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Find the solution set

  1. Jan 10, 2013 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    Find the solution set of [sin^-1 x]>[cos^-1 x] where [] denotes greatest integer function.


    2. Relevant equations

    3. The attempt at a solution

    I know that
    -∏/2 <sin^-1 x < ∏/2
    0 < cos^-1 x <∏

    But I am clueless what will happen if I enclose them within "those square brackets"!
     
  2. jcsd
  3. Jan 10, 2013 #2
    Those square brackets look to me like a havoc when it comes to these types of questions.
    These types of questions are best done by sketching the graph of the functions.
     
  4. Jan 10, 2013 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Remember that sin^(-1)(x) = a and cos^(-1)(x) = b are angles, with -π/2 <= a <= π/2 and 0 <= b <= π. The square bracket "rounds down", so [a] = greatest integer <= a. Thus, [a] and must be integers lying in the ranges -π/2 < [a] < π/2 and 0 <= < π (with >= 0 rather than > 0). What are all the integers lying in these two ranges? Now, by checking a few cases you can find the appropriate ranges of x.
     
  5. Jan 10, 2013 #4

    utkarshakash

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    Gold Member



    For a the integral values can be -1,0,1 and for b it can be 0,1,2,3. Now I can see that a will be greater than b only if a=1 and b=0. So the range of x comes out be (sin1,1). Thanks!

    PS- Can you please help me out on my other problems?
     
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