/sci/ - Science & Math

>>12785798
Yeah, but its a pain in the ass and my trig is rusty

>>12785798
Is transcendental, get fukt freshman don’t make me do ur homework

>>12785798
and y would i want to do that?

>>12785798
y = x - 1/2 sin(2y)

>>12785798
[math]y=x-\frac{1}{2}\sin(2y)[/math]

>>12785816
>Is transcendental, get fukt freshman don’t make me do ur homework

I know it's transcendental, but certain type of transcendental equations do have solutions in term of defined functions.

It's not homework. I'm an engineer at a multinational corporation. I've implemented a photographic filter to identify line widths. The filter is s convolution with a disc. When the line width is near the diameter of the disc I get an error. I've been using a linear function to transform back to width, but I'm interested if there's an easy way to get more accurate results.

>>12785868
>do the work I’m getting paid for for me
No.

>>12785920
>>do the work I’m getting paid for for me
>No.

As if you could solve it anyway. There were once very intelligent people who would give me very insightful answers with little to no effort from themselves. You clearly aren't who I'm looking for.

>>12785798
>tiktok

>>12785957
>do my homework or u r not smart enough
This didn’t work on me in 4th grade and it won’t work now, absolute brainlet. Fuck off

>>12785991
>>do my homework or u r not smart enough

I'm not asking you to do my work. I know you can't. What's 1+1? Did I just ask you to do a bunch of work again? So sorry. There are some people who lurk here who seem my question as 1+1. You are not them

>>12786022
K good luck finding someone to do your work for you faggot. I’m excited to see you out on the street begging for gibs because you couldn’t keep a job numerically solving transcendental equations

>>12785868
multinational corporations should be choked to death with tariffs fyi

>>12785957
ok beggar fag go beg somewhere else then

faggot. hint:

[eqn] siny cosy = y^2 j_0(y) j_{-1}(y) [/eqn]

>>12786072
>OP understands Bessel functions
Pearls before swine, anon.

>>12786085
it's like presenting a babe to a virgin. He wouldn't know what to do with it.

>>12786050
No they shouldn't, they should just be taxed for the land and resources they take up (if none, fuck off).

>>12785850
Nigga, what?

>>12786022
>What's 1+1?
[math]1 + 1 = 2[/math]
Don't thank me though, it really is no difficulty on my part.
Oh, and you don't have to tell your boss, lol, it's our little secret, my gift to you.
Now go out and profit from this knowledge fren, you deserve it :)

>>12785798
x=Im(1/2e^i2y+iy)
z=e^i2y+2iy
e^z=e^2iy e^(e^i2y)
w=a*e^a
a=W(w)=e^2iy
y=ln(W(e^(z)))/2i

>>12786227
based complex analfag

>>12786227

This is what I was thinking of. What is the W function called again?

>>12786072

I'm op and I don't see how this is helpful.

>>12786339
if you don't see how it's helpful, then you're clearly too stupid to handle this question. Quit your job and let a real mathfag handle it.

>>12786343
>if you don't see how it's helpful, then you're clearly too stupid to handle this question. Quit your job and let a real mathfag handle it.

Like I said. I use a linear approximation because the disc is 3 times larger than the line width. It's 99.9% accurate. I'm just curious if a super genius here can get me the last 0.1% with very low computational complexity.

>>12786343

It's still transcendental. You haven't solved anything.

>>12785798
I'm a university student and this question has me baffled. I have no idea how to solve this. Can someone point me in the right direction?

>>12785850

This is the best answer so far. Just iterate a few times and you get the eigenvalue.

>>12786382
Not all equations can be solved analytically. Also OP is a mouthbreather

>>12785798
arcsin(2x)/2/2=y

>>12786331
Lambert W function or product log
Its the inverse of xe^x

>>12786624
Hmm since I'm a dumb college freshman I decided to graph it as a function of y and pic related is what I got. How do I solve this equation without a calculator?

>>12786227
Wait how does this solve for y in terms of x? The final answer is y in terms of z, whose definition is independent of x.
z = e^i2y + i2y, but x = 2Im(z). I'm a bit confused here

>>12786109
put the thing the hole. doesn't really matter which hole as long as I get my fill.

you can use an inverse trig function for small values.

>>12785868
uze a zeries ezpanzion if you're zufficienzly cloze to ze zingularitzy

>>12785868
>using a linear function to transform back to width
surely you can come with a smart alternative to this

>>12786898
>uze a zeries ezpanzion if you're zufficienzly cloze to ze zingularitzy

There's no singularity

>using a linear function to transform back to width
>surely you can come with a smart alternative to this

It needs to work on a billion nimbers in a few seconds. I've done a fourier series, but it wasn't converging fast enough to be useful

>>12785798
Taylor it and calculate the zeros?

>>12786710
That would be a good example of when you can use my favorite technique of finding solutions, "just look at the graph"

>>12786710
Graph the right hand side and see where they intersect. Those are solutions.

>>12786710
Err. Left hand side. >>12788548

is that it? (pic related)

>>12786114
If a multinational business only makes a profit by arbitraging labor and environmental laws, then they should be tariffed out the door by any country that values its own sovereignty. If they provide anything of actual value that is generated multinationally for reasons unrelated to legal arbitrage, then they should be welcomed.

>>12785850
>>12785851

Iterate a few times the equation:

[math]y_{n+1} = y_n - \dfrac{\frac{1}{2}\sin(2y_n)+y_n-x}{2\cos^2(y_n)}[/math]

Start with [math]y_{0} = x[/math]
To get a close approximation as:

[math]y \approx x - \dfrac{\sin(2x)}{4\cos^2(x)}[/math]

>t. engineer

>>12788712
>approximation
Fuck off, exact answers or gtfo

>>12788712
what a gay approximation. sin(y) ~ y - y^3/6 is a far better approximation.

>>12788712
>he cant even simplify
[eqn] y \approx x - \frac{\tan x}{2} [/eqn\

>>12789767
You can neither tex nor simplify

>>12789753
you can iterate to arbitrary precision, retard

>>12785798
Arcsin(x)=-2y+y
-arcsin(x)=y
Yw

>>12786227
complex analysis once again proving its superiority

>>12788271
>There's no singularity
any point with special behaviour is a singularity you numpty

Yeah don't feel like it though

>>12788570
Test it. Why do you need me to tell you if you’ve found the answer? Numerically solve the zeroes and see if they match with the graph.

>>12790163
Why introduce another transcendental function? Just use a Taylor polynomial for sine and extract roots numerically.

>>12785798
it's a nondecreasing function since its derivative is 1+cos 2x which is always nonnegative, so just do the simplest iterative algorithm to approximate the solution

>>12785798
just solve for lim(2y) goes to 0, divide the equation by 2y, use sin(2y)/(2y)=1 and call it a day.

>>12785798
> literally types this into WolframAlpha to help solve OP's homework