help-10

[static beacon]

Where

Evaluate the double integral of (x² + y²) over the region R, where R is the area inside the circle x² + y² = 4 but outside the circle x² + y² = 1.

[stoic breach]

Can a helper pin this question?

The region R here is a ring shape (annulus).

Can you identify the inner and outer boundaries?

[dense yoke]

(in the future, please lead with the question so that the bot pins it and helpers can start work immediately.)

[obtuse pebble]

@static beacon Has your question been resolved?

Channel closed

Closed by @static beacon

Use .reopen if this was a mistake.

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[zenith vale]

how can i proceed

[stoic breach]

Have you tried square those equations up?

It would be a good move to determine a function's formula.

[zenith vale]

like both side square

[stoic breach]

Yes.

[zenith vale]

it was written in question that i need to find the intersection

i got the point of intersection

i need to find the equation of locus

but i will try ur way

[stoic breach]

For example, $x\cos{\theta}+y\sin{\theta}=a$ can be written as: $(x\cos{\theta}+y\sin{\theta})^2=a^2$

[warm shale]

Mercury.

[zenith vale]

alr

should i delete all the stuff

[stoic breach]

You got the point of intersection, but the question is asking, what shape is the function.

[zenith vale]

and redo it again

?

[stoic breach]

No need to, you can just make a blank space below and try second way.

Then you can compare your way and my way to see the differences, because it doesn't look bad for me.

If you got it, feel free to update it here and ping me!

[unreal musk]

(are you thinking of how to simplify the expression for x that you have?)

[zenith vale]

i got it

[stoic breach]

Correct!

After that by adding those 2 equations, seems right to me.

[zenith vale]

here is the whole solution

let me know if it is correct

[stoic breach]

Yes, well done!

I got the shape circle too.

[zenith vale]

sorry for my bad handwriting

[stoic breach]

No, it is magnificent

[zenith vale]

thank u

i will ask again when needed

[stoic breach]

No worries, feel free to do so!

[zenith vale]

thanks @stoic breach @unreal musk

is my previous solution wrong

or is it harder

[stoic breach]

Let me check it again.

[zenith vale]

to do that way

[zenith vale]

thisis

[stoic breach]

Hmm, from what I can see, that is not wrong, but it is for "hard mode".

[zenith vale]

alr

[stoic breach]

You picked right the hard part, but logically correct.

[zenith vale]

yeahh its hard to graph those points and find the locus

thanks i am closing this now i will open again if i needed

[stoic breach]

And at that last part just substitute in $1 - \sin^2 \theta = \cos^2 \theta$ and you are done!

[warm shale]

Mercury.

[stoic breach]

Over here.

[zenith vale]

lemme see

ohh

then we get x

[stoic breach]

Correct, it should give a beautiful solution.

[zenith vale]

x = a - bsintheta

[stoic breach]

Wouldn't it be $x=a\cos{\theta}+b\sin{\theta}$?

[warm shale]

Mercury.

[stoic breach]

I think you missed a plus sign?

[stoic breach]

It should be this.

[zenith vale]

there is minus here

can anyone tell me what does mean touching y-axis at the origin

[glossy basalt]

i think that means the circle pass through y-axis at (0,0)

or just basically, passes through origin

[zenith vale]

so

[glossy basalt]

but "touching" in this context sometimes has another meaning

[zenith vale]

something like this

cuz it needs to pass through

2,1

[glossy basalt]

which means just passes through y-axis "at one point"

[stoic breach]

Biscuity is correct.

[stoic breach]

Can you pin this message Biscuity?

[glossy basalt]

so, something like (I'll tryna draw)

[stoic breach]

Thank you Biscuity!

[glossy basalt]

something like this

but for Multiple choices, there's another way to tackle this question

do tell if you need more help😁 @zenith vale

[zenith vale]

hmm

[zenith vale]

yes i did that

@glossy basalt

[glossy basalt]

nice!

[zenith vale]

i dont know if this correct

[glossy basalt]

check B
again

[glossy basalt]

not yet correct

[zenith vale]

ohh yeahh

i messed up

similarly i this one

can u check this one too

[glossy basalt]

I'll check now

[stoic breach]

I don't think none of those is the correct option.

[zenith vale]

yes

i fixed it

[stoic breach]

Recall the circle formula: $(x-a)^2+(y-b)^2 = r^2$.

[warm shale]

Mercury.

[stoic breach]

Oh, what was your final solution?

[zenith vale]

b

is correct

since 2,1 is satisfying that equation

[stoic breach]

Correct!

[glossy basalt]

did you mixed up b and c in the last part?

[stoic breach]

Agree, b is not correct.

[zenith vale]

c is correct

option

on that one

i checked both points

first i checked the -2,0

then only b and c were satisfying

then i checked 0,-2

[stoic breach]

Correct.

But have you checked the case (0,-2)?

[zenith vale]

i am doing this one

[stoic breach]

That's the difference between b and c.

[zenith vale]

yes

[stoic breach]

What would it be then?

