geometry-and-trigonometry

[fast tide]

but I want to draw closed curves in desmos

so I need a function that sends points in the basis vector v to u

I know how to do it with complex numbers but I can't figure out how to do this in desmos

[fast tide]

$\frac{\left(\frac{\left|x\right|}{x}+1\right)}{2}x^{2}+y^{2}=1$

[somber coyote]

0000000000

[fast tide]

experimenting with a piecewise circle

[upper karma]

any good way to find length of a "squiggle" like any given curvy line with non linear or with no discernable patterns?

my only thoughts are split it up into segments of a bunch of different circles with different radii and sum them all up?

[oak elbow]

does anyone have a solution?

[sleek depot]

use basic proportionality

RV = VS-SR = 30-18 = 12

let TU = x, hence VU = 25-x

by basic proportionality, RV/RS = VU/TU

hence 12/18 = 25-x/x

[oak elbow]

Thanks for the help. My teacher was absent and just left us with work about proportionality.

[sleek depot]

on solving x = 15

[upper karma]

can someone help me with this please?

(ignore the scribble on "E" lol)

[sleek depot]

yes

sin 30 = opp/hypo
1/2 = 5√2/hypo

hence hypotenuse = 10√2

if u look at the isoceles right triangle

the base angles will be 45

hence sin(45) = x/hypo

1/√2 = x/10√2

hence x = 10

answer is e

[upper karma]

what is sin

ohhhh i just got it, thank you 😁

[sleek depot]

sine ratio

[pallid dome]

Yo how the hell did they get to line two?

Even though I'm very sure it's a typo but maybe not

Lol

[silent plank]

seems like a major typo

seeing that its not even an equation

think they meant:
$$1 + \tan^2\theta = \sec^2\theta$$

[somber coyote]

ℝamonov

[pallid dome]

Yeah

[upper karma]

https://cdn.discordapp.com/attachments/796875046982254593/798705218161344542/phpPNnWLy.png

for a) I got P = 62000cos((pi/46)(t)) + 138000
and for b) 81132.90
C) 28.26%

can someone confirm?

[native tendon]

Can someone pls help with 24, idk how they got 950/3 for one of the sides

[upper karma]

Can someone help plz

[obtuse tapir]

2x^2=12^2

f=g

[neon hamlet]

https://media.discordapp.net/attachments/326138757474680852/799031921665507358/unknown.png
How would you setup a proportion to solve this?

[native tendon]

Thank you!!

[ancient axle]

is anyone alive...

crap

[upper karma]

What's giving you issue?

Is this a test too? @ancient axle

[ancient axle]

@upper karma bro i dont even know where to start

@upper karma no this is extra credit

[humble pulsar]

well what's the glaring issue with solving it how it is?

[ancient axle]

its the cos 2 theta

i have 2cos2thetha + 7sinthetha= 0

[humble pulsar]

right, how might you deal with the cos2x?

[ancient axle]

i dunno

[humble pulsar]

do you know the double angle formulas?

[ancient axle]

no

all i know are identities

[humble pulsar]

double angle formulas are identities

[ancient axle]

oh

can u tell me what the double angle formulas are .-.

[humble pulsar]

✨ Google or your notes cause I doubt you never learned them ✨

[ancient axle]

i have my notes

i have repicorcal and pythorgeon fjksj;fkasfjkaf

notes

[young agate]

teddo

[ancient axle]

omg

wtf is that

[humble pulsar]

i dont see how you're expected to solve this if you never learned double angle. . .

[ancient axle]

i dunno blame my teacher

she also changed the due date

till TMRW

LIKKE WWHAT

[humble pulsar]

due date..?

[silk patio]

Did you go to class?

[ancient axle]

yea tmrw MORNING

yea

i did

[humble pulsar]

so is this a test / marked?

[ancient axle]

no

[upper karma]

There's a pinned message with all of the trig identities btw

[ancient axle]

extra credit / homework

[silk patio]

Okay well use the formula

[ancient axle]

how do i use the formula

oh shoot

dont tell me

[silk patio]

How you use every other formula

[ancient axle]

i got this

fuck

2cos^2(2)-1=1-2sin(1)?

man

[humble pulsar]

why do you have sin(1)?

[ancient axle]

cus theres nothing in front of the sin ._.

[humble pulsar]

,w sin(1)

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[ancient axle]

:<

[humble pulsar]

not sure why you subbed theta = 1

[ancient axle]

i hate this

[humble pulsar]

$2\cos{2x} + 7\sin{x} = 0 \implies 2[1-2\sin^2{x}]+7\sin{x} = 0$

[somber coyote]

moshill1

[ancient axle]

wtf

[empty parcel]

can anyone tell me if these are the same things

theyre not the same?

[silk patio]

Why would they be

[empty parcel]

hm okay

im trying to do the top one

[silk patio]

Trying how

[empty parcel]

and it feels like its too easy

can i send my answer?

[silk patio]

Send here

[empty parcel]

are there more steps im missing

[silk patio]

Ahh, noice

They are the same

Since they add to pi

[empty parcel]

so is that it?

[upper karma]

https://cdn.discordapp.com/attachments/689912561608818755/799068779077304340/unknown.png

I got A) 100, B) 300, C) 400, D) 80 can someone confirm

[pure wigeon]

can someone join a call and help me with 3 problems

[unique flower]

the track is circular

the diameter is 600 because it is the sum of the maximum and minimum of this thing

[pure wigeon]

@unique flower can you help me please?

with geomtery?

