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

Some trigonometric, exponential thing?

  1. Nov 3, 2012 #1
    How can we say:

    f(x)=A'sin(kx)+B'cos(kx)

    or equivalently

    f(x)=Ae[itex]^{ikx}[/itex]+Be[itex]^{-ikx}[/itex]??

    How are these two equivalent knowing that e[itex]^{ix}[/itex]=cosx+isinx

    I don't get this?
     
  2. jcsd
  3. Nov 3, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi M. next! :smile:
    They won't both be real.

    Try Euler's formula

    what do you get? :smile:
     
  4. Nov 3, 2012 #3
    it would be: A(coskx +isinkx)+B(coskx-isinkx)
    which's (A+B)coskx+i(A-B)sinkx
    .. A'coskx+iB'sinkx
    where's did the "i" go?
     
  5. Nov 3, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    so B' = i(A-B) …

    i told you they won't both be real! :biggrin:
     
  6. Nov 18, 2012 #5
    Sorry, i didn't check the site from since, I had some connection difficulties.
    So, my final question, can this be done? Is the exponential form an alternative for the known trigonometric one?
    And why do I use it? Why not keep it in trigonometric form. I am working on potential wells, free particles and so, if this information would help you answer my question.
     
  7. Nov 18, 2012 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi M. next! :smile:
    Yes, they're equally valid alternatives.

    You use cos and sin, or real exponentials, if you're only interested in real solutions,

    but you use complex exponentials if you're interested in complex solutions. :wink:
     
  8. Nov 18, 2012 #7
    Thanks, am grateful
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Some trigonometric, exponential thing?
  1. Exponential integral (Replies: 6)

Loading...