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Inverse cosine function.

  1. May 20, 2009 #1
    I have a cosine function, namely the function for oscillation x=A cos(wt).

    I want to separate the t out here, so I can solve for it. My teacher gave the the answer to be t= (arccos (x/a)/2pi)*T, but I can't quite see where he came up with that. Would anyone be as kind as to give me a more elaborate explanation of how this transition was made.

    (2pi and T comes from w=2pi/T).

    Sorry for bad English, not a native English speaker obviously :)
  2. jcsd
  3. May 20, 2009 #2


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    The inverse function of the cosine is the arc cosine. If a function [itex]f(x)[/itex] has an inverse [itex]f^{-1}(x)[/itex] then [itex]f^{-1}(f(x))=f(f^{-1}(x))=x[/itex].

    Divide the equation on both sides by A then take the arccos on both sides. Can you calculate [itex]\arccos(\cos(\omega t)) [/itex]now?
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