[unique flower]

from the graph you can tell that 100 is as close as the car will get to the light pole

c and b are easy from the information i gave

oh wait

[pure wigeon]

@unique flower '

[unique flower]

sorry i needed to go quickly

angle 5 should be 81....

angle 4 should be 35....

i think u messed up

angle 3 should be 64

figure out angle 1

[sleek depot]

angle 3 is 64

and angle 1 is 92

he is correct for first 3

[past harbor]

could anybody please help me out with this question

[sleek depot]

do I use trigonometry?

[past harbor]

yes

[sleek depot]

ok

[sleek depot]

cosine of an angle = adjacent side/hypotenuse

hence cos44 = t/22

cos 44 is approx 0.719

so u have t = 22*0.719 = 15.82

and u can approx that

[past harbor]

thank you so much

i got it wrong

oh never mind thank you

[sleek depot]

what was the answer?

[eager plover]

help please

[sleek depot]

use trigonometry (law of sines/cosines)

[eager plover]

i dont know how to apply it

[sleek depot]

law of sines: a/sinA = b/sinB = c/sinC [use calculator to find out sin]

law of cosines: c^2 = a^2 + b^2 - 2abcosC [use calculator to find out cos]

law of cosines is kinda like pythagorean thm, except u have to subtract 2abcosC

@eager plover

get it?

[eager plover]

ok got it

[lunar mulch]

How?

[sleek depot]

this goes in calculus

[lunar mulch]

No, the rewriting is trigonometry, there's no calculus involved

[sleek depot]

ok

[sleek depot]

so u dont want help with the integral?

if thats the case i can try and solve

[lunar mulch]

I wanna know how that trigonometric expression was simplified

[sleek depot]

@lunar mulch this is harder than i thought

[lunar mulch]

Yes

[silk patio]

It’s a standard trick, it’s called a t substitution

https://en.m.wikipedia.org/wiki/Weierstrass_substitution

You can solve pretty much any basic trig integral with this sub

But this one is easier if you multiply top and bottom by (1-sin(x))

[lunar mulch]

Thanks

It looked very familiar, I forgot about Weierstrass substitution

Oh wow, Euler invented this substitution but there were so many things named after Euler that they had no choice but to name it after Weierstrass

Suffering from success

[green osprey]

if any one can understand this what is bc

[upper karma]

looks like a direct application of thales theorem

[green osprey]

better image

[green osprey]

wat dat

[upper karma]

consider googling "thales theorem"

or looking up your notes/txt book

[green osprey]

its something to do with ratios

[upper karma]

yeah, look up specifically how the ratios work by googling it

[green osprey]

been looking online still cant find ;-;

[upper karma]

...

@green osprey literally the first thing i've found on google... try not lying next time

wikipedia also works...

can't comprehend how one can't find anything about thales theorem on google when there's probably 100 pages explaining the topic..

[green osprey]

i looked up geometry triangle ratio like you said

[green osprey]

there

OH the intercept theorem, okay that makes sence

[upper karma]

that's not what i suggested you to search.

[upper karma]

i even specifically stated you what to google

[green osprey]

you said look up ratios specificly

[upper karma]

no, i said look up how ratios work by googling it

and by it i meant thales theorem

[upper karma]

which shouldn't be suprise from this message

[green osprey]

oh couldnt comprehend my brain is literally dying

[hearty carbon]

how do I find x

[upper karma]

consider pythagoream theorem

[steep temple]

to not be confused with the thales theorem that has to do with circles, wikipedia refers to it as "intercept theorem" @upper karma

[cursive prawn]

Prove:
Sine3A/sinA - cos3A/cosA =2

[silent plank]

what've you tried?

[cursive prawn]

Nothing tbh

[silent plank]

at least try something, and see far you can get even if its just 1 step

[steep temple]

personally i am not a big fan of those denominators

[cursive prawn]

Alright I'll try "something"

Nvm solved it

[sleek depot]

Till then try writing the formula for sin3A and cos3A

Sin3A= 3sinA - 4sin^3(A)

Cos3A = 4cos^3(A) - 3cosA

[sleek depot]

Lmao I just saw this msg

[steep temple]

this dude didnt even have the courtesy to type anything he just posted a picture

[modern estuary]

well what more do i say

[steep temple]

you say what you have attempted to do

[modern estuary]

well i have no idea what to do

so

[steep temple]

ah yes the classic

alright hold on

are we finished or do i need to elaborate @modern estuary

[modern estuary]

Please elaborate

@steep temple

[steep temple]

ok what do you not understand

[modern estuary]

Literally everything

i am a freshman taking geometry and my teacher is god awful

[steep temple]

noone asked

i meant in the diagram

what do you not understand in the diagram

[modern estuary]

What R and S mean

you're saying A and B equal R and S?

[steep temple]

to me it seems pretty obvious that you can break 1 big right triangle into 2 right triangles in that picture

you seem to already have the measurements of one of their sides, respectively

and they both share h

[modern estuary]

Yes

How do I solve for H though

thats all i need

[steep temple]

so if only there was some way to solve for h you could pythagoras the hell out of a and b

[steep temple]

i wonder...

[upper merlin]

pugzii are u familiar with the formula up there

[steep temple]

even if he is not it is not hard to apply it

noone is asking him to prove the formula

[upper merlin]

h^2 is the product of the two pieces the hypotenuse is split in

[steep temple]

(which you are given)

[upper merlin]

i mean it would be nice to give the proof too so he can understand it better

[modern estuary]

No

wait

which theroem

or formula

[steep temple]

i wont lie to you i have no idea what its called

[modern estuary]

that makes two of us

[steep temple]

i just searched for "geometric mean" because "triangle altitude theorem" was not giving me it and i was not about to prove it

[upper merlin]

so do u know how if u drop an altitude from the right angled vertex of a triangle it splits the big right triangle into 2 triangles that are both similar to the original one

[modern estuary]

yes

[steep temple]

are you sure

[modern estuary]

no

[steep temple]

so why lie

[cursive prawn]

Pythagoras theorem?