[zenith vale]

u can see

in the solution

[glossy basalt]

oh

it's me that mixed up

[glossy basalt]

and yes, c is the answer

[zenith vale]

for this i simply put 1,2

on the options

got b satisfied

[stoic breach]

I do not think so.

Since the circle passes through the point (1,2), which is in the first quadrant, the center of the circle must also be in the first quadrant, right?

And when a circle touches both the x and y axis, the distance from the center to each axis must be equal to the radius r, if you see.

Then, recalling the circle formula $(x-a)^2+(y-b)^2=r^2$, we have:

[warm shale]

Mercury.

[stoic breach]

$(x-r)^2+(y-r)^2=r^2$

[warm shale]

Mercury.

[stoic breach]

Now can you expand it and solve for r?

Hope this lights up some ideas.

[zenith vale]

hmm

so my solution was wrong

[stoic breach]

Yes, logically.

But, let's try again!

[zenith vale]

ohh

so we need to put r=1

so that we can get the options

@stoic breach can u tell me if a circle is passing through a point why is it not the solution of that question

[stoic breach]

why only r=1?

[stoic breach]

What do you mean by this?

[zenith vale]

lets a circle is passing throuh a point that point should satisfy the equation

[stoic breach]

From here, since the circle cuts point (1,2), subs it in x and y.

[stoic breach]

Ah yes, please do so.

[zenith vale]

we can get radius

and then we can get equation

[stoic breach]

Correct.

Now you got $x^2+y^2-2rx-2ry+r^2=0$, let x=1, y=2, we have?

[warm shale]

Mercury.

[zenith vale]

@stoic breach

[stoic breach]

Correct.

Now let's solve the quadratic equation.

[zenith vale]

either use formual

or factorisation

[stoic breach]

Factorisation would be nice.

[stoic breach]

Right.

Now we have two cases.

Either r=1 or r=5.

Now can you subs r=1 and r=5 respectively into the original equation?

[stoic breach]

Correct.

Now let's compare them to the multiple choices.

Which one matches them?

[zenith vale]

lemme check

the first option

the first option matches it

its correct

[stoic breach]

Well done!

Q.E.D. that one.

[zenith vale]

what is QED

[stoic breach]

Quod Et Demonstratum - As desired.

[zenith vale]

can u help here

what to do

[stoic breach]

Completing the square.

[zenith vale]

i know that r^2 = f^2 + g^2

[zenith vale]

OHH

i gotcha

thanks for the hint

[stoic breach]

No worries

[stoic breach]

Looks right.

[zenith vale]

i dont know why probability question is dropped in the series of circle questions

[stoic breach]

Could be a mixed test, i do not certain about this.

[hushed bear]

u need help with that prob question ??

[hushed bear]

u can verify with the options

ig

[hushed bear]

check if the 2 points lie on the circle

[zenith vale]

is my diagram correct

[zenith vale]

i know

[hushed bear]

yeah

[stoic breach]

Looks correct.

What was your final answer?

[zenith vale]

is this correct

[hushed bear]

umm

the second equation is h+k = 7(from the circle equation)

everything else is correct

[zenith vale]

.close

[obtuse pebble]

Channel closed

Closed by @zenith vale

Use .reopen if this was a mistake.

[stoic breach]

Looks fairly right to me, OP.

[hushed bear]

28/4 is 7 they wrote 6, remaining all is correct ig

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dusty relic]

i was doing this and when I went to look at the answer

my answers were flipped around and I don't get it

[deep kraken]

If cosx =-1/5, what does it says about the quadrant?

[deep kraken]

,rcw

[dusty relic]

my cos^-1 was 101.5 but my teachers was 78.5

and I don't get it cuz we did the same thing

[deep kraken]

That is fairly strange, since it should be in 2nd and 3rd quadrants...

[dusty relic]

oh..

I thought I did it right for once

[dusty relic]

how the 2nd

(I don't get the A but ik it means all)

[deep kraken]

Cos is negative right

Then either 2nd or 3rd quadrant cos is not positive

[dusty relic]

oh

how did my teacher get the 1st quadrant then

cuz I thought it was the first aswell

[dusty relic]

I sorta get that

[stoic breach]

Hmm, but having the point there on first quadrant doesn't seems logic to me (Your teacher's answer).

But let me do a quick look.

[round nova]

urs i think is right..

yeah cos(x) = -0.2 is defeintly 101.5 what??

how did ur teacher get 78??

[stoic breach]

Yours seems correct...

It is in the form of 360n +-101.5 to be exactly

[round nova]

the only possible angelts are 101.5 and (258 i belive?)

[stoic breach]

Correct point.

[dusty relic]

mines also the first quadrant tho

[round nova]

no cos is impossible to be negative in first quadrant

[stoic breach]

No, that is 2nd and 3rd.

[round nova]

https://tenor.com/view/matematica-gif-7322246

[stoic breach]

I believe that is wrong.

[round nova]

look at this gif here^

[round nova]

(cosine is width)

[stoic breach]

-# Good gif by the way.

[dusty relic]

oh

so I am wrong

I got 1 and 3

[round nova]

notice how its only negative when its on the left?

