The discussion revolves around a sequence defined by iterative applications of sine and cosine functions, specifically: sin(1), cos(sin(1)), sin(cos(sin(1))), and so on. Participants are tasked with finding the limit of this sequence or proving that it diverges.
The discussion is active, with participants sharing thoughts on the implications of the limit conditions. Some guidance has been offered regarding the equations that must hold if the sequence converges, although there is no explicit consensus on the outcome of the sequence.
Participants note the challenge of finding subsequences that demonstrate divergence, as well as the implications of the limit conditions on the nature of the sequence.
nikolafmf said: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.
Homework Equations
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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 :)
haruspex said: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.]