Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Expansion for large tan(x)

  1. Oct 30, 2011 #1
    Hi, I was reading a review and I saw this equation,

    [tex]A^2 = \frac{|B^2 - C^2|}{\sqrt{(1-sin^2(2x))}} - C^2 - B^2 - 2D^2[/tex]

    Then at some point he writes: "expanding for large [itex]tan(x)[/itex], this expression becomes,

    [tex]A^2 = -2(C^2 + D^2) + \frac{2}{tan^2(x)}(B^2 - C^2) + O(1/tan^4(x)) [/tex]

    Could anybody explain how did this happen?
     
    Last edited: Oct 30, 2011
  2. jcsd
  3. Oct 31, 2011 #2
    Let t = 1/tan(x)
    Compute sin(2x) as a function of t.
    Bring it back into the equation.
    Develop it as a a series for t.
    When tan(x) tends to infinity t tends to 0.
    Remplace t by 1/tan(x) in the series.
    You will obtain the expected result.
     
  4. Oct 31, 2011 #3
    Thank you very much, JJacquelin! now I see it :D
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook