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How would this equation be simplified?

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data
    To satisfy my curiosity, I tried to come up with an equation that describes how a line reflects off a parabola. The equation I came up with is [(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y
    This equation works wonderfully but its just large and ugly.
    The wolfram alpha site for this equation is:
    http://www.wolframalpha.com/input/?i=[(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y
    It just helps visualize the equation. From there, I noticed that wolfram simplifies this down further to (-1500*y)/([y^2]-2500)
    How would I go about simplifying the original equation to the nice one wolfram gives?


    2. Relevant equations
    [(tan[2*arctan(-y/50)]*[1000-(y^2)])/100]+y


    3. The attempt at a solution
    I have tried to look at many trig identities involving the tangent functions but none of them seem to help in this case. I have tried moving things around but everything I try just seems to stop with those ugly tangents still left.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 17, 2013 #2
    You could use the identity:

    tan(2x) = 2tanx/ (1- (tanx)^2 )

    and tan(arctan x) = x
     
  4. Mar 17, 2013 #3
    I tried that but on the bottom, you would still be left with 1-(tanx)^2
     
  5. Mar 17, 2013 #4
    but remember x = arctan(-y/50).
    So, 1-(tanx)^2 = 1 - (tan[arctan(-y/50)]^2 = 1 - y^2/2500
     
  6. Mar 17, 2013 #5
    Yes! I see it now, thanks for your help :)
     
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