[modern estuary]

yea is that what hes talking about

[upper merlin]

uh you dont need pythagoras theorem to prove it

[modern estuary]

ok

[upper merlin]

so do u know of the angle angle criteria for similarity

[modern estuary]

Yes

i do know that

[upper merlin]

so if we go back here to this image

the triangle with sides r h and p is similar to the big triangle

[modern estuary]

mhm

[upper merlin]

because they both have a right angle and they both share the angle with r and p

do u understand that part

[modern estuary]

yea

yep

[upper merlin]

yeah so same goes with the triangle with sides s h and q, it has a right angle and shares the angle at the right with the big triangle

[modern estuary]

yes

[upper merlin]

so that means each of the two small right triangles is similar to the big one, and thus they are similar to each other

[modern estuary]

okay

[upper merlin]

now if the small triangles are similar to each other, the ratio of their corresponding sides is the same

[modern estuary]

okay

[upper merlin]

so that tells us p/h=h/q

[modern estuary]

ok

[upper merlin]

now we just clear the denominators by cross multiplying

[steep temple]

thales theorem moment

[upper merlin]

and we get h^2=pq

and thats the theorem

[modern estuary]

okay

thanks

[upper merlin]

that u use to solve for h

in the original problem

[steep temple]

take the principal square root of that bad boy

[upper merlin]

tru

[steep temple]

and pythagoras the hell out of a and b

[modern estuary]

Got it

ty

[steep temple]

good luck soldier !

[upper merlin]

||or alternatively youll realize quickly that all the triangles are 30 60 90 triangles||

[steep temple]

shhh

[modern estuary]

h=4sqaure root 3, -4 square root 3

correct?

[upper merlin]

can it be negative tho

its a side length

[modern estuary]

no

[upper merlin]

yeah so just 4root3

[modern estuary]

ty

and then just pythagorean thereom

[upper merlin]

yeah

[steep temple]

damnit dude

i just told you

[upper merlin]

||or 30 60 90 triangles||

[modern estuary]

i have a =8 and b=8root3

[upper merlin]

looks right

[neon hamlet]

does anyone know if this x is right?
https://gyazo.com/75f38444834968402400d02badfe0b5d
I feel like it's wrong due to the fact that AD is bigger then HE

[eager hatch]

Can someone help?

[dusky cedar]

https://cdn.discordapp.com/attachments/698425344285212672/799350258990841886/Screen_Shot_2021-01-14_at_1.52.29_PM.png

[rocky socket]

I know how to find surface area and volume but my questions is how do I make one one composite object with both circles and squares in the same object. my problem is coming up with a single shape that includes every shape asked

[tender prawn]

what does it mean the diagonals form a 60 degree angle?

does it mean like the picture i drew or

[sleek depot]

yes

[tender prawn]

ok t hx

[silk patio]

@tender prawn the other way is more natural

[tender prawn]

yeah it's actually the other way around

because the top and bottom triangles are isoceles

and like

[silk patio]

Equilateral even

Terribly worded Q

[tender prawn]

it actualy has to be like that because it says one of the diagonals measures 8

and like similar triangles and stuff

so it's impossible for that angle to be 120

i just had to dig a bit deeper lol i spent way too long wondering what the q meant

[faint hornet]

oooooooo

[tender prawn]

[tender prawn]

er

list a few ways you can prove two triangles congruent

er

yes? but how do you get that

you need to prove the two triangles are congruent

how would you do that

ok so one way to prove two triangles congruent is like aas

what else

[sleek depot]

Hypotenuse side

[reef parrot]

hi

what do you call these things

and how to solve the third angle using those things

[silent plank]

degrees, (arc)minutes

60 arc(minutes) in a degree

[oak citrus]

This is referred to as DMS (Degrees, Minutes, Seconds).

[reef parrot]

so when the arc exceeds 60, i add 1 degree and subtract 60 to the arc right?

[oak citrus]

You need the angle to be in degrees. To do that, you must multiply the minutes (denoted by ') with (1deg/60min), so it becomes 28(1/60).

That will give you a decimal in degrees that can be added to 61deg (angle A)

For angle C, multiply 53 with the conversion factor (1deg/60min).

Now you should have 2 angles in degrees.

In order to obtain the other sides, you will need either Law of Sines or Law of Cosines.

@reef parrot Understood so far?

[reef parrot]

i got thia solution from google

is mine different from what u explained?

[oak citrus]

No, they just did in different order.

I prefer converting both into degrees before subtracting from 180deg.

[tired stirrup]

Can someone help me with this?

[sleek depot]

try using general formula for cosine ratio

cosT = adjacent side/hypotenuse

or if you dont want to use trigonometry, you can use 45-45-90 triangle theorem

the hypotenuse is sqrt(2) times both sides

if x is the side

x√2 = hypotenuse

[tired stirrup]

What would the answer be? Would it be like 6.3?

[sleek depot]

yes

[sleek depot]

6.364 which approximates to 6.4

[tired stirrup]

I knew i was right but the problem is it the WRONG answer?

