- #1

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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)

- 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

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- #3

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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

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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.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.

- #5

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

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