# Finding a limit of a sequence or proving it diverges

1. Dec 2, 2012

### nikolafmf

1. The problem statement, all variables and given/known data

Given is a sequence: sin(1), cos(sin(1)), sin(cos(sin(1))) etc. Find the limit of the sequence or prove it diverges.

2. Relevant equations

?

3. The attempt at a solution

One way to prove a sequence diverges is to find two subsequences which converge to different limits, but I could not find such.

I would be thankful for any idea :)

2. Dec 2, 2012

### Dick

If there is a limit L, then it must satisfy both sin(L)=L and cos(L)=L, mustn't it?

3. Dec 2, 2012

### haruspex

Suppose it does converge to some value. What equations could you deduce regarding that value?
[Dick beat me to the Submit, and was a little more generous with the hint.]

4. Dec 2, 2012

### Dick

Yeah, probably too generous in retrospect. I like yours better as a starter hint.

Last edited: Dec 2, 2012
5. Dec 3, 2012

### nikolafmf

Yes, it is true, it must satisfy both sin(L)=L and cos(L)=L, from which follows that the sequence diverges :)

Thank you very much to both for the help :)