- #1

- 111

- 0

Hi,

I can't come up with a general forumla for x in this equation. Any advice ?

x = y sin(x)

I can't come up with a general forumla for x in this equation. Any advice ?

x = y sin(x)

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter sid9221
- Start date

- #1

- 111

- 0

Hi,

I can't come up with a general forumla for x in this equation. Any advice ?

x = y sin(x)

I can't come up with a general forumla for x in this equation. Any advice ?

x = y sin(x)

- #2

Mentallic

Homework Helper

- 3,798

- 94

- #3

- 269

- 24

Beyond an *analytic* solution, there isn't a unique solution. The function [itex]\mathbb R\setminus \pi\mathbb Z \to \mathbb R[/itex] taking [itex]x\to y=\dfrac{x}{\sin x}[/itex] isn't one-to-one. In fact, there are infinitely many places at which very-close-but-different values of [itex]x[/itex] are taken to the exact same [itex]y[/itex] value.

Last edited:

- #4

epenguin

Homework Helper

Gold Member

- 3,878

- 902

Beyond ananalyticsolution, there isn't a unique solution. The function [itex]\mathbb R\setminus \pi\mathbb Z \to \mathbb R[/itex] taking [itex]x\to y=\dfrac{x}{\sin x}[/itex] is very non-injective. There are infinitely many points at which it isn't even locally injective.

The intersection between those who would ask the OPs question and those who know who know what injective or locally injective must be null or a small number. A reasonable number that include me belong to neither class.

- #5

- 269

- 24

The intersection between those who would ask the OPs question and those who know who know what injective or locally injective must be null or a small number. A reasonable number that include me belong to neither class.

You're right! I'll edit it (though my quoted mistake is immortalized in your post). :)

Share: