clever fable]

Can someone help with this question please?

I've tried many approaches (like directly subbing in x into the equation and writing them all in terms of sin and cos)

I just need like a hint or a start

[dark sparrow]

consider: sec^2(θ) - tan^2(θ) = 1

[clever fable]

Thanks!

I've got it now 🙂

[loud shard]

pls help me with this question

[upper blaze]

Guys does anyone know how to calculate solid angles?

[proud plover]

can someone help with this question and how can i solve it please?

[upper blaze]

Is this from a test? If it is I am afraid we cant help if it isnt then for sure we can 😄

[proud plover]

it is homework

not graded

thats why i want to know how to solve it

[upper blaze]

well first to determing bounderys you take 12-x^2 = x^2 -6 and solve that to get -3 and 3

so those are fine

then you basicly need to see what function is above the other

In this case one that has -x^2 will be above the one that have x^2 so area would be integral of (12-x^2)-(x^2-6) which is not equal to what you have

it is negative that

ro you can put apsolute value I think but thats not what you ahve there

[proud plover]

thank you so much

[upper blaze]

mate you should put this in calculus section xD This is geometry mania here 😄

[proud plover]

oh mb sorry

[upper blaze]

Again, does anyone know anything about calculating solid angle for a given three lines in space that interesects in 1 point? It would be of great help even a computer simulation since it is only for experimental purposes

Again, this is not place for this question xD My answer for only for surfaces not for volumes xD I dont remember the formulas for those I do mostly geometry and algebra very little calculus and even when I do this I need to refresh my memory a bit. And for rotation like this I think you cant use same logic

[north cosmos]

hey smart people

can someone help me

<@&286206848099549185>

[valid harbor]

triangle ADE and EBC are congruents

can you see that?

[north cosmos]

@shell raven if u know geometry

[north cosmos]

yea

[shell raven]

sup

oh i do not know coordinate geometry (yet)

[valid harbor]

i guess then you know why they are congruent

[north cosmos]

i can see that they are congruent

[silent plank]

triangle ADE and EBC are congruents
no they are not

[north cosmos]

how to solv

[silent plank]

intersection chords theorem / power of a point

[north cosmos]

ok

[north cosmos]

so 4x=36?

and x=9?

[silent plank]

no

[north cosmos]

da fawk

[silent plank]

how exactly are you applying the theorems i mentioned

[valid harbor]

doesn't angle DAE equal to angle EBC and angle ADB equal to angle ECB

[silent plank]

doesn't angle DAE equal to angle EBC and angle ADB equal to angle ECB
yes

[north cosmos]

no clue

im dumb

[silent plank]

the triangles in question would be similar not congruent

[valid harbor]

similar is what i meant yeah

sorry english is not my main language

[silent plank]

do you know what these theorems state

intersection chords theorem / power of a point
and or are able to apply properties of similar triangles here

[north cosmos]

i have no idea

[silent plank]

look up intersecting chords theorem

[north cosmos]

oh

so

A times B = C times D?

no ok

[silent plank]

A times B = C times D?
what do A,B,C,D represent in that equation you've written

[north cosmos]

what will the equation look like

[silent plank]

have you looked up

intersecting chords theorem

and if so can you post an ss of what you found

[north cosmos]

why is math a thing

fuck math

[silent plank]

ok try applying that to your question

[north cosmos]

does A=9

[silent plank]

lowercase a

[north cosmos]

a=9

and b=x

[silent plank]

no

[north cosmos]

please help me so i can go use the toilet after i finish

[silent plank]

note that in the image you posted
a,b represent the segments of the same line (split at the point of the intersection)

[north cosmos]

yea i see

[silent plank]

so if you're setting a to be 9,
what should your b be?

[north cosmos]

4?

[silent plank]

yes

[north cosmos]

9 times 4 = 36

[silent plank]

and then similarly what would the c and d be?

[north cosmos]

c = x?

and

d = 4x?

[silent plank]

yes

[north cosmos]

so 36 = 4x square

[silent plank]

use ^ to denote exponentiation

36 = 4x^2

[north cosmos]

ok

x=3

[silent plank]

yes

[north cosmos]

finally

thank u

very much

[stone comet]

What’s the name of this shape?

[keen nova]

trapezoid

[stone comet]

How do I apply the area formula to it then?

What are the bases and what’s the height

[keen nova]

do you know the left and right side are at right angles to the base?

[stone comet]

Yes

[keen nova]

well then you can split it up into a rectangle and triangle

or you can apply the general trapezoid forumla

[stone comet]

What’s the height and what are the bases

[keen nova]

consider this, your trapezoid is actually rotated 90 degrees

like the "height" is actually a horizontal line for you

since it's the left and right side that's parallel, instead of the top and bottom

[stone comet]

Like this?

[keen nova]

yes

[stone comet]

Thanks!

