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Using the derivative of arcsine to solve for x

  1. Jul 9, 2008 #1
    Using the derivative of arcsine to solve for "x"

    Greetings,

    How can I use:

    [tex] \frac {d sin^-1(x)}{dx} = \frac {1}{\sqrt{(1-x^2)}} [/tex]

    to calculate values for arc sine?

    For example:

    [tex] arcsin(x) = \int\frac {1}{\sqrt{(1-x^2)}} dx[/tex]

    How can I use equation such that I enter “0.5” in for x and turn-the-crank and this equation spits out “30 degrees” or “0.524 radians”

    Just curious.

    Thanks
    Sparky_
     
  2. jcsd
  3. Jul 9, 2008 #2

    mathman

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    Gold Member

    Re: Using the derivative of arcsine to solve for "x"

    What do you have in mind by "turn-the-crank"? Assuming the range of the integral is (0,x) you need some sort of integration algorithm, like Simpson's rule. The answer will be in radians.
     
  4. Jul 9, 2008 #3
    Re: Using the derivative of arcsine to solve for "x"

    Since the integral would have a range - as you said (o,x).

    will I be able to enter a single number and get the arcsine of that number -

    I enter x=0.5 and integrate (somehow from x= 0.5 to 0.5 though I know this would give 0 - explanation help here??) and get 0.524 radians.

    If I do x= some point to some other point, would that result not be the difference ini two arcsine's?

    Thanks again
     
  5. Jul 10, 2008 #4

    HallsofIvy

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    Re: Using the derivative of arcsine to solve for "x"

    No, from 0 to 0.5, not "0.5 to 0.5".

    Yes, it would. And arcsin(0)= 0.

     
  6. Jul 10, 2008 #5
    Re: Using the derivative of arcsine to solve for "x"

    Mathman and HallsofIvy -

    Thanks so much!

    I'm going to play with this a little, I may have another question later.

    I wish I had Mathcad and Mathmatica so I could "turn-the-crank" on the integration a little easier.

    Does you know of any free / share ware out there that is can do some of the functions of mathcad / mathmatica.
     
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