[stoic breach]

Indeed, and maybe your teacher too.

[stoic breach]

No, cos = -1/5 here.

[round nova]

ur first answer was correct..

[dusty relic]

that's correct?

[round nova]

do u understand this kxro? this is really helpfully to understand btw^^

[dusty relic]

kinda I think

cos is width

tan is height

sin is idk

[round nova]

what is sin? what do u know is sins defention?

[dusty relic]

is tan not going up and down??

[dusty relic]

hell nah

[round nova]

sin = opp /hyp right?

[dusty relic]

ohh

yes

[round nova]

look here which side is (opposite) to the angle?

[dusty relic]

tan

if that's what you mean?

[round nova]

..

[dusty relic]

I'm slow

[round nova]

(ignore the yellow line)

[dusty relic]

opposite??

[round nova]

here

[round nova]

which side is oppoiste to the angle?

[stoic breach]

Just focus on the sine and cosine here specifically, the tangient one is just the derive of sine and cosine.

[dusty relic]

adjacent?

no

tell me😔

[round nova]

okay

i want u to open ur fingers like so ✌️

and image a line connecting the tips of them

notice how when u make the angle bettween ur finger bigger or smaller it affects how long that line is?

[dusty relic]

yes

[round nova]

SO thats is what (a little oversimplfied) bassicly sine means!

it bassicly says that when u have angel the side opposite to it grow porportianitly to that angle makes sense?

[dusty relic]

I think

ohh

like

opposite of the angle

[round nova]

YESSSS

[dusty relic]

when I move my fingers further

the line becomes longer

[round nova]

YESS

[dusty relic]

which means bigger angle

YESS

[round nova]

GDJGHJ WELL DONEE!!

[dusty relic]

TYY

[round nova]

okay so knowing this now look at this!!

https://tenor.com/view/matematica-gif-7322246

[stoic breach]

Pluto you are helpful!

Congrats!

[dusty relic]

pluto the goat

become a planet again pls

[round nova]

WAIT WHA-

[round nova]

... wdym i am a

planet

[round nova]

so notice how in the first and second quadrant the hieght is postive right?

[dusty relic]

everyone else that's told me the stuff about trig equations ( functions part mainly) I don't get them

your example helped more

[deep kraken]

Congrats!!

[dusty relic]

i had to send it again I don't like scrolling

it makes me lose focus ish

[dusty relic]

I think?

how it the left positive tho

[round nova]

look at the red line!

[dusty relic]

ohhh

[round nova]

even when u have it so the traingle is on the left its hieght is still Upwards right?

BUT in the 3rd and 4th quadrant its going Down!!

And so that means?

[dusty relic]

I'm still processing

im slow sry

[round nova]

its okay tyt!!

[dusty relic]

it's negative?

[round nova]

YES!

i want you to imagne it urself

make ur hand into fists

and make one the center of a circle and the other any other points on the circle

and start to rotate ur hands

and think about hieght when is the hieght upwards and when is the hieght downwrds

[dusty relic]

do I rotate both

or just the other point

[round nova]

nope one is the center so doesnt move

[dusty relic]

yeah I thought that

[round nova]

(think of it as planet earth orbiting the sun)

[dusty relic]

when my hands at the top it's always positive

when it's below it's negative

bc the height

[round nova]

yes!!

so when ur hand at the top from waht angle do u have

u have from 1 - 180 right?

but after u cross 180 its all negatives

does that make sense?

https://tenor.com/view/matematica-gif-7322246

[round nova]

well done btw!!

[dusty relic]

tyyy

[round nova]

?

[dusty relic]

like 180 up/down?

[round nova]

notice how this circle only exsists between angels 0 just looking straight to the right) and angle 180 looking to the left

[round nova]

(hint u can see the exactly Angle in the gif at the top at any moment in time)

[round nova]

and then after 180 degrees (so u are looking left u wuld start looking left and EVER so slightly downwards

[dusty relic]

then it goes negative below that black line

[round nova]

which would give us negative hieght

[dusty relic]

yes

[round nova]

so does it make sense why now sin is neg in quadrant 3 and 4?

now i want u to image Cosine (which is the width)
(so bassicly when the width is on the right ((remeber center is 0)) we say that the width is postive
BUttt when its on the left We say its Negative

knwing this information i want u to try to derive When cosine would be postive or negative!!

[dusty relic]

cosine is negative on the left??

[dusty relic]

I just took that from what U said here

[round nova]

-# @dusty relic let me know if u need any hints btw!!

[dusty relic]

I may need that hint

[round nova]

YESS!!

[dusty relic]

SOOHO

[round nova]

okay so look at this gif again and focus on width

[dusty relic]

WOOHOO

[round nova]

https://tenor.com/view/matematica-gif-7322246

So do u notice these cordinates on the right and left?

[dusty relic]

no I get that left is negative

[round nova]

look at

[dusty relic]

bc you asked if I need the hint before you said my answer was right

so I thought bc you didn't answer it mightve been wrong

[round nova]

no no i just didnt asnwer cause my intenret was bad oops-

sorry

[dusty relic]

bc left has a negative symbol and right is positivr?