[keen nova]

exactly

np

[dreamy pike]

Can someone help me with a question pls

[keen nova]

[dreamy pike]

Thank u here is the paper ☝️

[keen nova]

what exactly is the question you're having trouble with

[dreamy pike]

3.3 and 3.4 pls

[keen nova]

what part are you confused by, and what have you tried so far?

[dreamy pike]

Ohk firstly i sovled the gradient 3.1 which is 4 over 3.2 i got confused bcuz it says "Hence write down the Gradient of BC so I said negative 3 over 4. Now i'm confused on how to find X of (x; 20)

bczu I'm using Midpoint formula and it ain't working

[keen nova]

so you know the gradient of BC right?

but you can also find it using the 2 points B and C, so try writing that formula down and equating it to -3/4

[dreamy pike]

Do u mean like this

[keen nova]

yes

solve for x

it's just algebra

[dreamy pike]

Ohk so must I put them in they prime form them solve X

[keen nova]

prime form?

im not familiar with that

[dreamy pike]

I mean like this

[keen nova]

do you know how to solve for x there?

[dreamy pike]

I don't know

[keen nova]

try multiplying both sides by (x-12) and isolating x

[dreamy pike]

Ohk bro

U mean like this

[dreamy pike]

<@&286206848099549185> can U pls help me 3.3 and 3.4 pls

[keen nova]

yes

[dreamy pike]

Ohk cool thank you

is it correct @keen nova

[keen nova]

$(x-12) \times\frac{-3}{4} = 20-17$

[somber coyote]

Ninja

[keen nova]

is this what you meant

[dreamy pike]

Yeah that's wht i mean apologise for writing it bad @keen nova

[keen nova]

np, that is right btw

[dreamy pike]

ohk cool, now how do i multiply the fraction in too the bracket

[keen nova]

use the distributive property

[dreamy pike]

Wht is that pls

[keen nova]

$a(b+c) = ab+ac$

[somber coyote]

Ninja

[dreamy pike]

Oooohhhkkkk i see

Wait so my X equal to 11 @keen nova

[keen nova]

no

[keen nova]

you forgot the division by 4

$\frac{3x-36}{4} = 3$

[somber coyote]

Ninja

[dreamy pike]

Ohk so i must first divide by 3 first, then take my whole sum and divide is by 4. then when i divide by 4 I'll divide both sides by 4 @keen nova

[pallid pilot]

Sorry theres no flash my battery is low but anyone?

And ping me if u got an answer

[dark sparrow]

this is impossible to read

[pallid pilot]

Lmao

K hold upp

Any better?

The last one

[pallid pilot]

Any helpers in chat please?

[dark sparrow]

A rectangle, its diagonals intersect at M, the length of its diagonal is 6 cm, then the length of the median AM is .....................
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

for everyone else's benefit

idk what's up with the typesetting and the wording, and the apparent choice not to mention that the rectangle itself is (probably) named ABCD

but if you draw a diagram it should be pretty obvious

[pallid pilot]

Pretty much

Its not named nah

[pallid pilot]

I tried to but still

[dark sparrow]

oh you tried?

can you show the diagram you've made

[pallid pilot]

Thats pretty much all the info written

[noble heath]

Hopefully you have at least a conjecture as to what the answer is

[upper egret]

have you made a drawing?

[smoky palm]

Did you get the answer yet?

Can I give you a hand?

Do you know how to rotate a point around the origin?

[nocturne remnant]

hey just so you know the triangle is actually right-angled as well as isosceles so just computing one side length gives the answer directly

[smoky palm]

This is on the right track, but the negatives are wrong

Originally it is in the second quadrant

Moving it clockwise 90 degrees would move it to the 1st quadrant

Where both the points would be positive

Now that you have these points, do you know the formula for the area of a triangle?

Those are both correct

Does that make sense?

Have you guys gone over the Pythagorean theorem?

It is

Have you drawn down the triangle yet?

eh, I’ll do it

So there is the triangle, and I drew two other sides with what we know from the points

The hypotenuse of each of those triangles on the right should equal each of the sides

Yes

But a 2:1 ratio

To make it easier to see

Do you have it from here?

P is the original point

When you move the original point

You add a ‘ to the end of it

And you say prime

So the points are p and p prime

P is the original

Yep

Not new

Just another point stemming off of it

Yeah

New works

Sorry

So, those are the points

Because we have the points

We can figure out the lengths of sides from them

As from the photo I sent

We know that point p prime is 4 to the right and two up, forming a right triangle

With this, if we do the Pythagorean theorem

And we find the hypotenuse of the line from the origin to (4,3) is 5

Meaning that side of the triangle is 5

And you can do that with the other side

And see that that one is 5

So you have a triangle with the height 5 and with the base of 5

Using this

Of the pink triangle?

Or the pencil colored

To get the area, you have to get the base and the height

[silk patio]

It’s half a square

[smoky palm]

Because we know all the points of the triangle

[smoky palm]

Or rectangle

[silk patio]

Square

[smoky palm]

I mean, this one is

But, to get the base and the heigh, those are just two of the lengths of the sides

Because we know that we have the point (4,3)

We know it’s 4 along the x axis, and 3 up the way axis

And if we make a triangle out of this, we know it’s a right triangle

With the other side being the line between the origin and p’, and it is also the hypotenuse

Do the Pythagorean theorem, with the sides 3 and 4

3^2+4^2=25

Square root of 25= five

Do that for both, and you have the base and the height

[clever fable]

How do I simplify this expression by hand?

In previous questions, I used the identity of inverse functions that f(f^-1(x)) = x.. but I am not sure what to do now 😦

[livid moss]

There is an identity for cos(2x) that will reduce it to the form cos(x)

Might be helpful

[clever fable]

Yeah.. I thought of that but idk how we would use it in this case because the three different forms look messy after trying it out

[livid moss]

Use the one involving only cos and not sin

And tell me what you get

[clever fable]

ok

IT WORKS!

thanks!!!

[livid moss]

👍

[clever fable]

I got 2/a^2 - 1

as simplified form

[livid moss]

Looks right

[upper blaze]

Here is an interesting question. If we are given 3 points in space is there any geometric interpretation of point which coordinates are sum of absolute value of coordinates of 3 given points where you can posibly add minus somewhere in front of the result. Like (2,-2,-2) (-3,3,-3) and (-4,-4,4) and we get point lets say (-9,-9,-9)?

[marsh epoch]

Could you rephrase the question?

[silent plank]

the work is not correct

the notation in the first two lines has mistakes and notation issues

and it is unclear how you were able to reach the conclusion in the final line

[cloud stump]

is this the proper place to ask for help in descriptive geometry?

in case the answer is no does anyone know where I can get help

[upper karma]

Are these two expressions equivalent?

[swift shale]

can anyone help me really fast ?

[signal swallow]

depends on if you have a question to ask

[swift shale]

@signal swallow

i need help on these two

[signal swallow]

how do you solve for an angle normally?

[swift shale]

what do you mean

[somber coyote]

Inheritanc-e ♦

[royal citrus]

?

[velvet knot]

help someone

[dark sparrow]

do you still need help with this?

[velvet knot]

nope but i need help with this tho

[dark sparrow]

and which part of this do you need help with?

do i understand correctly that the instruction "Make your own example of an if-then statement" is beyond your comprehension?

@velvet knot

[velvet knot]

yea

[dark sparrow]

@velvet knot do you know what an if-then statement is?

[velvet knot]

yup

[dark sparrow]

okay then why are you unable to make your own example of one?

[jolly basin]

can anyone help me with this? (find value of x angles

[cerulean yacht]

whts tan45

[cerulean yacht]

x=70 degree cuz alternate interior angles???

idk

[jolly basin]

1 i think

[jolly basin]

nope

[velvet knot]

help

[upper merlin]

do you still need help with this?

[upper merlin]

recall, what is a linear function?

[velvet knot]

idk

[jolly basin]

yes

[upper merlin]

ok, in simple terms linear function is a function whose degree is 0 or 1

[upper merlin]

its a pentagon, what would be the sum of its angles?

[jolly basin]

540 degrees

[velvet knot]

HELP

[mystic karma]

y=x

[dark sparrow]

do not give out answers.

[mystic karma]

heh why ?

[dark sparrow]

there's this thing called #❓how-to-get-help that you might want to have given a read when you first joined this server.

and if you haven't, now is a good time to read it.

[humble pulsar]

Also don't be an ass

[wintry tundra]

Don't go to a help channel and be an ass to people who need help

[wintry tundra]

To find the answer you need you have to find an equation that when you input 0 for x you get 0 for y

Since the origin is at (0,0)

[true wave]

someone help me as soon as possible PLEASE <@&286206848099549185>

[wintry tundra]

First I'd square both sides

I think you should go from there

[upper karma]

looks like a geometric inequality with disguised law of cosines

ill give it a try

,rotate

[upper karma]

so let BP=b, AP=a, CP=c
let angle APB=60 and angle CPA =60

then by law of cosines, AB=sqrt(a^2+b^2-2ab*cos(60))

so AB =sqrt(a^2-ab+b^2)

similarly AC= sqrt(a^2-ac+c^2)

now use law of cosines on triangle BPC with angle P

BC=sqrt(b^2-2bc(cos(120))+c^2)

[true wave]

what does it mean when u write equality when a is on line bc?

because a isn't on line bc

[upper karma]

BC=sqrtb^2+bc+c^2)

[upper karma]

the only way to get BA+AC=BC is if the point A is on the line BC

lemme draw it

[clever fable]

Can someone help with this question, I tried using the formula arctan(m) = theta (where m is the gradient and theta is the acute angle with x-axis)?

[upper karma]

,rotate

[upper karma]

so AP is just the length of the angle bisector of triangle BPC

using a form of stewart's theorem we can get a relationship between a b and c in the equality case

https://proofwiki.org/wiki/Length_of_Angle_Bisector

where we get from the second to last step to the last step because the problem says a,b,c are positive reals

@true wave

[upper karma]

so for this one do you see why it's arctan(2)-arctan(1/3)?

from there it's just simplifying it

arctan(2)-arctan(1/3)=x

tan( arctan(2)-arctan(1/3) ) = tan(x)

use tangent subtraction formula on left hand side

you get 1=tanx

so x=pi/4

[clever fable]

Ohh yeah I got to the arctan(2) - arctan(1/3) part, I was just stuck from there

thanks!!

[clever aurora]

Is this polygon convex?

[past geyser]

i think so

if it was concave one of the interior angles would be greater than 180

[tight tide]

hey all !

so I've been studying maths on and off for a couple of years

and I'm trying to fully cover geometry and trigonometry

I've been using Khan Academy to help me but

I'm completely stuck on Congruence

specifically doing proofs

I'm trying to find something else that covers this stuff, but having a rough time

would someone be able to point me in the right direction ?

[past geyser]

@tight tide do you have a specific question

[tight tide]

any good books or courses on geometry

that aren't Khan Academy

[past geyser]

are you in hs?

an hs curriculum should be enough

[tight tide]

nope, self studying

[past geyser]

ok well uhhhhhhhhhhhhhhhhhhhhhh

use paul's online notes

for learning pre-calc

it covers trig if you want

¯_(ツ)_/¯

[tight tide]

@past geyser ok is brilliant any better ?

[past geyser]

Brilliant is really good but you need to pay

[tight tide]

ok good enough for me

but yeah thanks for the information

[lone sandal]

Help

[wintry tundra]

what is zr supposed to be

[daring bolt]

Plz I need help

[sage jolt]

place the degree between G and C

What type of curve is this?

[sage jolt]

<@&286206848099549185>

[pastel pewter]

Can someone help me to proof PX/XQ = - PY/YQ with menelaus theorm

my lecture need another answer and using another triangle (not using triangle PQC)

<@&286206848099549185> need a help ASAP :((((

[cobalt ferry]

Excuse me, sorry for interuption :"
Anyone can help me?

[upper karma]

Shortest distance with the constraint that it has to touch some lines along the journey, these problems usually have you use reflections to deal with the constraints and the fact that shortest distance between two points is a line

Lemme try it

,rotate

[upper karma]

This takes care of part a and b

For part C note that P is closer to line S than it is to line T

Let a= perperdicular distance from P to line S, b=vertical distance between P and R, and c=perpendicular distance from R to line T

,rotate

[upper karma]

The path from P to R'''' is the same as the shortest path from P to R that touches line t first, then line s, then point P

And notice there's more vertical distance between P and R'''' than there is between P and R''

So for part C the shortest path going from P to R touching line s and then t is shorter than the shortest path going from P to R touching line t and then line s

[floral saffron]

help? I don’t get 9x or 6x

[dark sparrow]

what do you mean by "don't get"?

[cobalt ferry]

Thank you so much, helped me a lot

[lone sandal]

Help

[dark sparrow]

@lone sandal do you still need help with this?

[past geyser]

Can I help them

[dark sparrow]

no

[past geyser]

Wait nvm school ending

[dark sparrow]

they've posted in the wrong channel

and also they've not replied in several hours

[past geyser]

It’s ok I need to walk home

Cya

[vast rover]

can someone help me pls

[crystal quail]

@vast rover start by listing your knowns. We know x (side AB) and we know theta. Then list what we need to know (BC). We need to find something that uses our knowns and can be solved for our unknown. Since it's a triangle (particularly a right triangle) perhaps a trig function may be helpful. You know of any that may be of particular use here?

[hot cove]

Can someone explain each one with the answer please

[prime vigil]

vejca dm me

@hot cove

[hot cove]

ok

[patent quarry]

$tan\theta=\dfrac{x}{BC}$
$\ tan39^{\circ}=\dfrac{7.9}{BC}$
$\ BC=\dfrac{7.9}{tan39^{\circ}}$

[somber coyote]

thatsouris

[patent quarry]

.

you should read up more on the trig ratios

khan academy provides great learning resources for them

[violet horizon]

Has anybody here ever read 'Euclid elements' and how did it feel after making it through chapter 1?

[hot cove]

does anyone think they could give me sentences explaining how E and F are solved pls

[violet horizon]

Wow where did you get this questions?

[hot cove]

my teacher assigned

[violet horizon]

All they are asking is if those conditions can form 1 (unique) triangle, the triangle is impossible (no triangle) or there are more than 1 triangles that satisfy that statement.

Do you get it from there?

[hot cove]

i know how to solve it i just need someone to write me sentences because i am having trouble for E and F just explaining how to solve them

[violet horizon]

To form a triangle from three side lengths, the sum of any two side lengths must be greater than the third.

Let us call the above prop 22. This means that if you want to form a triangle from lengths A, B, C then

A + B > C
A + C > B
B + C > A

And if your lengths do not satisfy these then forming a triangle is impossible. That is it will form 0 triangles and if it does satisfy this then it will form a unique, 1 triangle.

