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Repeatedly 'cosine'ing a number: convergence

  1. Feb 20, 2007 #1
    A curiosity I've had recently...

    When repeatedly taking the cosine of a number in radians, it appears to converge to a value.

    i.e. cos(cos(cos(...cos(x)...))) = 0.73908513321516064165531208767387...

    Any thoughts/explanations/exact solution etc?

  2. jcsd
  3. Feb 20, 2007 #2
    Yes, this value does converge to the solution to the equation cos(x) = x, because the input, x, must be the same as the output, cos(x), if it converges.
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