Solving cos x = -x: What Does it Mean?

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Homework Help Overview

The discussion revolves around the equation cos x = -x, exploring its solutions and implications. Participants are examining the nature of the solutions and related concepts in trigonometric functions and their intersections with linear functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find a specific solution for cos x = -x and questions the nature of the solution, suggesting it should be a simpler value. Other participants discuss the behavior of the function y = x + cos x and its asymptotic properties, questioning the treatment of infinity in this context.

Discussion Status

The discussion is active, with participants providing insights into the nature of the solutions and the properties of the functions involved. Some guidance has been offered regarding the treatment of infinity in relation to asymptotes, but there is no explicit consensus on the original question regarding the solution to cos x = -x.

Contextual Notes

Participants are navigating the complexities of transcendental numbers and the implications of asymptotic behavior in relation to the functions discussed. There is an underlying assumption that the original poster is seeking a more straightforward numerical solution.

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This is only part of my question and I need the answer to continue, when does cos x = -x? on my calculator it is -.7390... isn't it supposed to be a nicer number ie pi over something?
 
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Nope. I'm afraid that's as good as it gets.
 
does y = x + cos x have any asymptotes? (horizontal or vertical) Vertical = none, the limit as x approaches infinity is infinity? And for negative infinity its negative infinity? is that possible since infinity is not in the domain of cos? or are there also no horizontal?
 
Infinities not numbers. You don't generally consider infinity in the domain of any function. So yes, there are no horizontal asymptotes either.
 
I believe we can show that this number is transcendental over [tex]\mathbb{Q}[/tex].
 

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