You can check f to see if 7 + 8 > 12 and so on and you know what this implies.

[hot cove]

is this for E or F

@violet horizon

[violet horizon]

It is F

[hot cove]

ok should i write this all down ?

[violet horizon]

did u read it?

[hot cove]

yes

i just need a few or 1 sentence for E and F explaining how they are solved because i cannot seem to put the correct words together to make a sentence that makes sense

because everything i write is not making total sense so i need help

[violet horizon]

Ok tell me what u think of F

I'll help u make a better sentence

[hot cove]

ok

give me a few seconds i have to pull the page back up

if you do 7+8 is equal to 15 and 15 is larger than 12cm and that leads it to being a unique triangle

i just dont feel this is right

or i am not using the proper wording

i meant 7=8

btw

7+8

[violet horizon]

U are not checking one condition, three actually

[hot cove]

oh ok so what should i add or change in the sentance

sentence

[violet horizon]

It will form a unique triangle

[hot cove]

i mentioned that in the last bit

[violet horizon]

From the picture u are given an option

Right?

[hot cove]

yes

between a unique triangle, no triangle and more than one triangle

[violet horizon]

So which do you think?

[hot cove]

unique

i know the answers i just need sentences explaining how you find the answers

i just cant seem to put the right words together and make a sentence that sounds correct and is correct

@violet horizon

[violet horizon]

Like a proof?

[hot cove]

what do you mean by that

like proof i know how to solve the problem

??

[violet horizon]

Give me a sec

[hot cove]

ok

[violet horizon]

Let ABC be a 🔼 such that AB = 7, BC = 8, AC = 12 and let DEF be another 🔼 such that DE = 7, EF = 8, DF = 12 (try to sketch the 🔼 to see the idea).

Now we see that the assuming that the lines AB, BC and CA are unique ( Have you heard of two different or unequal straight lines joining the same points?), we have that AB is the same as DE, BC as EF and AC as DF, it follows that 🔼ABC = 🔼DEF as they coincide and 🔼 ABC is unique.

Generally any triangle constructed from three give side lengths is unique.

@hot cove

[hot cove]

ok this sentence is much better than mine do you mind if i use it?

@violet horizon

as well with E would you mind helping me with that

[violet horizon]

No problem

[hot cove]

ok

do u mind helping me with E as well you made this very clear on what i was to do with F

[violet horizon]

Not exactly sure of what a non included angle means

[hot cove]

here hold on i will get you a definition

A triangle drawn under the condition of two sides and a non-included angle is often thought of as a condition that does not determine a unique triangle.

i believe this is a non included angle

does this help a little

@violet horizon

[violet horizon]

Then you already have a sentence

[hot cove]

that is the definition of non included angle

[violet horizon]

How many sides are we given in E?

[hot cove]

A triangle with 8cm and 9cm side lengths and a non-included 70∘ angle will form

thats the question

[violet horizon]

Since it does not determine a unique triangle that means that it will determine more than 1 (Note that the definition above implies that at least one triangle is possible)

[hot cove]

ok thank you that is what i should write down?

[violet horizon]

You are sure of the definition you wrote. right?

[hot cove]

yes

[violet horizon]

Write it

[hot cove]

it is in my notebook from the notes my teacher told me to put

ok

[upper blaze]

Does anyone know any book that has some formulas on solid angles for tetraheedron?

[violet horizon]

Still seeking?

[upper blaze]

Yes, i found ways to calculate but still would be good to have book to read when i neeed some properties

[upper blaze]

Guys here is a curious question. Does inversion exsist in 3D? If yes does anyone can direct me to some book or article where I can see how it works?

[violet horizon]

1. "Measurement" by Paul Lockhart
2. "Euclid's Element of Geometry" by Euclid(300 BCE)

Book (Chapter) 13 of [2] above speaks precisely about the platonic solids: cubes, tetrahedron, octahedron, icosahedron and the dodecahedron but to understand it you might need results from previous chapters. [1] can be used as a modern alternative, since [2] is just facts and proofs.

[violet horizon]

What do you mean by inversion?

[upper blaze]

Thanks for this

[upper blaze]

And by inversion I mean inversion as hmm what is it called in english xDD Like central symetry, translation, homotethy or whatever it is called there is also "inversion" as transformation over a circle in plane. Can that be done in 3D

[violet horizon]

It surely can be done, although I don't understand the idea behind those geometry done using algebraic structures as groups

[lofty stream]

hi

i am struggling SO HARD with verifying & simplifying trigonometric expressions using identities

does anyone have any tips/helpful vids? i literally cannot comprehend it

[noble heath]

Are there times you think something is valid but it isn’t? Or that you aren’t sure whether something is valid?