[sleek depot]

no

6.3 shoud also be correct ig

then try 6.4

[silent plank]

leave it in exact form

[hushed flicker]

hello I'm new here, I'm having problems with my trigo, this is a true or false question and I would like to know how to evaluate this, any tips? 🙂

[native tendon]

Can someone pls help with 10)?

[sleek depot]

they are asking us to find angle and radius

use sector and arc formula

Area of sector = $A/360 * \pi r^2$

[somber coyote]

EclipseSword

[sleek depot]

Length of arc = $A/360 * 2 \pi r$

[somber coyote]

EclipseSword

[sleek depot]

u will get two equations in A and r

[reef parrot]

help

A triangle has vertices (1, 1), (3, 7) and (5, 4). What is the distance between the centroid and the line 2x = -y - 2?

i got 4.24 but my prof said it is wrong

i used the centroid formula and got point (3,4) and using the distance formula of a point to a line, resulted 4.24

[earnest echo]

Show your work

[earnest echo]

How did you Calculate the distance?

[reef parrot]

even when i made A=1, the answer was still 4.24

or do i have any miscalculations?

[earnest echo]

Why would you make A=1???

[reef parrot]

umm

from the general form

[earnest echo]

Compare Ax+By+C with 2x+y+2

What is the value of A,B and C?

[reef parrot]

2 1 2 respectively

[earnest echo]

Use commas to separate the entries

So if A=2

Why are you making it 1???

[reef parrot]

we were practiced by making it first into its general form
so from 2x = -y - 2
is x + y/2 +1 = 0

does A=1 is necessary in making it general form or nah??

[earnest echo]

No, it is not necessary

You'd get the same answer either way but making A=1 is nothing but extra work

[reef parrot]

my answer is still not in the choices tho

am i miscalculating something

[earnest echo]

Why do you have

√(9+16) in the denominator??

It's √(A²+B²) not √(x_1²+y_1²)

[reef parrot]

ohhhhh

whyyyyy

why am i always so careless

thanksss

i have to do something about my carelessness

[upper karma]

Try slowing down until you feel more comfortable, better to take some more time than doing it incorrectly.

[reef parrot]

ur right, im having a hard time to look for something wrong in my work myself

its like i need someone else to review mine. but the world doesnt run like that :(((

[past harbor]

could someone please help me with these 2 questions

[lament cobalt]

I don’t understand what to do. I know that a square can use properties of a parallelogram,Rhombus,and rectangle but Idk which one to use to help solve

[humble pulsar]

what angles do the diagonals make at the center?

[lament cobalt]

90 degree angles i think

[humble pulsar]

yes, and what's the length of KP?

[lament cobalt]

90?

[humble pulsar]

length

[lament cobalt]

1

[humble pulsar]

right, so you have a right triangle with the legs both having length 1

what type of triangle is LKP then?

[slim saddle]

how this wrong 😢

[polar summit]

@slim saddle I got the same answer

[slim saddle]

lol ill email teacher then

[polar summit]

alright

[red frost]

could someone help

[sinful tide]

@red frost I can help you right after I get out of physics, if no one has helped you yet.

[red frost]

yea thatd be great thanks

[red frost]

when do you get out of physics?

[sinful tide]

It'll be 30 minutes, I was going to draw on the image to explain it better, but I can do my best to explain it through just writing if you want. @red frost

[red frost]

ill private message you and thats fine if you draw on it

[sinful tide]

Ok, cool thanks

[sick ember]

help

[oak citrus]

With which one?

[sick ember]

5 and 6

[oak citrus]

Oof, I can’t help with that.

[sick ember]

9?

[upper karma]

Can someone help

[oak citrus]

Don’t post in multiple channels.

[hazy crane]

what is this exact value in radians

[humble pulsar]

calculator or use sin and cos

[hazy crane]

oh just simplify and its 0.57

👍

[humble pulsar]

that's not exact though

sin(pi/6) = 1/2
cos(pi/6) = sqrt(3)/2

so tan(pi/6) = (1/2)/(sqrt(3)/2) = 1/sqrt3

[hazy crane]

ohh that's what it means by exact

i did just put them in the calculator

thank u

[native tendon]

Question 10) pls I’m rlly stuck with it

[humble pulsar]

set up 2 equations with the angle and the radius, then solve them

[upper karma]

@native tendon don't multipost. Please read #❓how-to-get-help

[novel bobcat]

Anyone see a way I could start to set something up to solve for R?

Those aren't right angles btw

They aren't right angles

c^2=a^2+b^2 doesn't apply

If I had one angle I could do something with law of sines

[spark star]

Hello, can anyone help me with congruent triangles?

[umbral briar]

Hai there I need some help my home work if anyone’s willing to help me

[wintry tundra]

What do u guys need help with

I'll try my best to kill two birds with one stone

@spark star @umbral briar

[spark star]

Hello.

Congruent triangles.

[wintry tundra]

Be more specific

[spark star]

I forgot the equation.

Doesn't it always equal 180?

[wintry tundra]

The sum of the angles of a triangle is always 180

[spark star]

There you go.

[wintry tundra]

The formula for what the angle sum of any shape is is 180(n-2) n being the amount of sides

[spark star]

I have a question, kind of a big question.

[wintry tundra]

Ok lay it on me

[spark star]

Should I take an ap class?

[wintry tundra]

Which class

[spark star]

I'm not good at any subject.

But uh

Ap physics?

[wintry tundra]

Ap physics is hard

So unless ur good at math

[spark star]

Nope.

[wintry tundra]

Or ur very determined

[spark star]

Nevermind.

[wintry tundra]

Then dont

[spark star]

Uh

Any ap class that is easy?

