geometry-and-trigonometry

[tough token]

Thanks @frosty delta

[long geyser]

!nosols

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[simple vigil]

This same question is in class 10

[naive sierra]

How do I proceed with this,

[winged oyster]

guess

jk

ok

if ab = ac then their angles should be congruent right?

[winged oyster]

oh maybe i should ping

since its isosceles

ok well it prolly shouldnt matter

well the first thing we can do is find this measure

[naive sierra]

That's 70,after that I was able to get AE=BE, I don't know what to do next??

[winged oyster]

yeah

since angle A is 20

[forest dew]

looks like thales theorems

[winged oyster]

this should also be 20

[forest dew]

80 degree?

[winged oyster]

the whole thing is 80

[forest dew]

huh

what

[long geyser]

Yep!

[forest dew]

yeah i was gonna 60+50=110 180-110 70

[winged oyster]

yeah thats right for this one

[forest dew]

anyways

im keep getting PTSD from geometry

atleast a^2 + b^2 = c^2 is easy

[forest dew]

so they are equal

[winged oyster]

yes

[forest dew]

also what the hell is that profile

picture

x = [-b ± sqrt(b²-4ac)]/2a = quadratic equation?

[winged oyster]

shhhhh

[winged oyster]

well you can use that info to find this

which will give one measure of the triangle

ik i prolly shouldnt assume they're straight lines but they should be straight lines

[naive sierra]

I am only able to get angle abe equal to 20 in the triangle DBE. Non of the other angles

*none

[winged oyster]

hm

you should be able to get this too

[naive sierra]

I meant none of the other angles of the triDBE

[winged oyster]

oh

well with that you can find AEB = 140

i think i found an answer but idk if its right

[frosty delta]

Is that Q from that long beard Indian guy

[low ocean]

You can not angle chasing this problem

It does not work

[naive sierra]

I don't know my friend send me this

[low ocean]

Well, I'm lazy so

https://math.stackexchange.com/questions/6942/langleys-adventitious-angles

take a look at this ig

[naive sierra]

Thanks

[sour summit]

Hiii. I did some math exercises and I had to fill out this formula here and I could do it and understand it for the most part exept for the "-h2" part.

Wouldn't it be +h2 since it is higher up???

Cause this is like a formula for the grey area and I need to calculate the area of the whole big square h1 minus the white area which the integral is for. And I get it is not directly on the x axis but why do I put -h2 there and not +h2?

[dull sandal]

i'm thinking of -h2 as moving f down (or the axes up) so that its height (and hence the missing area) is not exaggerated by the constant +h2, but maybe i'm misunderstanding your question

[ember hare]

What is a log

[tribal rose]

A logirithim, the inverse of an exponent.

[ember hare]

Isn’t that just sqrt?

[tribal rose]

Square roots are only for numbers raised to the power of 2.

Sal Khan explains it much better than me.

[sour summit]

Oooh. No I think that answered my question. Tysmm 🙂

[shut thorn]

if A B C D are the angles of a cyclic uad and cosA+cosB = K(cosC+cosD) The value of K is

i have many uestions

first of all.
why is there Uadilaterals in a thing about triangles

😭

qaudilaterals.
i keep forgetting that the q key is rebinded to shift 🙏

[exotic yarrow]

,texsp Recall that ||$\cos \theta=-\cos \left(180^{\circ}-\theta \right)$.||

[somber coyote]

Civil Service Pigeon

[shut thorn]

ohh so from there. cosA = -cos(180 - A) and since it'd a cyclic

C = 180- A

so the value of K will be. -1? (cosA + cosB = -cosC + (-cosD))

[exotic yarrow]

mhm

[solid gate]

thank you so much for taking the time to explain 🙂 it all makes sense now.

[long geyser]

Ofc! I'm really glad

[cerulean lintel]

$log^2(8)$

[somber coyote]

emiya

[shut thorn]

😨

wait did you mean

$log_2(8)$

[somber coyote]

Cheze

[slim plinth]

It’s the form

log_(base) (argument)= (exponents;

[vocal pollen]

$\log_2(8)$

[somber coyote]

memegod

[steep lintel]

Can I ask something here? I started to learn about algebra and math not so long ago and what is the difference between goniometry and trigonometry?

[silent plank]

geometry concerns shapes in general
trig has a deeper focus on triangles

[ember hare]

3

[winged oyster]

trig is specifically triangles

geometry is all shapes

[steep lintel]

i'm sorry i didn't mean geometry, in my language we have goniometry and trigonometry.

[shut thorn]

should mean the same thing?

What content does goniometry have?

[steep lintel]

I searched that up and google said that goniometry (goniometrie in my language) and trigonometry is the same thing. I am sorry, my teacher always say goniometry and i thought that it is something different from trigonometry

[shut thorn]

Ok so goniometer is something used to measure angles. I'm pretty sure goniometry is something related to angles.

[steep lintel]

Google said that goniometry is like goniometric functions which can be also called trigonometric functions

[shut thorn]

I think because you can like. To find an angle, you can use the trigonometric ratios of a right triangle,

and since finding an angle is called goniometry, they can be called goniometric functions?

[steep lintel]

idk, I am only in 9th grade but i like math and learn math ahead

[gaunt latch]

yo

can anyone give me a hard equilibrium of forces question

[wild trail]

okie

A man is hanging a picture frame on the wall. The frame weighs 10 N, and he’s holding it with two strings at equal angles. Suddenly, one string snaps.

Question:
At what angle does the man’s panic reach equilibrium?