[dusty relic]

dwwww

[round nova]

YUP!

[dusty relic]

woohoo!

[round nova]

well actually more precisly this is because we are using a graph!!

and yk how on graphs when u go left

its negative??

[dusty relic]

yes

yes

[round nova]

YES!

and because we have our center at 0, 0

when the angle croses 90 we start going more left!

[dusty relic]

wait so are all graphs technically the functions??

[round nova]

anyways now you probably understand when sin or cos are + and -

[dusty relic]

can you test me again😭

I wanna make sure

I have an exam next week and I'm tryna bump up my grade

[round nova]

okays 3rd quadrant!! what is cos and sin?

[dusty relic]

wait im confused again

what am I meant to do

do I do the hand thing

[round nova]

Yes!! but imagne it goes all the way to the 3rd quadrant

and ask urself

am i more left or right from the center?

and am i up or down from the cneter?

and these are ur answers!!

[dusty relic]

so bc 3rd quadrant is tan

do I go up/down

[round nova]

(ignore astc rule for now)

[dusty relic]

oh

uhh

[round nova]

just imagne

[dusty relic]

left and down?

[round nova]

if u had ur hand on the third quarter

and ur other hand was at the center

describe to me where ur second hand is compared to ur main hand (center)

[dusty relic]

the second hand is

down left

[round nova]

YES!

so that means the hieght and width are??

• or - ?

[dusty relic]

NEGAITVE?M

NEGATIVE?

[round nova]

YESSSS!!

[dusty relic]

OHHHHH

[round nova]

now imagne 2nd quadrant!!

i wanan know what hieght is and what width is!!

[dusty relic]

POSTIVE

[round nova]

FOR HEIGHT OR WIDTH OR BOTH?

[dusty relic]

BOTH??

[round nova]

TELL IT TO ME IN TERMS OF LEFT RIGHT UP DOWN AND THEN TRANSLATE

[dusty relic]

UP RIGHT

[round nova]

^^

[dusty relic]

RIGHT IS ALWAYS POSITIVE
UP IS ALWAYS POSITIVE

[round nova]

second quarant!

[dusty relic]

I THINK

[round nova]

-# that is first quadrant

[dusty relic]

OHH

NO LISTEN

whenever I do cast diagram

I think of sin being first

I got confused by everything

second quadrant is:

left up

width-negative
height-positive

[round nova]

YESSS!!

well donee!!!

[dusty relic]

TYY

[round nova]

NOW first QUADRANT

where is ur hand comapred to ur center?

[dusty relic]

up right

[round nova]

SO?

[dusty relic]

both positive

[round nova]

YES!

okay 4th QUADRANT

[dusty relic]

YAYYY

down right
+width
-height

[round nova]

YESSS!!

OAKY OKAY NOW OUR LAST STRETCH

YK HOW TAN is = OPP/ADJ?

[dusty relic]

YES

[round nova]

AND YK HOW SIN = OPP/HYP
AND COS = ADJ /HYP

[dusty relic]

yes

YES

[round nova]

SO WE CAN SAY THAT TAN = (OPP/HYP) / (ADJ/HYP)

AND SINCE BOTH HAVE HYP

WE CAN JUST DO

[meager trench]

-# sorry for butting in pluto is such a hype squad i love this LOL

[round nova]

TAN = OPP/ADJ

does that make sense??

[dusty relic]

wait I need to process this again

[zenith vale]

why bro is typing everything in CAPS

[dusty relic]

I don't get this

[dusty relic]

it's helpful

and makes it seem like you acc care

[round nova]

i am exicteedd okayy- well iwas anyways ;c

[round nova]

okay okay so so lets explain this!!

if i have 10 * 2 / 6 *2

i can just says that 2/2 = 1 and therfore its (10/6 )* 1

so its just 10/6 right?

[zenith vale]

can i help ?

in trigo triads

[round nova]

yes ofcourse!!

[dusty relic]

ohhh

so like

10 and 6 the OPP/ADJ

2 is the HYP

[round nova]

since this can juse become OPP/ADJ / (HYP/HYP)

and because anything divded itself is 1

we just get opp/adj!

[dusty relic]

yesyes

[dusty relic]

OHHH

what do the arrows mean

[round nova]

ad yk how OPP / HYP = SIN and ADJ/HYP = COS

[zenith vale]

it means u need to look for top to bottom

[dusty relic]

OPP * ADJ
AND HYP * HYP= 1

[round nova]

(well its divide but same thing)

[dusty relic]

do I need to know this in an exam

or is this just clarification

[round nova]

no no u dont dw i am just clarficying how we get from tan = opp/adj

to tan = sin/cos

[round nova]

@dusty relic ^

do u udnerstand this?

