# Finding a limit of a sequence or proving it diverges

## Homework Statement

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

?

## 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 :)

Dick
Homework Helper

## Homework Statement

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

?

## 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 :)

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

haruspex
Homework Helper
Gold Member
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.]

Dick