@lofty stream

[lofty stream]

yup

literally 90% of the time

i find it extremely difficult because there are no rules set when it comes to simplifying or verifying you just gotta apply the identities and do whatever

and my brain goes empty cuz idk what to do other than applying those identities

[noble heath]

That may have to do with improperly learning things like variables, symbols, and functions in your past

[lofty stream]

yeah that’s true

whenever i ask my teacher for help he goes “just memorise the identities & you’ll know how to solve”

yet i still do not know how to solve ???

[noble heath]

He didn’t think of what I said for some reason

Hmmm ok let me ask this

Have you read or heard the phrase “there exists a number x” or “for all numbers x”?

[lofty stream]

no

example q?

[noble heath]

“True or false: For all real numbers x, x^2 >= 0”

[lofty stream]

yeah no

[noble heath]

Yep that’s the heart of identities

And solving equations

You’re told the letter x represents a variable number

But you weren’t told the letter x literally means a number

[lofty stream]

yeah

[noble heath]

A pronoun for a number, one might say

[lofty stream]

like honestly

i’ve completely forgotten how to factor, how to do distributive multiplication, how to cancel out like terms, like all basic algebra which i’m supposed to know

and it’s like really holding me back

[noble heath]

So all those algebra things you mentioned are rules precisely because they’re rules of “generalized arithmetic”

Distributive property, let’s take a look

3(6+5) = 3*6 + 3*5

This familiar? Is it obvious?

[lofty stream]

yes

[noble heath]

And it’s still true if I replace all instances of 3 with any number

Or all instances of 6 with any number

Or all instances of 5 with any number

So I can express that by using letters with each one representing a number

a(b+c) = ab + ac

for all real numbers a, b, and c

[lofty stream]

right so let’s say cos^2x(sec^2x-1)

how can i distribute that

[noble heath]

I think you typoed

[lofty stream]

that is my question

i think you’re meant to distribute?

or are you not

[noble heath]

Both distributing and not distributing are valid

You’re meant to try both and explore both options

Solving a problem is not a linear process

So for distributing

Do you notice an a(b+c) pattern

If so you can replace it with ab + ac

There’s also replacing every weird function like sec x with its definition

In fact, always do that tbh

[lofty stream]

that i know

ok example

cotx (cotx + tanx) = csc^2x

distribute first step?

[noble heath]

Whoa is that an equation to solve or an identity?

[lofty stream]

equation to solve 😃

[noble heath]

Don’t be afraid to distribute

[lofty stream]

i have to verify that the left side is equal to the right

[noble heath]

You just contradicted yourself…

[lofty stream]

noooo how

ok wait i’m sorry LMFAO

its

verify that cotx (cotx + tanx) = csc^2x is an identity

[noble heath]

There’s 2 things to try at the outset

Try them both, don’t freeze

Just because the official solution gives one way doesn’t mean another way isn’t valid

[lofty stream]

okay okay thank you

[upper karma]

try reducing what you are trying to verify into sines and cosines

[icy glade]

Please....

[eternal ermine]

I think i know how to do the first one

the vertex is (-b/2a, P(-b/2a))

you know the latter equals 8

[icy glade]

Ik nothing lmao -

[icy glade]

Okay Ik that

[eternal ermine]

plug in and see what that yields

[icy glade]

Huh

I don't get it but okay

[eternal ermine]

another thing you know is that b must be negative

because -b/2a = 8 & the func has a min so a>0

you can also plug in 2(a² + 5a + 2) in for b

[silk jacinth]

if I would say that function like f(x) = x * sin x is not a periodic function but instead has a periodically behaving element, would that be accurate?

[dark sparrow]

what's a "periodically behaving element"

[silk jacinth]

sin x

[dark sparrow]

no, that's not what i am asking

i'm asking you to give a definition of "<function> has a periodically-behaving element"

[silk jacinth]

umm let's see 😄 a function that, across its period, produces a pattern of values that is repeated identically across subsequent periods

english is not my native language so pardon any weird terminology

[dark sparrow]

...........

that sounds like 'periodic function' to me

[silk jacinth]

yeah, but wouldn't multiplication with x cause that function to uhh... lose its periodicity?

[dark sparrow]

yes exactly

x sin(x) is not periodic

you have not clarified what you meant by "has a periodically behaving element"

[silk jacinth]

hmm the more I think about my initial question, the more nonsensical it starts to sound even to me

[grand rivet]

Hey, I did this exercise a while back, and solved it

but I wondered, is there any actual reason why this is true for a hyperbola? Does $2\sqrt2|x-y|$ have any sort of physical meaning here? It seems like there must be some more satsifying reason why the inequality holds.

[somber coyote]

tim_e

[loud shard]

<@&268886789983436800> can you please help me with this?

[silk charm]

please don't ping mods for help with math problems

[loud shard]

ohh ook sorry

[loud shard]

who should i ping?

[silk charm]

helpers

please read #❓how-to-get-help and #rules

[patent quarry]

@loud shard

is there any other explanation or just express as a product

[raw tiger]

These will help you 🙂

[molten seal]

Is anybody really good with hyperbolas?

