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February 22nd, 2009, 05:38 AM   #1
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How to reverse arc tangent and sinus equation?

Hey!

Ive got a litte trouble with some math..

My Equation :

x = atan(y) * (sin(y) * y)

And I want to be able to reverse this... How can I do that?
I mean to get the 'y' value from the 'x' value..


Cheers,
Artheus
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February 22nd, 2009, 09:09 AM   #2
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Re: How to reverse arc tangent and sinus equation?

If you did manage to solve this for y = something with x's in it, the result would not be a function. One x value would have multiple y values.
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February 22nd, 2009, 03:54 PM   #3
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Re: How to reverse arc tangent and sinus equation?

hey Marz you have right the function is not injective (for a single value in the range of a function corresponds multiple values for domain)...that in the case that both x and y are real numbers ..the grephic of the function atan(y)*sin(y)*y is showed bellow
but you can find an inverse of that function if you specifies the domain for y in your case
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February 22nd, 2009, 03:55 PM   #4
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Re: How to reverse arc tangent and sinus equation?

i think you can specifies a domain for y like [0...pi]
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February 22nd, 2009, 04:31 PM   #5
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Re: How to reverse arc tangent and sinus equation?

No wait a second.....the function you have ...can be inverted if you take like domain between every tow consecutive zeros of it's derivative. You watch the graph of the derivative function and when it intersect y=o axis that is your zeros
But we still have problem find that inverse function...there should be a way....only consider y between tow consecutive zeros ...very important otherwise there is not any inverse fct.
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February 22nd, 2009, 05:21 PM   #6
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Re: How to reverse arc tangent and sinus equation?

i think you can't resolve this using algebra ...so far i don't get any answer but you can figure out the graph of the inverse function.
If you have a function f(x) the graph of the inverse is symmetrical in rapport of the first line bisector (x=y)
like in the figure
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