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Arcsin x + arcsin 2x = pi/2

  1. Dec 10, 2011 #1
    1. The problem statement, all variables and given/known data

    sin -1x + sin -12x = ∏/2



    2. Relevant equations



    3. The attempt at a solution

    My question is, is it possible for x to be a negative value? Since ∏/2 is positive. Or I should think that x can be negative because -(3∏)/2 = ∏/2?

    Please enlighten me...
    [
     
  2. jcsd
  3. Dec 10, 2011 #2

    SammyS

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    sin-1(x) has the same sign as x , so the answer to your question is "No, that's not possible."
     
  4. Dec 11, 2011 #3

    ehild

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    -3pi/2 is not equal to pi/2, but the angle -3pi/2 is equivalent to the angle pi/2.:smile:

    The range of the inverse sine function is [-pi/2,pi/2]. -3pi/2 is outside of the range.

    Hints to solve the problem:

    sin(sin-1(x))=x.

    sin(pi/2-α)=cosα.

    What is cos(sin-1(x))?

    ehild
     
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