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Aproximation arccos(1/4)

  1. Jan 25, 2009 #1
    how to aproximate arccos(1/4) by hand?
  2. jcsd
  3. Jan 25, 2009 #2
    Well the Taylor Series for arccos(x) begins as pi/2 - x - x^3/6, since (1/4)^3/6 = .003 this is a pretty good approximation:

    [tex]arccos(1/4) \approx \pi/2 - x - x^{3}/3 \approx 1.318[/tex]

    knowing that pi/2 is about 1.57 might help too.
  4. Jan 25, 2009 #3
    The derivative of f(x) = arccos(x) can be written as a power series (a binomial series). Find this series, integrate both sides, check for convergence, and plug in x = 1/4.
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