[wintry tundra]

Well seeing that ap means advanced program

No

[spark star]

Well

Most of them are just

Hard working

[wintry tundra]

If u can work hard then yeah

But remember

[spark star]

Hm?

[wintry tundra]

U could get a worse grade if u take an ap class

Bc its harder

[spark star]

I see

[wintry tundra]

So u gotta decide what u can and can't handle

[spark star]

I just want to challenge myself

[wintry tundra]

Then yeah

If u want a good challenge

[spark star]

I don't have any

Honors or anything

So I'm taking a big step

From normal to ap

[wintry tundra]

Hmm

U shoulda done honors I think

And some classes u can't take without previous classes

[spark star]

Right.

[wintry tundra]

Ap bio requires chemistry I think

Ap chemistry requires calc

And do does phys 2 and c

[spark star]

I have chemistry yeh

This year atleast

And might aswell just take physics

[idle bobcat]

Hi, I think i figured out the formula alright, but I'm getting the wrong answer when solving the second part

the correct answer is 4.89

not sure where exactly im making the mistake

4.46 is pretty close to 4.89 so i feel like its a really small arithmetic mistake i made somewhere but im stumped

[dire obsidian]

i havent. done geometry in a while

how do i do this

is it 8pi?

nvm 4pi

[upper karma]

@idle bobcat are you still stuck?

[obtuse tapir]

i havent. done geometry in a while
@dire obsidian pi radians=180 degree

[idle bobcat]

I found out that I shifted horizo tally the wrong way lol

[faint hornet]

Hi there I just made my first youtube video, which is Heron's Formula, but Proven Elegantly. For all you math lovers out there, or if you are struggling to understand geometry, I highly recommend this proof because it is a lot better than the conventional, trigonometric proof: https://youtu.be/3Rr5ZMlVF3s

[dusky cedar]

nba

can any of you send me random notes that u have for trig

literally any and i mean ANY bit of info helps

[faint hornet]

well one thing that helped me a lot was schaum's outlines trig book

[dusky cedar]

does it have stuff that can be thrown onto a cheat sheet

[faint hornet]

i think i had to make my own cheat sheet

or use https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

[dusky cedar]

yeah bro the assignment is a double sided cheat sheet

so its kidna just everything you know

throw it on

[silk patio]

@faint hornet Thats a really really clean proof, not seen that before, thanks for the knowledge

[faint hornet]

i am so so so so so happy you like it!!!!

[sly marlin]

nice proof subscribed

[faint hornet]

thank you!

[wintry tundra]

im gonna have to watch that

i dont know trig tho

besides the main functions used in it and what they do

[upper karma]

I am trying to learn how to give a general solution to a trig equation
I understand that one can write: $$v_n = v + 360n$$, however, according to my lectures notes, one can also write $$v_n = v + 180n$$., where v is an angle. What are the differences?

[somber coyote]

Elfen

[humble pulsar]

+360 means that solutions occur every 360 degrees (ex: cos(x) = 1)
+180 means solutions occur every 180 degrees (ex: sin(x) = 0)

[upper karma]

Is that for all integer values ?

[humble pulsar]

yes

[upper karma]

as in n being an integer

[humble pulsar]

$\cos{x} = 1 \implies x = 360n \forall n \in \mathbb{Z}$

[somber coyote]

moshill1

[upper karma]

ah

but

if $$v_2 = v + 180*2 $$ is that not the same as

as v_1 = v + 360*1?

[humble pulsar]

Yes those are equivalent

[upper karma]

oh they are equivalent

[humble pulsar]

however, if you're solving sin(x) = 0

valid x include 0, +/- 180, +/- 360, etc

so you wouldnt define x in terms of multiples of 360

cause then you miss out on +/- 180

[upper karma]

ah

so in short, I need to understand the angles periodicty to decide on which formula to use?

[humble pulsar]

Similarly if you had a function whose solutions occured every 90 degrees, you'd do x = 90n to account for them all

[faint hornet]

idk if ur talking about my proof or smth else but it doesn't have any trig

[humble pulsar]

yeah

[upper karma]

@humble pulsar ❤️

Thank you so much!

I am no longer confused

[humble pulsar]

[wintry tundra]

oh sry my mind was thinking about the previous question

i know geometry quite well so ill give it a watch

[faint hornet]

oops sorry

[faint hornet]

thanks :)

[wintry tundra]

@faint hornet what kind of content are u gonna further make with ur channel cuz the proof was cool

[faint hornet]

thanks! I am thinking of making more underrepresented, but interesting proofs (but idek yet tbh). I'm thinking my next video will be about AM>GM proof by cauchy induction

[wintry tundra]

nice

[faint hornet]

and also maybe a video about mass points, and graph theory eventually

[wintry tundra]

so u really like geometry? or just looking at herons proof

[faint hornet]

(those are separate not together)

ummmm well geometry has a bunch of nice theorems

but honestly it's the kind of math that I'm the worst at

i like algebra more

[wintry tundra]

same

me too

except i did prove the 30 60 90 law on accident cuz

i was curious i guess

[faint hornet]

cool!

[wintry tundra]

i really like the proof i used to find it thinking back

[languid lion]

yo can i get help w some math

[sleek depot]

[wintry tundra]

@languid lion a bit late but what's the issue

[cosmic pebble]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[reef parrot]

hiii i need some help

Line A has a slope of -4 and passes through (-25, -10). Line B has x-intercept of 10 and y-intercept of 25. Determine the distance of line A to point (8, -3).

line b is not needed for this right?

so i just basically solve for the equation of line A, then use the distance formular for between a line and a point (8, -3)?

