Iterations Of the Sin and Cos Functions

by Chris Hood

When an iteratation is done on the sin function, it means that we are doing the following:

y=sin(sinx) (This is iterating the sin function once.)
y=sin(sin(sinx)) (This is iterating the sin function twice.)
and so on.

Viewing the graphs of the iterations of the sin function will give us a better understanding of this concept:

The graph above is six iterations of the sin function. It is easy to see that iterations tend to decrease the amplitude of the sin function. The sin function also seems to be approaching 0.

Taking a look at this on Microsoft Excel may give us more of an idea about why these iterations are approaching 0.
This give us more of an idea of what the graph of a sin function would look like after it has been iterated for more than fifty times.

Now, some iterations of the cos function.
A graph from Algebra Expressor gives us the following:

The cos functions looks to be approaching close to one.
A look at the sequence on Excel will give us an idea of what is happening.
The iterations seem to be approaching a value of about .74.
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