😭

[hasty stump]

what

[tiny acorn]

Depends on his reaction time

[prime saffron]

I am working on light reflections, but I am a bit unsure on how I can find the vector of the reflection. I all ready know how to find the point of intersection on the surface, the normal of the surface and the angle theta 1, however I am a bit unsure on how to find the vector of the reflection, could anyone please help me out?🙏 😊

Below is an illustration of my thinking, where P is the intersection, L is the light origin, n is the normal of the surface vector, v is the direction vector for the light, r is the reflection vector which I want a method for discovering

anything will help me at this point, i'm quite stuck on this :-)

I noticed a small error in the image, in the last line there is supposed to be plus P instead of plus L

[delicate ocean]

Ayo I thought trigonometry was easy only needed angles,degrees,tan/cos/sin wth is this shi

[flint pine]

Same dawg

[dense matrix]

is there a relation between tangent to circle and tangent in trigonometry?

secants as well

[dark sparrow]

yes actually there is

lemme make a diagram

you know the unit circle, right?

like conceptually, rather than value-bashing

[winged oyster]

what if i only know sin² + cos² = 1

because cos is x and sin is y

wouldnt that mean sin + cos also equals 1

oh wait nvm

[dense matrix]

yeah

[dense matrix]

yes yes

[dark sparrow]

aight yeah. so here in my diagram BP = tan(theta) and BO is sec(theta)

the idea is that if you extend the terminal ray of theta until it meets the line x=1 you land at the point whose y coord is tan(theta)

[dense matrix]

ohh

[slim plinth]

Guys

[slim plinth]

I’m also doing this

[dense matrix]

thats pretty neat

[slim plinth]

After Pre-Calc

I’m doing Co-terminal

Coordinate

[dense matrix]

but if we do not have a circle with unit radius then BP/OP=tan(theta)

[lucid ferry]

jesus christ what the hell

[queen juniper]

u don't need theta to derive it

just decompose v into the part tangential to n and the part normal to n, and since reflection only flips the normal component, it's easy to solve from there

[celest path]

Help

[craggy egret]

whats your question

[queen juniper]

coordinate bash

actually no

[celest path]

I can't solve number (2)

[prime saffron]

thank you

[fast junco]

We meet again.

[cinder harbor]

How J can be the intersection point of BF and CH ??????

[dense matrix]

I was hoping for Kenobi, why are you here?

[deep jolt]

I took the perpendicular line from the given tangent. Why is the second intersection at (2,0) on the x axis? (for circles that pass through 0,0)

[exotic yarrow]

One of the diameters lies along the blue line

and you drew the tangent at (0,6)

So the diameter along the blue line has one endpoint at (2,6) and its midpoint at the centre (1,3)

the midpoint formula gives you that the other endpoint of the diameter is thus at (2,0)

[lapis heath]

can i js send my problem here

[exotic yarrow]

Reposted here: #1472365768485109893 message

[lapis heath]

mb

[winged oyster]

pythagorean theorem

[winged oyster]

this ones more interesting

its half of an equilaterial triangle

because its 30-60-90

using that we can find that the hypotenuse is sqrt(40)

and then you can do pythagorean theorem from there

[lapis heath]

i got sqrt30/3

what i did was sqrt10 = xsqrt3 and got sqrt30/3

[winged oyster]

it shouldve been just sqrt(30)

[lapis heath]

how

[winged oyster]

was sqrt(30)/3 right

[lapis heath]

no

[winged oyster]

it shouldve been x = sqrt(10)*sqrt(3)

[lapis heath]

o

[winged oyster]

yeah its okay

[lapis heath]

what i did for the base was sqrt10 =xsqrt3

bc the base would be equal to xsqrt3 and the vertical leg bein js x

the hyp we dont care abt which wouldve been 2x

[winged oyster]

the sidelength with angle 60 is x

then the one with angle 30 is xsqrt(3)

[lapis heath]

wait wha

😭

[winged oyster]

(well not actually x)

[lapis heath]

noooo what

i mean the hyp is js blank

we js dont care abt it correct?

ye

the line that goes from 60 to 30 would be 2x

but we r not gonna use it

[winged oyster]

yeah

[lapis heath]

im lowkey scared to enter sqrt30

bc if i mess this up, my grade is going to drop

im on my last attempt

[winged oyster]

it should be right

[lapis heath]

mhmm

alr ima js ask her in-person on thurs lol

thx tho

🙏

[silver timber]

sybau

i got A* in mathematics it never really asked about trigon or pythagoras

[hasty stump]

no way

[dark sparrow]

op left the server

[mortal belfry]

Hello

[winged oyster]

how do i do rotation around a point

[near cliff]

Hmmm essentially when you rotate 90 degree your horizontals become verticals and vise versa. So say from point A it took you 4 sides to the left and 2 up to get to the point of rotation. It would be now 2 left and 4 up. However if you were asked to do a 180 degree then the movement would stay the same.

Literally take your finger and just do a 90 degree rotation if it helps you visualize. You will very clearly see vertical -> horizontal. And work 180 stays the same!

[winged oyster]

oh ty

[near cliff]

Yea

Np

[balmy tree]

Help plss!

I solved it but I'm not sure about the answer

[dark sparrow]

,rccw

[plucky sail]

6.84cm

my working too messy btw

[exotic yarrow]

Reposted: #1472602966883176489 message

[plucky sail]

Mine messier

[ionic ingot]

I have a bit of an off topic question but many an in topic question idk

If your chapter in mathematics involves in geometry and your teacher let's you on your phone, is geometry dash the next best thing?

[silent plank]

no

[shut thorn]

i mean youre dashing through geometry (geometry dash)

[marsh wing]

geogebra

pulls out imo p6

[coral herald]

Playing GD on mobile feels like pure ragebait z

[coral herald]

Tan(60°) = sqrt(3) = x/sqrt(10)
x=sqrt(30)
I wish I had such questions 🥀

[slim plinth]

If you see these set proportion

[drifting apex]

Wdym lol

[plucky sail]

U can find real values with proportion

[slim plinth]

Really

[quaint sinew]

i need help with trigonometry of 9th class

[winged oyster]

post a question

[spiral lodge]

Be more specific

[slim plinth]

Yea I agree

[sacred spade]

@fickle marten

@fickle marten

[fickle marten]

Ye

Forza

Cya

[sacred spade]

oh k

[novel island]

guys 1+1= 11

[winged oyster]

I disagree

[sacred spade]

💀

[sacred spade]

lol

[novel island]

there are 2 one’s right?

If we combine them

[sacred spade]

Alr

[novel island]

we create 11

[sacred spade]

That makes sense now!

means 7 + 7= 77?

[novel island]

Im albert einstein from TEMU

[novel island]

yes

[sacred spade]

wembu is good

[novel island]

yes im very smart

[sacred spade]

but parrot is 🔥 🔥

[winged oyster]

so whats 6 + 7

[sacred spade]

....