[dusty relic]

did I not just explain it there??

sorry if that sounds rude

[zenith vale]

so sin is P/H and cos is B/H and tan is P/B
and cosec is H/P and sec is H/B and cot is B/P

[dusty relic]

is that not the explanation

[round nova]

(well its divide not multiply BUT YES)

[dusty relic]

yeah I meant to say divide

[zenith vale]

@dusty relic u can remember this

[dusty relic]

maybe

[zenith vale]

this will help

[round nova]

OKAY SO NOW we can conclude!! TAN = Sin/Cos

[meager trench]

ive not seen this notation before

soh cah toa up on top

[dusty relic]

I am the notation

[round nova]

@dusty relic makes sense?

[zenith vale]

did u saw it now

is it make sense

to u

[dusty relic]

yesss

[meager trench]

soh cah toa

sine = opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent

[meager trench]

yeah ive just not seem adjacent expressed as b and opposite as p

(sorry for butting in again)

[round nova]

AND SINCE TAN = SIN/COS
AND we know when SIN and COS are NEg or postive KNOw we can also GET TAN IN EVERY QUADRANT!!
So in the 1st quadrant Since everything is postive can uguess waht tan wil lbe?

(pos)/(pos) = ? pos or neg?

[dusty relic]

uhh

wait so everything is positive

tan is negative?

both negative

[fierce ingot]

Pandit bhudri parasad har har bolo sona chandi tolo

[dusty relic]

tf

[meager trench]

mm, not quite

[fierce ingot]

This is a trick to find any trigonometric functions

[meager trench]

positive / positive = positive

[dusty relic]

so

is tan positive

[meager trench]

yep!

in the first quadrant, tangent is positive

[round nova]

yup!!

and now in the second quadrants! can u get both sin and cos

then do sin/cos!

to get tan!

and u can do this for every quadrant!!

https://tenor.com/view/matematica-gif-7322246

[dusty relic]

OMDS I SEE WHERE I WENT WRONG I THINK

[round nova]

does this gif make sense now??

[dusty relic]

I can't explain it now

it only makes sense in my head

[fierce ingot]

Nope eee

[round nova]

-# oh wouldu also like to understand?

[round nova]

oKAY OKAY so YOU KNOW HOW TO GET ALL OF SIN and ALL OF COS RIGHT?

we already did that earlier!!

[fierce ingot]

Bro u wanna do some inverse integral questions

[round nova]

please no

[fierce ingot]

🥲🥲heheheheheh

[round nova]

-# also please no offtopic-

[solar stump]

Bro u wanna just not?

[meager trench]

hey this is a help channel which is specifically intended to help specifically the question asker, sorry if this is kind of crude but please stay on topic or just take this to #discussion or #math-discussion or contribute here!

[dusty relic]

how did we do that again

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on hand center!

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O YES

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other hand circle

we do orbit!!

[dusty relic]

yes ges

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check hieght for sin

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planets n stuff

[round nova]

and cos for width!

[fierce ingot]

Why r u angry

[dusty relic]

she isnt

it's just simple facts

it's literally just interrupting

[dusty relic]

yes yes

[meager trench]

sorry if it came off that way but yeah, its interrupting and not the place to ask LOL

[round nova]

-# please there is alot of channel on the serverrrr just go to somewhere i promise poeple there would reply to you alot more than we do..

[round nova]

okay go for it!! tell me sin and cos in 2nd quadrant!!

[dusty relic]

is the second quadrant the top left

[round nova]

so that would be?

[dusty relic]

-width
+height

so

-cos

+sine

[round nova]

and so sin/cos will be?

(if u cant colsve it think of just any postive / negative number over any postive / negative number depening on ur result ofc
so for example here sin is postive so we can do 1(sine)/-1(cos) ((since cos is neg here)

so that means that tan will be waht pos or neg?

[dusty relic]

so think of it like +sin/-cos

tan is negative?

[round nova]

YES!

OAKY NOW

check 3rd quadrant

something really cool happens

[dusty relic]

it's like how tan= sin/cos

but since we have a negative

it stays

so -tanx

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yes

[round nova]

so what is answer for 3rd quadrant!

[dusty relic]

so

bottom left

-cos
-sin

which means

-cos/-sin = tan

[round nova]

so pos or neg?

[round nova]

YESSS!!

THIS IS WHY 3rd quadrant is CALLED TAN!

does it make sense now??

now now try 4th quadtant!!

[dusty relic]

because

we have a -width and -height

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it is the quadrant where only TAN is postive!

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OHHH

THIS MAKES MATHS INTERESTING

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YESSS

NOW NOW

TRY 4th QUADRANT

[dusty relic]

bottom right

+cos
-sin

+cos/-sin= -tan

[round nova]

YESSSS!

so know you know where the "ASTC" rule comes from!!

[dusty relic]

OHHH

[round nova]

THIS IS BTW WHY

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WDYM

[round nova]

^^

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^^

[dusty relic]

I genuinely forgot about that..

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"cos is impossible to be negative in first quadrant"

[dusty relic]

is the first quadrant sin?

bc when you do the cast diagram

sin is top left

[round nova]

first quadrant is top right..

[dusty relic]

oh

[dusty relic]

it's just the way I've been perceiving it

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here!

look!

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so A is first

BC YOU GO HAVE BOTH POSITIVE

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we start Looking to the right and we start turn left that is how we number each quadrant

[dusty relic]

OHHHH

[round nova]

YESSSSSSS!

