/sci/ - Science & Math

>>10574070
Use Newton's method and iterate to get the precision you need.
People who have issues with numerical methods don't get far.

>>10574070
>>10574080
Alternatively, just Taylor expand sin(x), add x and subtract 1. Then evaluate at zero. Probably better that Newton's method.

>>10574070
I'd go to this link: https://www.wolframalpha.com/input/?i=sin(x)+%2B+x+%3D+1

>>10574070
Dealt with this one recently (solving Kepler's equation for eccentric anomaly).

1=x+sinx
x=1-sinx
x=1-sin(1-sinx)
x=1-sin(1-sin(1-sin(1-sin(.....

And so on. You can have Excel do it just by circular references and get a numerical solution. Close enough for my purposes, anyway.

>>10574080
Newton's method is trial and error in essence.
I don't have problems with numerical methods, my question is just if there is anything else. It is a simple expression, after all.

>>10574096
It's more sophisticated that straight trail and error. I actually don't know if there's any other way. Bump for an answer.

>>10574100
It's more sophisticated, but he's right in that it boils down to guess and check. There are several other ways of finding a numerical solution, but they're all roughly similar - different processes that can get you an answer arbitrarily close to the true value, but as far as I know there is no know closed-form solution to this problem.

>>10574070
https://en.wikipedia.org/wiki/Lagrange_inversion_theorem

>>10574110
>but as far as I know there is no know closed-form solution to this problem
No, because 1 isn't special as an angle, such as a rational multiple of pi.

>>10574134
This is the closest to a closed-form you can get.

>>10574070
Take the MacLaurin extension thingy a couple of terms and do an approximation

>>10574149
this.

>>10574096
>>10574110
Neither trial&error nor guess-n-check converge to a result,
whereas the Newton-Raphson algorithm usually does.

>>10574070
After you factor the x you end up with x = 1/(sin + 1)

>>10575632
b8

"Closed form" is a state of mind.

Just assign a symbol as being the solution to the equation, and you're done.

Better yet, assign a function f(y)=x, where sinx+x=y. Then the solution is just f(1).

>>10574100
>Amphibian expert Jodi Rowley, a senior lecturer in biological sciences at the University of New South Wales, threw further light on the story, pointing out on Twitter that the male cane toads were in fact trying to mate with the python.
wtf

sin x = x for small angles x.
Therefore we have x + x = 1.
x=1/2

>>10575640
Baited

>>10574080
this

>>10575691
unfortunately 1/2 is not a small angle

>>10574070
take derivative of both sides and use that additional information to solve the original

i would plot graphs for 1-x and sinx and try to calculate approx values of x where the two curves meet. i am also dumb.

>>10575783
or just graph y=sinx+x and y=1 and find intersection

>>10575677
sin doesnt have a closed form either

>>10574070
x=0

>>10575795
Exactly. But if a solution could be written down in terms of trigonometric functions, or their inverses (or logarithms, or square roots, etc.) everyone would be perfectly happy accepting that as "closed form", because of some arbitrary distinction.

>>10575778
cos x = 0
x = 1/2

interesting.