AY ay

[novel island]

Bruh

[sacred spade]

aya

ay

[novel island]

67

[sacred spade]

jk

[novel island]

long live the new king

[fickle marten]

Height square + base square = hypotenuse square

[tall niche]

also hello

[quiet galleon]

I DONT UNDERSTAND. pls help

[exotic yarrow]

this is the parameterisation for a circle of radius 1 centered at the origin

you can see this by considering the pythagorean identity

,w graph x(t)=cos t, y(t)=sin t

[somber coyote]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[exotic yarrow]

Further hint: ||diameter||

[quiet galleon]

OH I thought they were just normal functions

[winged oyster]

huh

wouldnt it be ||sqrt(2)|| and not ||2||

[exotic yarrow]

diameter and radius are essentially equivalent

and either of those trivially gives you the answer

I couldn't give the whole thing away

but I did give away most of it tbf

@winged oyster

[winged oyster]

oh

[quiet galleon]

is there a propability section for pre-Uni

[exotic yarrow]

eh ig just use the help channels

#❓how-to-get-help

[lime drum]

Oh how i love triggy

[cosmic plaza]

couldn’t be me

[upper orbit]

LOLL

[queen juniper]

triggy wiggy

[lime drum]

triggy

[cosmic plaza]

piggy

[shut thorn]

Riggy

[wise imp]

Diggy

[sacred spade]

@fickle marten

@fickle marten

[sacred spade]

ez

[gleaming fjord]

hi guys idk if this the right channel to ask but i was hoping if someone can help me understand how and why 2x - y + 4 = 0 was multiplied by -x. the questions are already solved i just forgot why and how it was done

[barren pewter]

helpppp

[hasty stump]

pythagoras theorem

[barren pewter]

what's that...

[hasty stump]

a^2 + b^2 = c^2

[celest path]

It's an impossible shape

[hasty stump]

it works for right angled triangles

wait but your length will be negative

[barren pewter]

then 36- 49 = x^2?

[barren pewter]

wdym

[hasty stump]

the hypotenuse is shorter than your opposite side

[celest path]

According to the Pythagorean theorem, x² + 49 = 36, so x² = -13. Solving this quadratic equation yields x as an imaginary number, but since the length is a positive number, that is, a real number, there is no solution.

[barren pewter]

i get it know , thanks!

[hasty stump]

yeah correct

[muted river]

Good morning!~

[cosmic plaza]

can’t u do it opposite like c^2-b^2=a^2

[slow niche]

Where did you find it?

[hybrid stump]

also I think I got it now, thanks anyway

[mortal belfry]

Hi

[swift spoke]

Do you guys have any good video lectures or books (although videos are preferable) to study trigonometry?

[cosmic plaza]

check out aops

they have everything

[spiral lodge]

KhanAcademy and Organic Chemistry tutor, for instance.
But there are others, such as these:

• https://youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&si=sz4umxNEy2z5jZti

• https://youtube.com/playlist?list=PL5KkMZvBpo5DdtHcMLtodrdN7nr79GJIJ&si=vdsixKK7aJgXizcL

• https://youtube.com/playlist?list=PL085526F86A268B57&si=Pt-lHnWeQYYAjeBL

• https://youtube.com/playlist?list=PLU_DCVXL8MyNp2vqZjZvDTRDxf6oCuf7l&si=iptfTkpHryITCpGC

• https://youtube.com/playlist?list=PL5KkMZvBpo5DDsJNijZJqCBALQjOc_X7F&si=vqDuQVYUzcK51XYh

• https://youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP&si=3LuWS8fSGGcLvHAq

• https://youtube.com/playlist?list=PLX2gX-ftPVXWiPVqdVFdCvLDGEtCj8iyy&si=p3bZrLxEomMBG3U-

• https://youtube.com/playlist?list=PLX2gX-ftPVXVczHKMUwtJIIlItoROHFej&si=C_RNcTdqs8v4EqK5

• https://youtube.com/playlist?list=PLX2gX-ftPVXUU9Aq60SaPJkE_swgri-59&si=f3ooBnYezC0XJJms

• https://youtube.com/playlist?list=PLX2gX-ftPVXUtjPmE-h3Ck2_2j4m_a7mV&si=okk9ee783BSl9MVs

• https://youtube.com/playlist?list=PLX2gX-ftPVXXlobs95yV8ihqVCCbZ72n_&si=xvblMuLlnWwLDaIx

[rugged basin]

professor leonard is also goated if you want really long in-depth lectures

[spiral lodge]

Exactly, that's indeed the first in this list I've just sent 💪

[swift spoke]

wow that's a big list, thanks

[spiral lodge]

Yeah I know, probably it's too broad. But I guess each of us has their personal stylistic choice, so I can't know exactly which YT teacher fits you better. So I gave you a wide choice 🤗 🤗

[winged oyster]

this isnt possible

[karmic void]

(idk if anything i said is right btw so just double check) wait they did not multiply by –x, they multiplied by –1.
You had: 2x - y + 4 = 0; At some point it becomes: -2x - y + 4 = 0; That happens if you substitute x with –x (for example, when reflecting across the y-axis) Because: 2(-x) - y + 4 = 0; Simplify: -2x - y + 4 = 0; Then they multiply the entire equation by –1 to make it look cleaner (so the x-term is positive): (-1)(-2x - y +4) = 0; Which gives: 2x + y - 4 = 0. They basically wanted to just rewrite the equation for it to be in a nicer form which led them to do that.

[mild jungle]

is that school math?

ive had stuff like that in school be4

[gleaming fjord]

Ooooo okok ty!! Makes so much more sense now

[torpid pine]

Guyz can anyone help me

I wanna improve my skill in geometry

[gray vessel]

Could anyone help me with a problem of trigonometry?

[sly urchin]

Does anyone have files on Hagge circles and their
applications? Please share

[sacred spade]

ez

hypotenuse square = height square + base square

to finde base

base square = hypotenuse square -height square

guys if im wrong correct me!

@fickle marten

i did not read the question tho

hypotenuse is shorter than height? 😭 😭

what

[shut thorn]

it's not a poss8ble shape for a triangle

The base has to be imaginary for it to work

[sacred spade]

oh

[barren pewter]

helpp

[hasty stump]

wait sine cannot be more than one right?

[shut thorn]

ye it can't be

[celest path]

There's no solution

[shut thorn]

there's no solution as the range of sinx is 1, -1

[hasty stump]

if u look at a graph

[celest path]

At least in terms of real number

[hasty stump]

maximum and minimum points

[shut thorn]

ok so that implies that there's a solution in imaginary solutions

?