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SO ONLY 2,3,4 CAN BE NEGATIVE

NO

2,4

[round nova]

FOR TAN YES!

https://tenor.com/view/matematica-gif-7322246

[dusty relic]

OHHHH

[round nova]

LOOK AT TAN LINE HERE

[dusty relic]

is it the video or pic

cuz it's not moving anymore

[round nova]

NOTCE HOW IS 2nd AND FOURTH ITS DOWN?

oh wait lemme send u the vid

soeme sent it earlier!

[round nova]

oaky yeah look at it!

notice how TAN line is DOWN when its 2nd ANd 4th quadrant!!

does that make sense now?

[dusty relic]

but it isn't down in the 2nd?

[round nova]

look at the yellow line

yellow line is tan

[dusty relic]

i was like looking at red

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red line is SIN

red line is hieght of traingle

cos is Width of traingle

[dusty relic]

wait so what is tan

[round nova]

tan is Hieght/width

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ohh

[round nova]

This is why its areally long line because it appreoaches stuff like 0.9999/0.001

because as sin (hieght) gets taller

cos (width) get smaller

[dusty relic]

so tan cant be negative either?

[round nova]

no tan IS negative! at the 2nd quadrant and 4th quadrant jsut like we calculated earlier!!

remeber tan = sin/cos

[dusty relic]

yes

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(Down means neg)

although dont include tan in ur hand orbit ismulation thingy

cause it will confuse u

i am just explaning the gif further!

[dusty relic]

hand orbit is only

cos son

sin

[round nova]

YUP!

[dusty relic]

ahhhhhhhhh

[round nova]

this is why when i saw cosx = -0.2 IK it had to be in either 2nd or 3rd quadrant!

Because it is IMMPOSSIBLE for the cos (wdith) to be negative in the first quadrant!!

does that answer ur question now?

[dusty relic]

yessss

wait so was i right? or

I forgot what I put tbh

[round nova]

ur cos was 101.5

and that is correct!

[dusty relic]

so I would get full marks for that question??

[round nova]

,w cos(101.5)

,h

[warm shale]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[round nova]

oaky well cos on my calc for (101.5)

gives me -0.19993

which is bassicly -0.2

[dusty relic]

ahh

[round nova]

-# if ur proffesour realizes they are wrong then yes..

ALTHOUGH

FUNFACT-

[dusty relic]

YES

[round nova]

there is actually TWO possible angels here!

if one of the is 101.5

I WANT U TO TRY To think AT WHAT OTHER ANGLE

could we possible get a width of -0.2

also u dont have to tell me the exacl angle just the quadrant!!

[dusty relic]

wait

is -0.2

tan

bc it's negt

[round nova]

nope..

[dusty relic]

idk

I don't get it

[round nova]

-0.2 describes the distance of a line to the left

wait let me draw -0.2 for you

so cos(x) = -0.2 that means that whatever angle is in cos it gives us a width of 0,2 (the green line)

[round nova]

notice how the red line for example is from point 0,0 and -0.5 FOR example!

[dusty relic]

yeah

[round nova]

OKAY SO SO

Q

IF U HAD TO VISuALIZE

101.5

HOW WOULD U VISUALIZE IT

JUST A LITTLE OVER 90* right?

[dusty relic]

what's the * meant to be

[dusty relic]

yeah

[round nova]

degrees-

[dusty relic]

ohhh

[round nova]

discord isnt lettmeing send images ugh..

THERE WE GO

[round nova]

OAKY SO NOTICE HOW AT 101 DEGREES NOTICE HOW THE WIDTH IS A LITTLE LINE TO THE LEFT (NEG)

THAT IS BASSICLY THE Q

THE Q ASKS AT WHAT ANGLEEE DO WE HAVE A LINE OF WIDTH -0.2

does that make sense? @dusty relic

[dusty relic]

one seccc

OHH

ues

so like

when the width is -0.2

what is the angle

[round nova]

WELL-

you already solved it!

[dusty relic]

101.5

[round nova]

101.5

YUP!!

[dusty relic]

SO THATS WHAT THE INVERSE IS?

[round nova]

THAT IS X IF U DO COS(101.5) U GET -0.2

[round nova]

wdym by inverse-

[dusty relic]

cos^-1

[dusty relic]

ohhh

[round nova]

OKAY OAKY BUT LET ME SHOW U SOMETHING REALLY COOL

[dusty relic]

YES

[round nova]

LOOK ATTHIS VIDEO

AND ASSUME POINT 0.2 IS KIND OF LIKE A FRIEND WE SAY HI TO EACH TIME WE PASS

IN A FULL ROTATION (360) DEGREES HOW MANY TIMES WOULD WE SAY HI?

[dusty relic]

1?

[round nova]

look at the videoooo-

[dusty relic]

or is it both -0.2 and 0.2

[round nova]

NOPE

just -0,2

okay oaky

let me expalin it this way

[dusty relic]

4?

bc 4 quadrants

[round nova]

lets say you walk from home to school everyday-

[round nova]

nope-

[round nova]

^^

[dusty relic]

damn

[round nova]

dont just guess..

guessing = le bad ;c

understanding = le goooood!!!

