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Homework Help: Sin and inverse sin multiplied

  1. May 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following:

    Sin^-1(sin(19*pi/7) in terms of pi

    3. The attempt at a solution

    i cant see any other way apart from the functions cancel to give 19pi/7 but checking on wolfram gives 2*pi/7, can anybody explain or help?

  2. jcsd
  3. May 8, 2012 #2

    I like Serena

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    Welcome to PF, binalbean! :smile:

    The inverse sine is defined to yield a result between -pi/2 and +pi/2.
    So they do not just cancel.

    The typical method is to draw a unit circle, find where the angle 19pi/7 is, and find the angle that has the same y coordinate but which is between -pi/2 and +pi/2.
  4. May 8, 2012 #3


    Staff: Mentor

    The equation f-1(f(x)) = x is true only if x is in the domain of f, and f(x) is in the domain of f-1.

    For example, ln(e-1) = -1, but eln(-1) is undefined. Here -1 is not in the domain of the natural log function.
  5. May 8, 2012 #4


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    And a nit-pick. The Sin-1 and sin aren't "multiplied". That is a composition of the two functions, or "function of a function".
  6. May 9, 2012 #5
    Thanks very much for your help!! :D
  7. May 9, 2012 #6

    I like Serena

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    You're welcome. :)

    This problem is an example that these conditions are not sufficient.
    x also has to be in the image of f-1.

    Btw, it's weird if f(x) is not in the domain of f-1.
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