[celest path]

Yeah

[
\sin x = 1.1
]

[
\sin z = \frac{e^{iz}-e^{-iz}}{2i}
]

[
\frac{e^{iz}-e^{-iz}}{2i} = 1.1
]

[
e^{iz}-e^{-iz} = 2.2i
]

[
e^{2iz} - 2.2i,e^{iz} - 1 = 0
]

[
e^{iz} = i\left(1.1 \pm \sqrt{1.1^2 - 1}\right)
]

[
iz = \ln!\left(i\left(1.1 \pm \sqrt{1.1^2 - 1}\right)\right)
]

[
x = \frac{\pi}{2} \mp i \ln!\left(1.1 + \sqrt{1.1^2 - 1}\right) + 2\pi k,
\quad k \in \mathbb{Z}
]

[somber coyote]

Epsilon

[shut thorn]

uh huh

[barren pewter]

helppp

[celest path]

Impossible

[silent plank]

What class are all these weird geometry problems coming from?

[barren pewter]

idk my teacher is sending me those

[celest path]

It is contradictory because according to the pitot theorem, 2+9 = 3+6

[barren pewter]

so there is no answer, again...?

[celest path]

Yeah

If it's really from the teacher's request

I seriously think that person lacks the character of a teacher

[barren pewter]

okay ima send the new problem soon

[celest path]

if the teacher's intention was to see the insight to find the fundamental errors before this solution, then the teacher is very good

[barren pewter]

yay

help....?

[silent plank]

this one is actually reasonable, assuming that outer curved shape isn't a circle,
apply angle sum of a quadrilateral

[barren pewter]

is the sum 360?

[silent plank]

yes

[barren pewter]

i sent him 129 deg and he told that its not the right answer...

[silent plank]

how are you getting 129

[barren pewter]

ohh 119

[somber pendant]

uh are those numbers the length of sides?

that doesn't really make sense

[somber pendant]

that's a circle?

dude these questions are underspecified as hell

[spark yacht]

Whaat

Not even possible

[spark yacht]

Use property of a quadrilateral

[river rivet]

119 degreed

[celest path]

The proportions of the picture are strange, but I will solve it for now. Since the sum of the diagonals of the rectangle inscribed in a circle is 180°, 127° + phi = 180°, phi is 53°.

[river rivet]

Its not circle

[celest path]

I think this problem causes much more thought enhancement

[celest path]

If it's an ellipse, 119° is correct, but if it's a circle, there's an error in the problem itself.

[cosmic plaza]

it travels a quarter circle

i think i. can do this hold on

[hollow lily]

||From B to A' the distance between O and l is constant, so it's just BA'||

[cosmic plaza]

how do i hide my text

[hollow lily]

|| your text ||

I never said it's total distance

[cosmic plaza]

|| i did circumference divided by four ||

[hollow lily]

"From B to A'. "

[celest path]

Oh, I misunderstood

[cosmic plaza]

although i don’t think im correct

or wait

|| can’t it be seen as a triangle? and u do pythagorean ||

[celest path]

The answer is 6pi cm

[cosmic plaza]

that’s from the circumference right

but since it’s a quarter circle don’t u divide by 4

[celest path]

The distance point O travels from point C to point C' is equal to the distance the circle has rolled by half, so it is equal to the length of an arc on a half circle.

so 2pi×3×0.25×2+2pi×3×0.5=6pi (cm)

[cosmic plaza]

is that for the whole thing? or just like one circle

[celest path]

Whole thing.

[cosmic plaza]

oh i did it for just the single circle

[simple vigil]

What's this question?

[cosmic plaza]

this

i read it wrong

[barren pewter]

help?

[fickle marten]

[raw relic]

6 units

[barren pewter]

what's the solution??

[raw relic]

Wait a sec

[summer cradle]

(r + 2)² + (r + 3)² = 5²
=> r = 1
Height = 1 + 2 = 3
Base = 1 + 3 = 4
Area = ½ × 3 × 4 = 6

[raw relic]

Well the tangents drawn on a circle from a point are of same length

[barren pewter]

thanks

[summer cradle]

np

[river rivet]

Wrong

[raw relic]

How?

@river rivet How?

[river rivet]

Wait its right

Mybad

Im sorry

I miscalculated

[raw relic]

👍

[river rivet]

More questions where?

[slim plinth]

Hey

[spiral lodge]

Hi

[slim plinth]

Which one is easier; Intro to Trig, Evaluating Trig, or Special Right Triangles

It’s like I learned SOHCAHTOA and it’s reciprocal

[queen juniper]

i never used soh cah toh 😭

i just forced it into my brain

[rugged basin]

unit circle is way more intuitive once you get the hang of it anyway

[queen juniper]

yep

[winged oyster]

what do you use to learn reciprocals

[slim plinth]

Take these formula and make it like H/O, H/A, and A/O

[winged oyster]

shochatao

[slim plinth]

But it’s

csc, sec, and cot

[abstract wing]

hii does anyone have any resources to study geometry

[cerulean lintel]

Khan academy

@abstract wing

[royal crescent]

Kind of stupid question but can anyone tell me what this symbol means I see it in my math all the time:/

[abstract wing]

Its theta, its apart of the greek alphabet

Its kinda js a varable like x or y

so if you see sin theta, its js refering to angle theta

[royal crescent]

ohhhhhwwww

Thank you I was so lost😊

[abstract wing]

nwss yww!

[abstract wing]

dyk any online textbooks asw by chance

cs imo khan academy isnt helping me

or any other resources to get questions from

/learn the content

[cerulean lintel]

Not really except gauth app

No websites tho

Sry 2 resources i use

[abstract wing]

nwss tyy

geometry is the end of me omg

[cerulean lintel]

😭

Desmos can help

Desmos.com

[abstract wing]

i mean yeah it does but like its moreso applying it during class

[cerulean lintel]

Well then those are my 3 but i wish you luck on finding something truly beneficial

To helping with geometry

[cosmic plaza]

theta

oop someone already said that mb

[abstract wing]

tyy

[celest path]

6

[cosmic plaza]

the hypotenuse is 5

so a^2+b^2=25. we can do 4 and 3 (9+16) 4.3=12 divided by two is six

[flat valve]

how do i know if 3 measurements make a triangle

the triangular theorem or whatever

[exotic yarrow]

Triangle inequality?

[graceful jacinth]

It feels wrong with 90 degree right triangles that you need visual representation for the adjacent/opposite sides.

Based on my terrible independent studies you would need one angle, one side and the visual representation of that triangle to determine the adjcent/opposite sides, although I could be wrong.

[half bone]

assuming that the one angle isn't the right angle itself, this cannot be truer

[rough bronze]

love the username

[velvet pumice]

Guys Im having a hard time while trying to solve the questions based on trigonomety questions at analytic circle

as an example
This question was asking whats de |DE|/|AB| and it was kind of confusing for me
Any suggestions you guys have?

Or should i just try to solve more and more till i get used to these questions

[willow fox]

Here is the solution of the question

Try doing some questions like these they are a bit easier and will polish your memory about theorems

[sacred spade]

ik this but i cant remember how to solve 😭

[dense ruin]

I love the cursive. I would love to use it but I am always scared to get marked down if the prof doesn't like it or something.

[willow fox]

Ohh thanks, my prof doesnt care if I write cursive he's a chill guy

Also now if I think about my solution

I could have just use similarity

That would be a bit easier

[frosty delta]

This one's a 10th class Q

Um so the point which is at circumference that is joined with centre, join that to one end of diameter like the side opposite to the theta angle
The angle formed there will be half of theta due to a property of circles that says angle subtended by an arc at the centre is twice of angle subtended by same arc at any point on circle's circumference

@willow fox

I hope you understand what I am tryna say, ask if there's any confusion

[willow fox]

yeah absolutely i understand what you are saying

as i said the question isnt hard

but it does require you to remember the theorem

so i thought that by solving these kind of questions

that person can solve these questions pretty easily

@frosty delta n i didnt knew it was for 10th

[storm zephyr]

Help me with this plz....

[tepid charm]

Construct DE parallel to BY, E being on AC

Use BPT

That's my first idea.

By using midpoint theorem on triangle BYC, note YE = EC

After which it is basic manipulation ig

Or alternate method that kills the problem: Mass Points

I proved it

With Mass Points, since D is the midpoint of BC, we position masses on B and C such that D is the centre of mass. If we let mass on B be 1, and mass on C be 1, then D's mass is 2 (centre of mass), and we achieve the desired ratio of length on BD and DC (equal attraction).

Given: AX/XD = 2/3. If mass of D is 2, then mass of A is 3, which achieves this ratio of lengths.
Mass of A is 3. Mass of C is 1. Then, Mass of Y is 4.
Then, BX/XY = Mass of Y / Mass of B = 4 / 1
BX = 4 XY

https://en.wikipedia.org/wiki/Mass_point_geometry
Look into this article, if you are unfamiliar about MPG.

[frosty delta]

Oh you got the difficult set in maths

[storm zephyr]

My friend got this set I asked him to send this but I couldn't get the approach so I shared it on discord

[frosty delta]

Construct DE parallel to BC where E is a point on AC then use BPT and the dots will start connecting

Not BPT tho, mid point will do the work actually

[storm zephyr]

I haven't learnt about mass point geometry but thanks

[storm zephyr]

I tried that actually, I guess it needs more than 1 construction and bpt will make it out

[frosty delta]

I cant remember dude, I did this Q last year

[storm zephyr]

Oh, which grade you're in

[frosty delta]

10th, like I am having my boards currently

[storm zephyr]

Most of questions weren't hard expect one two in all combined sets, but people lack critical thinking

[storm zephyr]

Oh best of luck bro

[frosty delta]

I thought like this but children are dependent on two or three youtube teachers

[frosty delta]

Thanks

[frosty delta]

I saw some sets which the students called "difficult", man they were so good and so conceptual based, my set was so basic, it was so boring tbh

[storm zephyr]

Yeah maths should be explored more, not just consolidating all in a 2-3 hrs video

[frosty delta]

10th grade maths is like a no brainer if a student really studies but everyone tryna go for the short way and hope that some youtube teacher gonna tell them the exact Qs which are gonna come in the exam

[frosty delta]

Exactly

It's good that cbse is finally setting the bar high

[storm zephyr]

I also got a simple set, like easy to moderate

[storm zephyr]

Now students have to learn how to think critically and implement known theorems, otherwise they will cry in finals

[frosty delta]

Yeah

Over all of which is going on in the country rn, you hear students crying because their rott learning didnt help them and they got a conceptual based exam

That's funny

[spark yacht]

Haha

Yesterday

I gave a normal bpt solution

And people

Weren't understanding

When I was looking about bpt and mpg

@storm zephyr

Did u get normal sol

[storm zephyr]

They just rott learn some type of questions and patterns and when there is a different type of questions, they panic and claim that is toughest among all papers

[spark yacht]

Join topmost to the semicircle end

[willow fox]

ik how to it i was trying to tell the guy who asked the question with the unit circle

[storm zephyr]

I cannot understand it in first glance but I'll try, btw I found an approach, it's need more than one construction and bpt that's it, if I solve it correctly i will share it

[spark yacht]

Try

[abstract wing]

is anyone able to explain why this is the answer?

[exotic yarrow]

AC=BC=a -> a is fixed -> (a,a) is also fixed

[abstract wing]

wait what

so since they equal a it means a cant change?

but b,b works since b can be any value its not set to just be that one length

oh wait do we js assume that the slope is X

or

[exotic yarrow]

sure

[exotic yarrow]

the slope is a fixed number

use the slope formula and you'll see

[fickle marten]

Gng hypotenuse is the largest side dwag. If any of the other sides are bigger the triangle cannot be classified as a right angered triangle!

@sacred spade

[fickle marten]

Use algebra

U are already given 2:3

Just telling so the solution will be shorter and it would take less time

[sacred spade]

ye ik

[spark yacht]

Huh

What algebra

[fickle marten]

.

[warped warren]

what was euclid trying to prove in elements proposition 2 book 1

or

is there a more modern book that fills the gap on euclids elements

seems like the language tht all translations of the elements use is really fancy

[frosty stream]

Like for analytic geometry?