[raw tiger]

I’m sure plenty of us can help you 🙂 what is your question?

[molten seal]

#help-6

Also thank you for the kind words

[lapis inlet]

Hey so my shsat test is in 4 days and I am not too good in geometry

@everyone

[upper karma]

Study

[raw bobcat]

Hey I have an Algebra II/Trig honors quiz tomorrow and was seeing if anyone could give me some advice/pointers

[silent plank]

do some practice quizes (under test conditions) to help identify your knowledge gaps

[gentle sable]

where can i find exercises like this

[orchid sluice]

How to solve 7 b

Please help me with this i've been struggling to find the answer

[zinc mural]

Is someone good with applications of trig derivatives?

[rare sierra]

I request assistance with Law of consine, particularly the arccos aspect of it

[silent plank]

what's your issue with arccos

[patent quarry]

,rotate

[clever fable]

Hi can someone help with this question..

Tbh I got the answer which is that it is -8/5, but I used a dodgy method (I used the Sum-to-product formulae and used the fact that sin(x-y) = -4/5 and rewrote tan(x)cot(y) = 3 as 2sin(x)cos(y) / 2 cos(x)sin(y) = 3. After that using sum to product formula for sine, I algebraically manipulated to get sin(x+y). It would be great if someone can quickly go through this (I'm not sure if there was anything in this case that I am not allowed to do)

Thanks!

[river cliff]

help

[past geyser]

Sure

Turn everything in terms of cos and sin

[spiral mural]

if theres 47 liters per m^2 water in a 1m^3 volume cube is the height of water 4.7 cm?

[keen eagle]

idk if this counts as algabrea or geokmetry

[smoky palm]

Witchcraft

[keen eagle]

agreed

[nocturne pebble]

10 is incorrect right

It should be x/169 = 25/x

[sand zodiac]

Help!

How is that 35?

[nocturne pebble]

which is square root of 4225

[sand zodiac]

65

[nocturne pebble]

which is 65

[nocturne pebble]

THANK YOU

had to prove someone wrong

in an agrument

[sand zodiac]

lol haha np 👍

can you help me? @nocturne pebble

[sand zodiac]

here

[sand zodiac]

<@&286206848099549185>

[nocturne pebble]

Uh which grade is this

[sand zodiac]

9th?

[nocturne pebble]

And what is it called I'll look it up see if I remeber

[sand zodiac]

what grade

are you in?

[nocturne pebble]

9th but im in math 2

[sand zodiac]

congruent figures

stuff like that

[sand zodiac]

oh kk

[violet horizon]

Have you gotten the answer to your question?

[sand zodiac]

pls someone help

[sand zodiac]

yes

its 35

i just dont know why

im trying to figure out why its 35

but idk

[violet horizon]

How did you get 35

[sand zodiac]

idk

thats what im asking

its an answer key

[violet horizon]

Ok
Do you know that the sum of angles in a quadrilateral is 360 degrees?

[sand zodiac]

yes i do

but it aint a quadrilateral

my g

[violet horizon]

Look again

[sand zodiac]

its got 3 sides

just look

[violet horizon]

Is this not the question

[sand zodiac]

its just asking for the value of x

LMNP congruent to QRST is just the given information

[sand zodiac]

so ye

[violet horizon]

I am not typing on a pc

So let us make an alias

[sand zodiac]

?

[violet horizon]

Q1 is QRST

[sand zodiac]

ok

[violet horizon]

Q2 is LMNP

[sand zodiac]

alr

[violet horizon]

So Q1 is congruent to Q2

[sand zodiac]

yep

[violet horizon]

Now both q1 and q2 have 4 sides and a rule is that the sum of angles in both will be 360 degrees

[sand zodiac]

how

they both have 3 side

s

look

1 2 3

so shouldn't the sum be 180?

cause its a triangle sum

but when i solved it by using corresponding congruent parts

i did

$5x+3x+x+45=180$

[somber coyote]

Fire FTW

[sand zodiac]

so therefore

[violet horizon]

LN and QS are not straight lines. Check again

[somber coyote]

Fire FTW

[sand zodiac]

they are congruent figures

its already been stated

QRST is just a slightly turned triangle of LMNP

[sand zodiac]

so then i got

$9x = 135
which equates to:
x = 15$

[somber coyote]

Fire FTW

[sand zodiac]

so like

thats not gonna work but thats the only way i could think of it

cause its 180

[violet horizon]

Why do u think it is 35

[sand zodiac]

i honestly don't know

[violet horizon]

If u got 15

[sand zodiac]

thats teh answer key

my guy

the answer key says its 35

but idk how

[violet horizon]

Let us keep all the math aside, is the figure a triangle or a quadrilateral and I need just one answer

[sand zodiac]

triangle, sir

[violet horizon]

Now if it is a triangle, why would it have four distinct points

[sand zodiac]

because they just added

a 4th point

in the middle

for some reason idk why man

maybe you are right i guess

but i thought like it has 3 sides in total

so like

yea

oh waittt

you are right lmao

im so stupid

srry man

ty

i got it now

why its 35

i just did

$5x + 3x + x + 45 = 360$

ok thx

[somber coyote]

Fire FTW

[sand zodiac]

@violet horizon ty

[violet horizon]

Happy to help

[sand zodiac]

👍

[quiet bramble]

Can anyone help me solve the point p?

