rotation

[shy relic]

When we rorate axis then how does the intercept of a line at axises change?

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[charred hill]

rotate both axes at the same time?

[shy relic]

Yeah

[charred hill]

fix some line Ax+By=C

rotate the axes (in the positive direction) by some angle alpha, then your new axes are lines in the unrotated picture

calculate the intersections with the line Ax+By=C

that's how I'd think about it

alternatively, rotate either axis (possibly by different angles) and repeat the process

doesn't seem that complicated

[shy relic]

This is I am asking how? Steps?

[charred hill]

you do know how to calculate intersection of two lines don't you?

[shy relic]

Yes i know

[charred hill]

1. write out the line equations of the rotated axes
2. set them equal to the green line

[shy relic]

No idea sorry

i only know the rotation matrix

Where we change the coordinate
x'=xcos theta+y sin theta
y'= x cos theta-y sin theta

[shy relic]

Re read your message carefully

[charred hill]

I even drew a picture it doesn't get any more basic than this

the rotation matrix as you wrote it is used for calculating coordinates of rotated position vectors

you are not rotating with respect to the xy axes

you are rotating the axes

it's a different situation

instead of blindly applying formulas you know very little about, try thinking about it instead in more elementary ways

the rotated x-axis satisfies the line equation y = tan (alpha) x

set it equal to the green line in the picture

basic geometry

[shy relic]

Did you read it?

I only expressed my thoughts. And i have written that i only know this for coordinate

@charred hill

tan alphax=(-c-ax)/b

x = (c-btan alpha x)/a

[charred hill]

yes, I'm giving you "steps" to follow and you are giving excuses in return

I'm getting upset because you just namedrop some known formulas that might have nothing to do with it - this in turn shows how little effort you are putting into solving these problems

and it all stems from your lack of basics, no sugarcoating, you will not progress like this and you will definitely not be able to teach people

something has to change

[charred hill]

now solve this

also, the rotated y axis follows the line equation y = tan (pi/2 + alpha) x, again set it equal to the green line in the picture

[shy relic]

it is already put equal to green line and i got this x and y

[shy relic]

same thing to you....now solve this what I solve it yoyu always give me steps in broken pieces which upset me too? there is nothing to solve clearly I have found the point of x,y

maybe you want me to find slope and put the x,y into it and new line equation or something

maybe the coodinates set (x,0)

(0,y)

[charred hill]

1. Don't ever ask me to solve the problem for you.
2. If you don't understand in the first 10 seconds, then think more. Or ask for clarifications.

[charred hill]

close

I have given you two lines (the rotated axes). Your task is to find the two intersection points with the green line. I HAVE to assume you know how to solve a system of linear equations.

[shy relic]

i guess you are not understanding my situaltion

do you thik i am unable to find intersection points?

[charred hill]

yes

[shy relic]

the lines are not clear to me

MIXING

[charred hill]

you rotated both axes by an angle of alpha

what is there to understand

[shy relic]

by y=tanalphax and y=tan(alpha+x)

[charred hill]

the slope of the line is by DEFINITION tan alpha

..again definitions are amazing, aren't they?

[shy relic]

hang on

noo here defnitions are not amazing

[charred hill]

alright, the angle of the x-axis with respect to x axis is 0, yes?

[shy relic]

i know this is what you are saying

y=mx+c

m is angle with x axis

wait a second let me find two

two two two

[charred hill]

m is the tangent of the angle

i.e the slope

[shy relic]

that is not the point

[shy relic]

see this one

what you want here?

[charred hill]

nothing, you've solved the problem

[shy relic]

BRO

if you want me to write intersectin points by first equation

[charred hill]

your task was to find both intersections

you found them

[shy relic]

i only can do for you is i will put back the y into the equation

then why are yo syaing irrrelvalnt things

that i have not fiound

[charred hill]

because you keep talking and that shows me that you don't really understand what you did

[shy relic]

🥺

[charred hill]

or more importantly, why you did it

[charred hill]

touche, and why are you talking about rotation matrices? 😄

[shy relic]

because i wanted to show you the level of knowledge

which you make embarassement like i do not know

[charred hill]

you will not impress me simply by namedropping formulas or famous theorems

[shy relic]

i know things in pieces but do not know how they works exacalty

i am here to fix my mistakes

[charred hill]

I will find it a lot more impressive when you are able to come up with a solution to a problem and explain all your work

no matter if it's complicated or simple math

[shy relic]

okay fine be ready with uniform contunity is on the way

that is why i have not closed yet

because i am reading the topic deeply and will write my answer and make you impress😢

LOOL

[charred hill]

as for uniform continuity, you should really study the topic in detail

limits, continuity and then uniform continuity

[shy relic]

yes i only finished epsilon delta defnition yet

[charred hill]

and definitely study examples

[shy relic]

you teach me each day

but i become upset angry

😭

[charred hill]

and I will continue to do so since I am sympathetic to your situation

but I will not be easy on you

[shy relic]

thanks again for understand my situation

i hope you will not mind my harsh words

sorry

[charred hill]

no need to apologise

I am assuming you want to learn

[shy relic]

yes sir

[charred hill]

but your base education is of poor quality, sadly

[shy relic]

hmm i want to fix them too

[charred hill]

but you have to understand that it takes time

[shy relic]

i have very very little time

that is the reason i am ingufing

[charred hill]

the unfortunate thing is as you have said, you don't have too much of it

but trust me when I say this, what you have been doing is not helping you too much

[shy relic]

]

do you teach such topics too?

[charred hill]

yes, this is analysis/geometry/linear algebra

[shy relic]

does this thing inportant in continuity?

or i skip?

[charred hill]

lipschitz continuity is a special kind of continuity, and it's important in analysis

it's not mission critical for you to know this but it won't hurt either

at least the definition and some examples (and non examples)

[shy relic]

If i have sequence (111111111)

Is it bounded or unbounded?

I guess bounded

Fx<=1

[charred hill]

that's also why I say definitions are important

the answer is obvious if you know what "bounded" means

[shy relic]

yooo

an<=m

so clearly bounded

[shy relic]

+close