[warped warren]

no

[frosty stream]

Wdym by fills the gap on Euclid then

[warped warren]

e.g it provides more explanation on geometry that euclid didnt include in his elements

[frosty stream]

Any intro Euclidean/analytic geometry and elementary number theory textbooks would work, unless you mean one that specifically expands on Euclid’s elements

[warped warren]

i mean

sumt like analysis books

but instead of

the real number line or sumt

you talk about geometry

euclidean geometry to be precise

[frosty stream]

Analytic geometry isn’t analysis

[warped warren]

yea thts trivial

wht i mean by "something like analysis books" is tht it has pretty much everyth analysis books typically hv (logical rigour, entire subj based on proofs, etc.) but you specifically discuss euclidean geometry

[frosty stream]

Ohh

[warped warren]

analytic geometry in other hand defines a coordinate uh

euclidean geometry doesnt require one

[frosty stream]

You might be better off asking in
#book-recommendations

[quaint pecan]

any help ?

ignore the stuff i wrote after the question i was tryin to pen it down but i drew 2 constructions and been stuck ever since

[simple vigil]

Can't really think that much but definitely triangle congruency or similarities will be used

[quaint pecan]

yeah i kinda understood by intuition that it will be similarity, can't see any congruencies tho

[simple vigil]

Yeah ok
But if you are stuck and not able to think anything

Then write all things possible using properties of circle you know

And try to find relation between them

[quaint pecan]

i did, still couldn't

I spent around 5 hours on the problem trying to do all the brute forcing and stuff but couldn't get to those smaller triangles up and down

[spice bridge]

Anyone here ???

Plsss explain this

[spice bridge]

Evaluate

I did the half but I can't do further

[potent hollow]

do you know your reciprocal trig functions?

[spice bridge]

Yes

[potent hollow]

where are you stuck?

[spice bridge]

After substitution i did the LCM of it to make the denominattor equal after i don't wht to do like when I checked the guide the number have been changed I don't knw how

[potent hollow]

can you show me what you got?

[spice bridge]

Wait one sec

[potent hollow]

kk

[spice bridge]

I have understood the sum where I have done the box

[potent hollow]

do you know how to simplify it?

[spice bridge]

The first step i understood

But the second

Is not entering my head like wht to do

[potent hollow]

ok youre just dividing a fraction by another fraction

so instead of one big fraction think of it as (a/b) thats the top bit, divided by (c/d) thats the bottom bit

and like swap the numerator and denominator to make it multiplication

[spice bridge]

Ohh i see

[potent hollow]

gl

[spice bridge]

How

[potent hollow]

do you know how division works with fractions?

so like dividing $x $ by $ \frac{1}{2}$ is the same as $ x * 2$

bruh im bad at latex

[spice bridge]

Ohk

Thnx very much

[potent hollow]

np

[spice bridge]

Whr r u frm

[potent hollow]

australia

[spice bridge]

Oh nicee

[potent hollow]

you?

[spice bridge]

India

[potent hollow]

nice

pretty much all my friends who like math are also indian lol

[spice bridge]

But I suck in maths 😭😭🙏

Any tips to improve

[potent hollow]

you can get better

i mean if you apply yourself then you should improve

[spice bridge]

Thnx

[potent hollow]

maths isnt something if youre bad you stay bad at it forever

as you learn more math you get better at just thinking about it

[spice bridge]

Hmm

Any tips like how to improve

@spice bridge

[potent hollow]

when i learn new topics i try to link it back to ones i already know through making my own questions, if that doesn't really sound like your thing then doing a wide variety of problems can help with calculation and thinking

you should be able to find plenty of problems online

[spice bridge]

Nice idea 💯

[potent hollow]

np happy to help anytime

[spice bridge]

Ohk

[spice bridge]

Y can't I send u frnd request

[potent hollow]

cus i blocked from this server

just ping me if you need me

[spice bridge]

Thn how r u able to msg

[potent hollow]

wdym?

[spice bridge]

Like whts this

[potent hollow]

i blocked friend requests from here

and message requests

[spice bridge]

Ohk

[shut breach]

Hi, sorry about you having to be sent around to different channels, but this is probably best suited for #discrete-math or maybe #recreational-math

I think there was a little bit of an overreaction in the algebraic geometry channel, but some people are frustrated because we get occasional posts from material that is really not related to algebraic geometry, since algebraic geometry is more usually upper undergraduate or graduate level mathematics, involving for example many other subjects like abstract algebra/rings and ideals/commutative algebra/differential geometry/etc.

[final comet]

Alright, moving it there

[winged oyster]

nothing is really

[surreal dirge]

Dear lord what the heck is this

[little flame]

#❓how-to-get-help

[lapis heath]

alr

unc

[charred willow]

(A+B)²= a²+2ab+b²

[hot ferry]

I need help with if anyone can help

Perimeter of Compound Shapes

[silent plank]

just ask

[hot ferry]

Ok

[hot ferry]

A garden is shaped like a rectangle but with one corner cut out (stepping inward). The total width across the top is 100m. The bottom horizontal side is only 60m. If the total height on the left is 80m and the inward vertical 'step' is 30m, what is the total length of the wall needed to enclose the garden?"

something like this

[silent plank]

start by drawing a diagram

[hot ferry]

Oh ok

[opal grove]

Guys, is the triangle correct? I got 655m² but my tutor got 685m²

[silent plank]

no, you didn't calculate what they asked for

[winged oyster]

you forgot the other triangle

[silent plank]

you've ignored all the orange parts
and
included the base of a normal triangular prism (that's now hidden in the composite solid and won't be part of the external surface)

the tutor's answer already includes all parts

[silent plank]

not the issue here

10 * 3 already accounts for both triangles

[winged oyster]

oh wait mb

[opal grove]

Hold on give me 10 min I need to do smth for my parents

[opal grove]

It does? I just looked back at it and realised that I only included one 3*10 and forgot the back existed

[opal grove]

Wdym ignored all orange parts

[silent plank]

area of triangle is bh/2,
and there's 2 so bh gives area for both
I assumed that's what you did

and you don't have any calculations for the orange part

[flat valve]

guys how do you know if different lengths form a triangle

[silent plank]

triangle inequality

[flat valve]

what’s that

[silent plank]

in a triangle, sum of lengths of any two sides will be greater than the third

so if you sum the two shorter lengths and that's greater than the third,
you'll be able to form a triangle with those lengths

[opal grove]

Area of triangle is bh/2 even for a singular triangle

Not just a triangular prism

So in that case I forgot the backside

[silent plank]

yes, but you had bh, which is double bh/2

so if you used bh for the front triangle, and also forgot the backside
that would've been two errors (that end up cancelling each other out)

[swift niche]

Hi i need help with the task below.

