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

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In summary, the conversation discusses the values of cos x on a calculator and its relationship to transcendental numbers and asymptotes. It is stated that the value of cos x is not a "nice" number and there are no asymptotes for the function y = x + cos x, as infinity is not considered in the domain of any function. It is also mentioned that the number in question is transcendental over \mathbb{Q}.
  • #1
grapeape
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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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  • #2
Nope. I'm afraid that's as good as it gets.
 
  • #3
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?
 
  • #4
Infinities not numbers. You don't generally consider infinity in the domain of any function. So yes, there are no horizontal asymptotes either.
 
  • #5
I believe we can show that this number is transcendental over [tex]\mathbb{Q}[/tex].
 

What is the meaning of solving cos x = -x?

Solving cos x = -x means finding the value or values of x that satisfy the equation. In other words, it is finding the values of x that make the cosine of x equal to the negative value of x.

Why is it important to solve cos x = -x?

Solving cos x = -x is important because it allows us to find the points of intersection between the graph of the cosine function and the line y = -x. These points have significant applications in fields such as physics and engineering.

What are the different methods for solving cos x = -x?

There are several methods for solving cos x = -x, including graphing, using the unit circle, and algebraic manipulation. Each method has its own advantages and may be more suitable depending on the context of the problem.

Can cos x = -x have more than one solution?

Yes, cos x = -x can have multiple solutions. This is because cosine is a periodic function, meaning it repeats itself at regular intervals. Therefore, there may be multiple values of x that satisfy the equation depending on the interval or domain specified.

How can solving cos x = -x be applied in real life?

The solutions to cos x = -x can be applied in real life situations such as finding the maximum or minimum value of a function, determining the period of a periodic function, and solving real-world problems involving periodic motion or oscillations.

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