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Summation of Tan functions

  1. Jan 29, 2007 #1

    [tex]\sum_{1}^{n} \tan(a f_{n} ) [/tex]

    [tex]\cos x = 1 - {x^2 \over 2!} + {x^4 \over 4!} - \cdots[/tex]
    [tex]\sin\left( x \right) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots[/tex]
    [tex] \tan(x) = \sin(x) / \cos(x)[/tex]

    There might be equations for the summation of a series of sine functions or an equation for the summation of a series of consine functions. I don't know what they are. I have no idea how to go about deriving this.
    Last edited: Jan 29, 2007
  2. jcsd
  3. Jan 29, 2007 #2


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    What are you assumed to find???
  4. Jan 29, 2007 #3


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    What is the fn(x)? Everything depends on that doesn't it?
  5. Jan 29, 2007 #4
    Sorry. That wasn't very clear.

    Find t
    [tex]B = \sum_{1}^{n} \tan( f_{n} t ) [/tex]

    Right now I'm just trying to get rid of the tan function. Getting rid of the summation sign might help.

    I wrote down [tex]f_{n}[/tex] incorrectly.
    [tex]f_{n} = a n^{2}+c b_{n}^{2}[/tex]

    where [tex]b_{n}[/tex] is an arbitrary constant
    Last edited: Jan 29, 2007
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