The task
"The graph of a sine function of the form f(x) = Asin(cx) +d intersects the positive part of the x-axis at the x-values 1, 5, 13, 17 and so on. The graph intersects the y-axis at the y-value 3."

(a): What are the period, the midline, and the horizontal shift along the midline?

I have found the period, but i am not sure how to find the midline

[quiet galleon]

I hate geometry and number theory

And I hate number theory more

[agile jolt]

Any hint?

[trim hazel]

hmm

lemme think abt it

i haven't had geometry for 2 years now

[upper echo]

Use the law of cosines

[trim hazel]

or maybe you can do it with height

no, wait, you can't

wait, you can, my bad

you can do it using a formula for height 2*sqrt[s(s-a)(s-b)(s-c)]/b and s is equals to the sum of sides divided by 2

and that would be the height of

b

lemme draw it

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[slim plinth]

This one is a good one

[quiet galleon]

HI

HELP

the people in #algebraic-geometry said that i am stupid

and that i need help

and they said go back to elementry school

[violet sluice]

Do you know the pythagorean thm

[queen juniper]

i don't think u know what algebraic geo is 😭

[quiet galleon]

no

jk ik

[violet sluice]

Cool so

What's the formula for the area of a sqaude

Squade

Square

[quiet galleon]

s^2

[violet sluice]

What is s

[quiet galleon]

idk

4

4cm

[violet sluice]

No I meant what does s mean

[quiet galleon]

side

[violet sluice]

Yeah sure side length

[quiet galleon]

im not a kid

[violet sluice]

So the small square has an area 16 cm^2, so what does that imply about all of its side lengths

[quiet galleon]

4

cm

[violet sluice]

Great

[quiet galleon]

you're getting me nowhere

[queen juniper]

😔

people are trying to help you

[violet sluice]

Ur right

[quiet galleon]

where am i

[violet sluice]

I guess I will leave this to other people if I'm getting you nowhere

[quiet galleon]

no pls dont

[quiet galleon]

continue you're ritual

[quiet galleon]

are you a mod

[quiet galleon]

40

[slim plinth]

What if I said it’s 50

[quiet galleon]

what

[quiet galleon]

it cant be

[slim plinth]

Oh

Their the same

[quiet galleon]

no

no they are not

[slim plinth]

Oh

There is no right angle

[quiet galleon]

there is

[queen juniper]

yes there is

[slim plinth]

It’s perpendicular

[queen juniper]

90-50=40

[slim plinth]

And bisect the lines into two

[quiet galleon]

ask #algebraic-geometry

[slim plinth]

Okay

[quiet galleon]

they are experts

[slim plinth]

Okay

[slim plinth]

I don’t have access

[quiet galleon]

oh

even if you did just dont ask them

they are so mean

[slim plinth]

What

So I’ll stay here

[frozen ocean]

They aren’t being mean; they’re just telling you that you were using the wrong channel. Algebraic geometry doesn’t mean it’s the kind of “geometry” you’re posting, especially if it’s related to high school. Make sure you read the channel description next time.

[quiet galleon]

are you a mod?

[frozen ocean]

no but im just telling you they weren't mean in there

[quiet galleon]

then shut the freack up (JK , i'm bipolar)

[quiet galleon]

yes they wear

a mod tried to threaten me there

[frozen ocean]

you started it

[quiet galleon]

they liked it

[potent hollow]

What the sheaf is a sheafification!!!

I cant spell

[quiet galleon]

why are you angry???

pls dont kill me

[frozen ocean]

google it

[frozen ocean]

wdym? im not

[potent hollow]

It was a youtube video title

[quiet galleon]

so we're good

?

[quiet galleon]

https://youtu.be/p2bFLG_Q7Lo?si=ZSpBY46RcTAyJUst

[potent hollow]

Yeah that one

Oh its wtf not what the sheaf

Too many sheaves

[quiet galleon]

are we good??

[potent hollow]

Yes definitely

[frozen ocean]

ye

[quiet galleon]

https://tenor.com/view/benjammins-idk-this-person-questioning-random-person-this-who-gif-5295285761881556675

[potent hollow]

Idk

I wish i knew

Still tryna find out where i left my hat

[quiet galleon]

YAY

What an amazing day meeting mods and very cool people

[quiet galleon]

how are you cool?

how do i become cool

[violet sluice]

Moderators have to like you

[frozen ocean]

can you please stop replying me on useless stuff

if you wanna learn about roles, check #info

[quiet galleon]

but they like me

ig

[quiet galleon]

kk

[quiet galleon]

some do some dont

[wispy sun]

Does anyone understand this

[frosty delta]

Draw Diagram
Use Sin 30° so that hypotenuse becomes 2x
Now use pythagoras theorem to get the base
Put in values and get sin and cos value

[agile jolt]

But we need to find angles?

[frosty delta]

By angle sum property BAC would be 150 - (theta)
Now put the values in the provided ratio and get the value of angle ACB
Now find value of x by comparing initial value of Sin theta which you have shown and the actual value of sin theta (as you have already found theta now)

@wispy sun

[trim hazel]

yeah, you can by finding the value of x and then you have two right triangles where you can find the values of sin and cos based of the sin(angle)=opposite side/hypothenuse and when you have a value of sin, you can get to the angle

and the third angle is easy to find

and you do the same with the other right triangle

[agile jolt]

How can I have angle from sine?

[trim hazel]

by using sin^-1 or arcsin

there is a method to do it on paper, but i forgot, because i did trigonometry a few years ago

[agile jolt]

Ah so it's just use calculator after finding the value of sine or cosine

I've found cos(A) = 0.925

[trim hazel]

or do it with calculator

there is definitely some other way that i forgot that's probably shorter and easier, but i came up with this at the moment

[agile jolt]

Thanks for helping

[trim hazel]

no problem

math is interesting because you can approach the same problem in different ways

[slim plinth]

I get 2 x angle BAC =210

[slim plinth]

I’ll give u the ice ties you will use

Laws of Sin

sin(45)=sqrt(2)/2

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

[next swallow]

Math is hard

[strange narwhal]

any hint for 6? (prove that if f is periodic, then alpha is rational)

[exotic yarrow]

Did you try using Google?