[silent plank]

what have you tried?

you should be able to get p from ||midpoint|| formula

[quiet bramble]

is (5b, 5b) correct?

I tried using it

[silent plank]

yes

[quiet bramble]

Thank you

[rare prism]

can someone help me prove this equation

[remote hill]

mhhh

[remote hill]

https://m.youtube.com/watch?v=yGQFEZGeZWs

[clever fable]

hello can someone explain the last part to this please, I got two values x = -1 and x= -9, but the solutions say that I need to reject x = -9 since the domain is only from [-3,3]

where do they get domain restriction from?

(Also if you need the solutions just ping and I can send too)

[nocturne remnant]

I think it has to do with the domain restriction at the very beginning

From which you can show x is restricted to [-3,3]

[upper karma]

hey @upper merlin i am unable to find the answer of that ques.....
i got the inradius of ABC as r=d-89 where r is radius and d is altitude , now i am unable to proceed

[upper merlin]

wait we can use similarity in that question and use their inradius to find the ratio between the sides of the triangle ABD and ACD

I didn't notice this at that time

cuz inradius would be proportional to the sides of the right angled triangle

[upper karma]

ok

[upper karma]

yes the ratio of AC:BA = 56:33

[upper karma]

then what to do?

[upper merlin]

you can find BD in terms of d and subsequently AB too

after that it's trivial to find d

[upper karma]

ok i'll try

[modest pivot]

hello, if i was trying to find the longest line u could fit in a regular pentagon would it be like this?

[smoky palm]

You could fit a longer curvy line

[modest pivot]

I mean a straight line

[clever aurora]

https://tenor.com/view/correct-futurama-the-best-kind-of-correct-yes-yep-gif-5787390

[dark sparrow]

yes

[modest pivot]

ok thanks 🙂

[gusty vale]

does a + b > c work on a right triangle to determine if 3 lengths work

[smoky palm]

Assuming c is the longest side, yes

[silent plank]

no assumption is needed

[upper karma]

i got all the sides in the form for altitude d but unable to calculate it

[upper karma]

i one of the steps d cancels on both the sides of the equation

[upper merlin]

use that inradius formula in any of the triangles

[upper karma]

ok plz wait for 2 min

[upper karma]

i got the d as 77 plz confirm

[upper merlin]

I got something else

[upper karma]

what

?

[upper merlin]

154

[upper karma]

yes the ans is 154 only

[upper merlin]

you got the complete solution now right?

the funny part is that the square of the inradius of the big triangle is the sum of the square of the inradius of the smaller ones

I am curious if this is the case for all right angle triangles

it actually is

[grave nova]

Can someone help me solve this? Idk what “a” is, it says the solution is -7/24 but idk where that came from.

[dark sparrow]

Idk what a is

you can solve for it

by knowing that P lies on the unit circle

thus (4a)^2 + (3a-1)^2 = 1

[grave nova]

Oh you’re right! I completely overlooked the fact that that would be radius

[wet nymph]

i find it from tanjant rate for tranform the equation to one variable but we have to know value of log3^2. can u find it from another way that we dont have to use logarithmic scale

they ask length of DB

and c corner is on the top of this triangle

[pliant cave]

I believe I have Figured out the Trisectrix, and, as proof, I have constructed a Regular Enneagon using only Compass & Straightedge equivalent methods.

[dark sparrow]

and are we supposed to instantly understand every detail of your construction from this big unlabeled mess of circles?

[pliant cave]

I may need help with laying out the directions, But I promise that I can walk people through how to do it. just give me a moment.

[worthy igloo]

we have pretty good proofs that this is impossible, so your construction probably has a mistake somewhre

[dark sparrow]

those red segments look like they form a regular pentagram. is that the case?

[pliant cave]

yeah. I tried with a regular pentagon, seeing as it's an already exisiting example of three equal angles, but the positioning was wrong, so i used the length between the intersection of a circle centered on the corner of the angle and the angle itself to construct a regular pentagram with Euclid's method of finding the Golden ratio with the given length.

[dark sparrow]

jesus

is a simple yes or no answer with no extra fluff too much to ask for

[pliant cave]

sorry

nervous

[dark sparrow]

so, you started with a line segment (black) and made an equilateral triangle with it as one of its sides (orange)
then you made a circle centered at the apex of said triangle with radius equal to the triangle's side length

do i follow you correctly thus far?

just answer yes or no. do not try to explain anything further.

[pliant cave]

more or less

[dark sparrow]

what do you mean, "more or less"

is that a YES or a NO?