[dusty relic]

oui

[round nova]

https://tenor.com/view/le-fishe-au-chocolat-fish-chocolate-gif-276207395680097828

[round nova]

and on ur way u see an old grandpa sitting on his lawn chair in the street

so u say hi to him everyday u see him

now remeberr u have to GO to school and also COME back from school

[dusty relic]

2

[round nova]

how many times do u say hello to him?

YESS!!

SO IF UR HOME IS 0,0

AND SCHOL is (-1,0)

HOW MANY TIMES WOULD U PASS POINT -0.2

[dusty relic]

2??

[round nova]

YESSS

[dusty relic]

OOO

YOU MAKE MATHS FUN

AND INTERESTING

[round nova]

THIS IS WHY cos(x) = -0.2 SECRETLY HAS 2 SOLUTIONS!!

YES 101.5 IS CORRECT (and u probably dont need to know the 2nd solutiion for now BUT)

LEMME SHOW U SOMETHING

[dusty relic]

YES

[round nova]

SO NOTICE HOW IF WE WAIT UNTIL HIEGHT GOES DOWARDS WE CAN GET A POINTWHERE WE ARE -0.2 TO THE LEFT

SO THIS IS the 2ND TIME WE WILL GET -0.2 WHEN WE ARE RETURNING

CAUSE IF U NOTICE WIDTH GOES FROM 0 -> (-1) THEN (-1) -> 0 AGAIN

[dusty relic]

OH YEAHHH

[round nova]

SO ALTHOUGH 101.5 IS THE FIRST TIME WE MEET THE POINT (-0.2) ON THE WIDTH

WHILE COMING BACK WE ALSO MEET IT

[dusty relic]

BC IT GOES TO SCHOOL THEN GOES BACK HOME (WTV THE REFERENCE WAS)

[dusty relic]

OO

[round nova]

AAND BECAUSE WE KNOW THE ANGLE DICTATES HOW (WIDE) WE ARE THAT MEANS THAT THE ANGLE THAT MADE THE FIRST TRAINGLE (-0.2) WIDE IS ALSO THE SAME ANGLE (SINCE IT THE EXACT SIAM TRAINGLE JUST FLIPPED) SO THE ANGLE IS ALSO FLIPPED

[dusty relic]

OHHH

THAYS COOL

[round nova]

SO FROM THIS IMAGE WE CAN FIGURE OUT THAT SINCE OUR ORIGNAIL ANSWER WAS FROM THIS TRAINGLE

CAN U GUESS HOW MUCH X IS IF WE KNOW THAT THE ENITRE ANGLE IS

IF WE KNOW GREEN IS 101.5 CAN WE GET X?

((thinkabout it u got this))

[dusty relic]

UMM

180-101.5??

[round nova]

why 180?

[dusty relic]

no I'm thinking of bearings

180⁰ in a triangle

[round nova]

okay

here this might help

look at this

[dusty relic]

101.5-90

[round nova]

YESSSS!

[dusty relic]

THIS REMINDS ME OF A BEARING QUESTION EARLIER

OOO

[round nova]

AND SO THE ANGLE LEFT 11.5

AND HERE IS THE COOL PART YK HOW THIS ANGLE IS OPOPOSITE TO THE WIDTH HERE

DO U KNOW WHAT SIN(11.5) WILL GIVE US NOW?

LOOK

[dusty relic]

OK IM BACK

[round nova]

WELCOME BACKKK!

[dusty relic]

0.19

0.2

WAIT HAT

WHAT

COOLLLLL

[round nova]

YESS

BECAUSE THAT GIVES US THE ACTUAL WITH

BUT ITS POSTIVE BECAUSE REMEBER WE ARE ONLY DOING 11.5

NORMALLY 11.5 IS IN WHAT QUADRANT

WE KNOW 1-90 IS FIRST QAUDRANT SO

[dusty relic]

1

[round nova]

YES SO THATS WHY SIN GAVE US A POS OUTPUT

MAKES SENSE?

[dusty relic]

ES

YES

man fuck you too

[round nova]

<@&268886789983436800>

-# sorry for ping

[dusty relic]

mods ban him- nickeh30 ref

[round nova]

OKAY SO SO

[dusty relic]

YES

[round nova]

NOW HERE IS THE HARDDD PART-

[round nova]

SO KNOW THAT WE KNOW x = 11.5 CAN U TRY TO GET THE TOTAL ANGLE HERE AS IN THE ANGLE OF THE GREEN PART

BECAUSE IF WE PUT THAT ANGLE INTO COS

IT SHOULD GIVE US ALSO -0.2

OKAY SO SO LETME ASK U

HOW MUCH ANGLE IS IT IF U GO ALL THE WAY TO 3 QUADRANTS?

[dusty relic]

huh

[round nova]

OKAY WHAT IS THIS ANGLE?

[dusty relic]

180

I think

[round nova]

noope think about it

how many 90 degrees angle is it?