[strange narwhal]

not quite, thank you

[strange narwhal]

that's a more general question that I ended up thinking of and it led me to ideas of commensurability and lcm

[vast night]

eitakk

[wispy sun]

Anyone wanna prob trigonometric identitites together

Prove**

[strange narwhal]

let's

[modest rapids]

if it’s useless why did you take the role

[frozen ocean]

???

[modest rapids]

yes, it reads: if it’s useless why did you take the role

[frozen ocean]

which role are you talking about?

[modest rapids]

the same role mentioned by the other guy

[frozen ocean]

very cool ppl?

its not useless if you found out what do you get lol

I was telling the guy to stop pinging me on useless stuff cause they are already explained in #info

[sand bluff]

No, it's 9776367.

[queen juniper]

hmmm

[tidal anvil]

67..is crazzzyyyy

[sand bluff]

https://tenor.com/view/getout-gif-16327023334064302194

[tidal anvil]

u started it

[sand bluff]

You brougt it up, the simple mentioning of 67 does not mean i am talking about the meme.

[tidal anvil]

hmmm surrreeeee

jk im srry chat

[olive dagger]

Can anyone explain me law of cosines?

I got law of sines down

but Law of cosines doesn't make sense to me when I'm applying it to triangles

does it matter if I switch the a,b, or c variables from the law of cosines formula?

[tidal anvil]

watt?

[olive dagger]

You know

Law of cosines

trig

[tidal anvil]

ooh yesss....sadly

[olive dagger]

?

sadly what?

[tidal anvil]

trig

[olive dagger]

I know the formula

but does it matter if I rearrange the variables?

oh ok

guess I'll just have to watch vids on khan

[cosmic plaza]

oh!

[violet sluice]

❓

[frosty delta]

<@&268886789983436800>

[neon prairie]

Take it somewhere else

[royal pier]

how do I make this face the y direction? (So that the tip faces negative y)

[royal pier]

I've tried switching x, y and z around, and changing adding to subtraction, but it didn't work.

It's facing the z direction. The green line is the y axis.

[gray blade]

its not possible to rotate it ?

[royal pier]

Idk how

[gray blade]

On the top right rheres an arrow thats turning maybe its that ?

[royal pier]

It rotates the view around

[gray blade]

Damn

Maybe input R key

Bc it can be a shortcut for rotate

[royal pier]

Im gonna try to rotate it with the equation

Cuz it needs to be an equation

[gray blade]

Wbu switching the x and y values

[tidal niche]

are there any formulas to find hyperbolic trigonometric identities

[wild dagger]

a^2 = b^2+c^2+2ab cos A

[royal pier]

Maybe not an equation, but something that can be written

And is a surface

Im gonna ask chat gpt actually

The equation would be y=abs x+ abs y but it can't have an equals sign, the software im using doesn't support that

[gray blade]

whats abs

[royal pier]

Absolute value

[royal pier]

It forms this shape

[gray blade]

absolute value means the positive form ?

no negative right

[royal pier]

Yeah

[wispy sun]

How did you all pass equation graph bro

[royal pier]

Idk what that is

But I think i figured it out

I just need to input abs x+ abs z

[royal pier]

Yeah it works

[potent hollow]

What

What unearthly formula is that

c^2 = a^2 + b^2 -2abCosC

[wanton yacht]

That's the Law of Cosines

Before you had Pythagorean's Theorem which relates the side lengths of a right triangle. Now, you have the Law of Cosines which relates the side lengths of a more general triangle. Now, the triangle doesn't need to have a 90 dehree angle, you just need one more term to account for that

Remember, formulas in math aren't just arbitrary variables that you apply operations to. Each variable models something physically. In this case, a, b, and c are lengths, and C is an angle.

[surreal tiger]

I need help pls @ me

[exotic yarrow]

(See #help-7｜zen1thxyz )

[tidal anvil]

chat i got u hold plzzzz

[exotic yarrow]

idt they need help tbh - they were adding into the current discussion

[tidal anvil]

ooh....u mean i was doing someone else's math for nooo reason :((

[exotic yarrow]

The help channels and #1021175428326633542 are designed for help

In general, read carefully

Ex. Try not to help someone who is the helper if things are going fine

[tidal anvil]

oooh lol was i doing thatt???

[exotic yarrow]

Just a general statement

Mostly from experience

Partially from annoyance

[tidal anvil]

lol

soooo u like math??

[exotic yarrow]

I’d say so

[tidal anvil]

lol thats good, i lwk think its mid but i will and can do it pretty easily..yk?

[pale sentinel]

uh-huh, sure buddy, you do you

[tidal anvil]

bro watt?

[pale sentinel]

You're on a maths server what did you expect 🤣

[tidal anvil]

lol real

[fading geyser]

<@&268886789983436800>

[crystal kiln]

hey guys

Who is online rn?

Need someone to check an issue with my work

[shut thorn]

?

just send it. Someone will reply in an hour or soon

[crystal kiln]

okk

lmk if you can't see clearly

for the c part

for the second equation

mu is not part of my 3b

does it mean smths wrong or I can still solve it like that?

[shut thorn]

hm wait for someone else.

can't do it

sorry

[crystal kiln]

okk

tyy

[ashen sparrow]

can someone explain to me how pi works in trigonometry

like is tg(pi/4+x) the same as tg(x)

cs ik with regular pi or sum it was

[spiral lodge]

Do you know the formula for tangent of a sum?

[crystal kiln]

nvm, copied question wrongly
that's why there were issues

[slim plinth]

Hey I would need little help about ” What Quadrant are you in?”

Like cos theta < 0, cot theta > 0

[spiral lodge]

Hint: cot is cos/sin

So if cos is negative, sin must be ...

[slim plinth]

ATCS

[slim plinth]

Positive

[spiral lodge]

Nope

[slim plinth]

negative

[spiral lodge]

Yes

[slim plinth]

Ik radius cannot be negative

[spiral lodge]

So what's the quadrant with cosine and sine both being negative?

[slim plinth]

4th

[spiral lodge]

Mmh you sure ?

It's the 3rd

[slim plinth]

I’m confused about the location

Of the graph

[slim plinth]

Can I just make a triangle on a graph to figure out

[spiral lodge]

Wdym?

[slim plinth]

I meant

Write out definition of trig ratio and put negative on it

[slim plinth]

Like cos(theta)= x/r

r cannot be negative

[spiral lodge]

Well, you should already know/remember that cos is positive on 1st and 4th quadrant