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Why is this true about the angle theta

  1. Apr 17, 2009 #1
    1. The problem statement, all variables and given/known data
    From my notes:

    Picture2.png

    Why is:
    [tex]V_{e} \times sin \Theta \cong V_{e}\Theta[/tex] ?

    The only thing I know is that the assumption: [tex]\Theta \rightarrow 0 [/tex] has been made, but that doesn't make the above equation clear to me...

    Thanks in advance!
     
  2. jcsd
  3. Apr 17, 2009 #2
    Re: Angle

    I'm not 100% sure what you're asking, but it looks like you are just talking about the small angle approximation of the sine function. That's easy to show if you know the Taylor Expansion for sine.

    [tex]\sin{\theta} = \theta - {\theta^3 \over 3!} + {\theta^5 \over 5!} - ...[/tex]

    Now, since [tex]\theta[/tex] is very small, any positive integer power of [tex]\theta[/tex] will go to 0 even faster than [tex]\theta[/tex] itself. ie. [tex]\theta^3 \to 0[/tex], [tex]\theta^5 \to 0[/tex], etc.

    So [tex]\sin{\theta} \approx \theta[/tex]
     
  4. Apr 17, 2009 #3
    Re: Angle

    That was exactly my question, the answer is clear, thanks a lot!
     
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