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

[grapeape]

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?

 

[Dick]

Nope. I'm afraid that's as good as it gets.

 

[grapeape]

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?

 

[Dick]

Infinities not numbers. You don't generally consider infinity in the domain of any function. So yes, there are no horizontal asymptotes either.

 

[Kummer]

I believe we can show that this number is transcendental over \mathbb{Q}.