[dusty relic]

1

[round nova]

no the green part

[dusty relic]

oh

2

[round nova]

how many 90 degrees are in the green part

[dusty relic]

0

[round nova]

okay wait maybe this maybe be more helpfull

look at this?

how many 90 degree angels does it have?

[dusty relic]

3

[round nova]

YESSS!

(for future refrence each quadrant always has 90 degrees)

SO WHAT IS THE TOTAL ANGLE

[dusty relic]

270

[round nova]

YESSS

KNOWTHING THAT

CAN U SOLVE FOR THE GREEN HERE-

[dusty relic]

uhh

[round nova]

okay lemme simply theimage!

[dusty relic]

ty

[round nova]

so we need to get the pink angle!!

and we solved for x earlier and it was 11.5 !!

So knowing that!!

how do u get pink angle?

[dusty relic]

270+11.5

or smth

[round nova]

why plus?

[dusty relic]

bc were in tan

[round nova]

for refrence here is how 270+ 11.5 would look like

[dusty relic]

258.5??

[round nova]

YESSS!!!

[round nova]

WELL DONEEE

[dusty relic]

BC WE TAKEAWAY

[round nova]

YESSS

[dusty relic]

SINCE WERE IN TAN

[round nova]

OKAY NOW NOW

[dusty relic]

YES

[round nova]

DO COS(258.5)

ON UR CALCULATOR

[dusty relic]

i swear

this is gonna shock me

it's gonna be like 0.2

WHAT

[round nova]

THIS IS WHY I SAID THIS ^^

[round nova]

YES ITS ALSO -0.2

SO 258.5 IS THE SECRET SECOND ANSWER TO THIS QUESTION

ALTHOUGH U PROBABLY DIDNT TAKE THIS YET SO DONT TELL ANYONE

[dusty relic]

We've been talking about this for 2 hours now...

[round nova]

DO U GET IT NOW??

[dusty relic]

aYesss

YESS

[round nova]

well yeah we are donee!!

sorry for the time btw

[dusty relic]

ITS ALL GOOD

YOU HELPED SM

[round nova]

DID U UDNERSTAND THOUGH??

[dusty relic]

YEAHH

BTWW

ANOTHER QUESTION ABOU IT

[round nova]

OH TELL ME

[dusty relic]

YK WHEN I GET TO THE CAST DIAGRAM PART

CAN I USE THE HAND ORBIT

[round nova]

WDYM BY CAST DIAGRAM

AS IN ASTC

TO CHECK FOR POS / NEG ON SIN AND COS?

[dusty relic]

YEAH

[round nova]

YES U CAN!!

ACTUALLY FUNFACT TRY IT IF UAHVE THE TIME AND COMPARE IT TO ASTC!! AND U WILL NOTICE ITS THE SAME!!

[dusty relic]

Oo

[round nova]

THE HAND ORBIIT IS WHAT MADE ASTC

[dusty relic]

OHHH

[round nova]

LITTERLY ASTC IS MADE FROM THE FACT THAT NUMBERS ARE POS AND NEG ON UP AND DOWN AND LEFT AND RIGHTACORDING TO WIDTH AND HIEGHT

THIS IS THE REASON IT IS THE ORIGIN

YES ALSO U CAN SOLVE A QUESTION AND COME BACK!

[dusty relic]

OHHHHHHH

[dusty relic]

do you want me to DM???

so I can close this so others can get help?

[round nova]

for math questions ehh prefferbly not because here other helpers can see and help if i cant help (or if i make a mistake or if i dont understand) or i if i am gone!!
BUT if u wanna explinations on certain topics form time to time u can ask anywhere u like!! here or dms!!

[dusty relic]

oh yeah fair enough

[round nova]

u can close here! and reopen it later ORR u can just open a new one and Ping mee!!

[round nova]

well i really like the comfort of knowing i can always ask out for help from other helpers since iam not perfect at math either!!

[dusty relic]

yeah I totally get that

[round nova]

BUT REGARDLESS FEEL FREE TO DM IF U NEED ANYTHING ANYWAYS I WILL ALWAYS HELP REGARDLESS!!

[dusty relic]

TYSMMM

btw quick question sry

last one

[round nova]

YES YES OFC-

dw i have bee ranting for 2 hours its okay!

[dusty relic]

yk at the start of the equation

I have 7sinx =1 now

so I divide by 7

[round nova]

yes!!

[dusty relic]

do I write it as 1/7

[round nova]

yeah u can!

[dusty relic]

or 0.14

does it matter

[round nova]

up to you it doesnt matter

[dusty relic]

ohh okayy

[round nova]

unless ur prof is extremly strict and prefers it written in acertain way..

[dusty relic]

he isnt

so it should be fine

[round nova]

but this bassicly means that the hieght of the traingle is pos (0.14)

[dusty relic]

bc sin is the height

[round nova]

YESS!!!!

SEE U GET IT NOWW!!

[dusty relic]

SEE I LEARNED

YEAHHHH

[round nova]

YESSSS!!

[dusty relic]

TYSMMMMMM

I APPRECIATE IT LOADS