[reef parrot]

<@&286206848099549185>

[earnest echo]

Yes, line B is not needed for this problem

[normal patio]

Why is this the right answer?

[reef parrot]

nvm i got the answer already

[normal patio]

<@&286206848099549185>

[silent plank]

the provided answer is a bit poor.
cos(a) = 0 if a is an odd multiple of pi/2

$x + \frac{2\pi}{3} = \frac{(2k+1)\pi}{2} \ \
x = \frac{(2k+1)\pi}{2} - \frac{2\pi}{3}$ \
(for $k \in \bZ$)

[somber coyote]

ℝamonov

[silent plank]

do a bit more algebra to simplify,
and sub in appropriate values of k to generate numeric solutions if needed.

[normal patio]

ty

[left zinc]

<@&286206848099549185> please help me with these 2

[cosmic pebble]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[upper karma]

@left zinc please read #❓how-to-get-help

After so, i won't mind helping.

[sleek depot]

try using pythagoras theorem

[left zinc]

okay

[steep temple]

This proof seems bad

How do I improve?

[silent plank]

manipulate one side only

[steep temple]

here i am relying on manipulating tan so i can arrive at the cos2x identitity

but i guess you already know that

[silent plank]

most teachers prefer LHS,RHS proofs

start from what feels like the more complicated side, in this case the left.

and manipulate that only until you reach tan(theta)

[steep temple]

@silent plank i proved it

but i havent mentioned anything about the conditions(?) of the question

i mean the theta ne npi/2

at the same line where i show sinx/cosx should I make the connection there?

i.e. sinx/cosx = tanx = RHS, x ne npi/2, n in Z

[silent plank]

the condition is just there to ensure that your expressions are defined.

don't really need to restate it

[steep temple]

ah alright

thanks

[upper karma]

cos^2(x) + sin^2(x) = 1?

[olive jacinth]

im completely stuck on this problem

i set up partial fraction decomposition

[upper karma]

@olive jacinth what are you trying to find? f'(x) or just to open it?

[olive jacinth]

Open it in order to then solve for a b and c

the part I’m stuck on is

[upper karma]

I am not a native speaker but I will try to do it in paint so you will understand

[olive jacinth]

After setting it up I don’t understand how you eliminate the denominator with lcd

Why is A multiplied by (x-1)(x+1) but b only by (x+1)

[upper karma]

Uhh it's hard for me to explain in english 😄 One second will send it as a paint

[olive jacinth]

ok thank u :#

:3*

[upper karma]

(x-1)^2 = (x-1)(x-1)

and A only got (x-1)

I hope you can understand from the drawing, sorry that I can't express the answer in words, I just don't know how to explain it in English. Hopefully someone can.

[olive jacinth]

i kinda get it but

[steep temple]

its ok dont worry about english we speak math

[olive jacinth]

i just dont know why the numbers distribute like that

[upper karma]

Yeah the problem is I don't know how stuff are called in English 😄

[olive jacinth]

hmm its okay thank you so much for the help

maybe someone will explain it later haha

[steep temple]

ok so the goal here is to multiply everything by (x-2)^2(x+1) / n where n is the thing they are already being divided by

in the case of A:

A/(x-1)

A is already being divided by (x-1)

so (x-1)^2(x+1)/(x-1) = (x-1)(x+1)

therefore you multiply A by (x-1)(x+1)

comprende?

well it's more like

$$ \frac{A}{(x-1)} \cdot (x-1)(x-1)(x+1) = \frac{A(x-1)(x-1)(x+1)}{(x-1)} \equiv A(x-1)(x+1) $$

[somber coyote]

dlp

[steep temple]

fuckn latex

[olive jacinth]

sry went to feed cat. yes makes lots of sense actualy

tysm

[steep temple]

@upper karma he says thank you

[olive jacinth]

yes thank u both of u

lots of help < 3

[upper karma]

No problem but you the one who explained better 😄

[steep temple]

is this how you solve trigonometric equations

or is this cursed

i cant tell

[silent plank]

why did x change into theta
and we're you supposed to determine x or tan(x)

[steep temple]

determine x

x changed into theta because the online compiler did not like \tanx

[silent plank]

parentheses around the argument is recommended.
\tan(x)

anyway

get the general solution for 2x first

then divide both sides by 2 to get the general solution for x

[steep temple]

ah

right

but what is wrong with my method?

nothing

nothing is wrong with my method answer-wise

[silent plank]

mathematically valid, just doest get you what you need

[steep temple]

except that it is longed out for no reason

yea thanks

[silent plank]

it's be a pain to take the inverse

without a very good calc or being already familiar with that value

[steep temple]

don't i have to take the inverse of tan(2x)=1 anyway

[silent plank]

nope

1 is a special ratio

[steep temple]

it is?

[silent plank]

for tan anyway

[steep temple]

oh

right

tan(pi/4) = 1

i don't need a calculator

i see thanks

[silent plank]

you'd need to use more than just pi/4 otherwise you're losing a lot of solutions

[steep temple]

need to solve for interval 0 < x < 2pi

so yeah i'll take pi/4 and 5pi/4

[silent plank]

note that tan is pi periodic

[steep temple]

i acknowledge

so pi/4 + 4pi/4 = 5pi/4

[silent plank]

those would be for 2x,
upon isolating x,
you'd only get solutions between 0 and pi

also you meant x not n right?

[steep temple]

yes

[silent plank]

0 < x < 2pi
0 < 2x < 4pi

[proven halo]

Anyone here good with geometry and algebra 2

[cosmic pebble]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[upper karma]

Just post your q.

