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Homework Help: Bit foggy on this trig question

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data
    arccos(cos2[tex]\Pi[/tex])




    3. The attempt at a solution
    cos of 2[tex]\Pi[/tex] =1
    how do I get the arccos of 1? Without a calculator.
    Thanks
     
  2. jcsd
  3. Dec 2, 2008 #2

    Defennder

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    Homework Helper

    You have to use either some log tables or your memory. More specifically if you know how to sketch the graph of a cos function then you would know immediately that [tex]\cos (2\pi n) = 1 [/tex] where n is any integer (including 0).
     
  4. Dec 2, 2008 #3
    Yes, I know how to get cos of 2[tex]\Pi[/tex]. It equals 1
    I don't know how to get arccos of 1.
    Could you help me with that?

    I know that, for instance arccos [tex]\stackrel{\Pi}{4}[/tex] = [tex]\stackrel{1}{\sqrt{2}}[/tex]

    But how do I figure out arccos 1.

    I know it = 0 but I can't see how to derive this
     
  5. Dec 2, 2008 #4
    arccos is inverse function of cos. So If you know that cos(2п)=1 you will know that arccos(1)=2п. Do you understand now?

    Regards.

    P.S arccos(1 / √2) = п/4
     
    Last edited: Dec 2, 2008
  6. Dec 4, 2008 #5

    HallsofIvy

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    Science Advisor

    For any number, x, between 0 and [itex]\pi[/itex], arccos(cos(x))= x. That follows from the very definition of "arccos".
     
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