@proven halo

[proven halo]

I need someone to review my answers for me

[upper karma]

Please read #❓how-to-get-help

Specifically:

[cosmic pebble]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[wintry tundra]

so trig is based on the fact that all triangles are made of right triangles?

[placid bone]

not necessarily

you can do trig with non-right angle triangles

@wintry tundra

but to start with, yes

[wintry tundra]

yeah im taking trig on khan academy

and it seems like its built on finding angles of triangles based on right triangles

[placid bone]

well yes, that's where you start

but as you advance, you'll learn other things

[wintry tundra]

ok

[placid bone]

stuff like sine rule and cosine rule

it gets pretty interesting imo

hf!

[wintry tundra]

thx

im taking maths i may need for physics rn

so i can understand physics more

is sin(2x) = cos(x)?

wait no

[steep temple]

no

complementary angles are 2 angles which add up to 90 degrees

cosine is the complement of sine because sin(x) = cos(90-x)

[hidden fern]

I need help

[wintry tundra]

ok

if its geometry i can help

trig i cant promise anything

[hidden fern]

the question given to me is 1. Solving the following for a, correct to 1 decimal life.

a/sin 15=230/sin 110 degrees

[wintry tundra]

decimal life?

[hidden fern]

idk what to do

[wintry tundra]

u mean like tenth hundredth

[hidden fern]

the videos my teacher made are unclear

[wintry tundra]

ok so

[hidden fern]

idk what he means by 1 decimal life

[wintry tundra]

$\frac{a}{sin(15)} = \frac{230}{sin(110)}$

[somber coyote]

hiidostuff

[wintry tundra]

this?

[steep temple]

btw you can escape sin

$$ \sin $$ looks like this

[somber coyote]

dlp

[wintry tundra]

assume that 1 decimal life is nearest 10th

ive never heard of "decimal life"

[steep temple]

we are in the same boat

[wintry tundra]

im just gonna assume nearest 10th

and when u only have 1 variable u should assume to isolate it

[hidden fern]

is this the answer? or the equation

[wintry tundra]

thats the equation

[steep temple]

what do ya think

[wintry tundra]

the solution would be something like $a = x$

[somber coyote]

hiidostuff

[wintry tundra]

with a on one side

and x being whatever a is for ur equation

so what could u do to isolate a on one side @hidden fern ?

[steep temple]

this person has bigger issues than solving for a

[wintry tundra]

i mean

not really

since the question is solve for a to the 1st "decimal life" which im guessing is the tenths place

[steep temple]

this person does not understand how to isolate variables and also can not distinguish between a solution and an equation

[wintry tundra]

aww come on give em a break

[steep temple]

dude they seriously have bigger issues

noone is just going to hit them with the sine rule as their welcome into mathematics

[wintry tundra]

well we are here to help em

[steep temple]

where have they been for the past 5 years

[placid bone]

if you multiply both sides by sin 15, the sin 15 on the bottom of the fraction on the left side disappears, and you only have a

[wintry tundra]

^

[placid bone]

@hidden fern

[wintry tundra]

come back dlp is just being a party pooper :((

[placid bone]

so you get $a=\frac{230\times\sin{15}}{\sin{110}}$

[somber coyote]

lofi hip hop radio

[steep temple]

this person is going to carry on having trouble unless he understands the mathematics behind what is going on here

[placid bone]

and chuck that into a calculator

as for what a decimal life is, i assume it's just a decimal point

so if i had 1.32198302193829032

[wintry tundra]

i mean if they dont know how to do it themselves then i doubt they will have too much math trouble in the future

[placid bone]

that to one decimal life would be 1.3

[hidden fern]

so a = 63.3

[wintry tundra]

probably

[placid bone]

yeah

[wintry tundra]

but yeah trig = algebra with a calculator for what i know

[hidden fern]

thank you very much

[wintry tundra]

looking at a triangle then using calculator

[placid bone]

was it you that was doing trig on khan?

[wintry tundra]

yes

[placid bone]

ah well

that was sine rule

[wintry tundra]

it looks like isolate then use a calculator to me

[placid bone]

yep pretty much

[wintry tundra]

wait thats what sine rule is?

[placid bone]

but yeah sine rule

mhm

pretty simple

[wintry tundra]

just 2 sines being in the denominator

[placid bone]

mmm

you could also have 2 sins in the numerator

takes a bit longer in the execution, but same concept

[wintry tundra]

or 1 in num 1 in den?

[placid bone]

isolate the sine

inverse sine it

and then oom answer

no as in

sinx/5=sin34/3

idk i made that up

but like

[wintry tundra]

ok and find x

[placid bone]

multiply both by 5

inverse sin what you got on the rhs

[wintry tundra]

so then u just solve the side then inverse sine

[placid bone]

and then youve got x

yeah

[wintry tundra]

ok cool

[steep temple]

if you cant prove sine rule what u doing

[wintry tundra]

well i couldnt prove sine rule 5 minutes ago

[placid bone]

it's not too hard

[wintry tundra]

i dont really know how define it besides "just isolate the variable"

[placid bone]

the proof for sine rule i mean

its not hard

but for high school, you likely wont get asked to prove it

[steep temple]

who cares

[wintry tundra]

id like to prove it

[steep temple]

you should want to be able to prove it

[wintry tundra]

i want to know how

[steep temple]

otherwise u r a false mathematician and u will go to mathematician hell

[placid bone]

youtube t

[wintry tundra]

oh

[placid bone]

ah but i don't intend to be a mathematician

well professionally, that is

and mate dlp if you're so good at maths, go solve the millennium problems or something

[wintry tundra]

neither do i lofi

[steep temple]

why are you being toxic in #geometry-and-trigonometry go do that in #chill

[wintry tundra]

LMAO

i bet dlp has been waiting to say that

[steep temple]

he has.

[placid bone]

you're one to talk lmao

[wintry tundra]

dlp is faking toxicity i think

[placid bone]

eh

well

we've both got better things to do

[wintry tundra]

theyll probably reply that they arent but who cares

[rugged marsh]

I need help with a question, so do I post the question here? could like anyone give me a hint?

A median AM is drawn in a triangle ABC. Determine the area of ΔABC, if AC = 3√2, BC = 10,
angle MAC is 45°.

It says to use cosine rule, but where do I use cosine rule?

[wintry tundra]

if u tell me what cosine rule is i may be able to help

emphasis on may

[somber coyote]

ForJoke

[rugged marsh]

and this is cyclic

[wintry tundra]

remember that emphasis on may

i dont think i can help but if u mention helpers someone may be able to

[sleek depot]

i can help

i need to draw a fig to visualise tho

ok

so if AM is median on BC, then BM = MC = 1/2 BC

BC is 10 so BM = MC = 5

now in triangle AMC, AC = 3√2, MC = 5, MAC = 45

determine AM using law of cosines

then solve for AB using apollonium theorem

and solve for area with herons formula

[rugged marsh]

I solved it

[silver slate]

help plz?

My teacher gave me instruction but i still dont understand

[hidden fern]

I need help

a^2=(5 x 5)+(11 * 11)-25 11* cos36.5 degrees

told me to solve the following for the variable by simplifying the equation

[wintry tundra]

for multiplication on a computer pls use * @hidden fern

bc using x when its also a really common variable is confusing

so its $a^2 = (5 * 5) + (11 * 11) - 25 * 11 * cos(36.5)$

[somber coyote]

hiidostuff

[wintry tundra]

u know what

at this point just use LATEX

its easier

[hidden fern]

Latex?

[wintry tundra]

the math writing i use

[hidden fern]

Idk how to use that

[wintry tundra]

idk why u dont just write it as $25 + 121 - 275 * cos(36.5)$

[somber coyote]

hiidostuff

[hidden fern]

its 2*5

[wintry tundra]

oh 2 times 5?

why cant u solve this tho just solve the one side then get the root of it

[hidden fern]

a^2=(5 * 5)+(11 * 11)-2 * 5 * 11 * cos36.5 degrees

[wintry tundra]

trig is just using a calc

[hidden fern]

Idk how

[wintry tundra]

u dont know how to use a calculator?

[hidden fern]

do I just punch in these numbers?

[wintry tundra]

well

yeah

[hidden fern]

I feel like an idiot

[wintry tundra]

like when u press letters on a keyboard

ur fine man but for this its just using a calculator

[hidden fern]

you said find the root of it

@wintry tundra I have punched put it all in a calculator and what I got is

[wintry tundra]

round it to the nearest hundredth for me

[hidden fern]

a^2=25+121-0.803

@wintry tundra the cos?

[wintry tundra]

how did u get 0.0803

[hidden fern]

I multiplied the 2, 5 and 11 and multiplied it by the cos36.5

was it wrong?

[wintry tundra]

did u put 110cos(36.5)

[hidden fern]

yeah]

[wintry tundra]

uhh

thats equal to 88.42

[hidden fern]

oop

[wintry tundra]

u might need to take a pic

show me how u put it in a calc

[hidden fern]

must have punched the wrong number

my calc says 88.42

now

[wintry tundra]

HM

oops caps

[hidden fern]

how do I solve for a?

[glacial bough]

radians?

[wintry tundra]

did u have radians or degrees on

[glacial bough]

thats my big mistake

happens all the time

[wintry tundra]

bc 88.42 radians is a lot of radians

[glacial bough]

im not sure what the context of the problem is

but check that first

[hidden fern]

which one should I have it on?

[wintry tundra]

how do u think u solve for a?

[silver slate]

<@&286206848099549185>

[wintry tundra]

a goal of yours if you have trouble with math is to develop intuitive thinking

jobs like intuitive thinkers, they are good problem solvers and leaders

[hidden fern]

do I just punch the numbers back into the calculator and thats what a is

[wintry tundra]

?

well a isnt isolated just yet

if a was isolated on one side it would just say a

but does a have any transformations to it?

[hidden fern]

it has an exponent

[wintry tundra]

mhm

so how do u reverse an exponent to get the number that has the exponent to be the normal number

[glacial bough]

https://tenor.com/view/cut-trunk-log-gif-13221641

[hidden fern]

take the log from both sides?

[wintry tundra]

hmm

not exactly

ur thinking too advanced now

if we have $a^2$, what could be done to make it a?

[somber coyote]

hiidostuff

[hidden fern]

I saw log so my mind went to log

[glacial bough]

lmao sorry

[hidden fern]

divide it by itself?

[wintry tundra]

well yes

but theres another thing you can do to make another side that doesnt have a be able to equal a

because if u divide the other side of ur problem by a

it cant divide by a

so it wont do anything

[hidden fern]

that wouldnt make sense

yeah

[wintry tundra]

what else could be done to have $a^2 a$?

[somber coyote]

hiidostuff

[wintry tundra]

oops

no space between those

what could be done to make $a^2$ be $a$?

[somber coyote]

hiidostuff

[wintry tundra]

its one of the simpler algebraic functions that you learn in prealgebra