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Math Help - Eulers formula trouble

  1. #1
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    Eulers formula trouble

    How do I write

    2sin²5xcos3x

    to a sum of cosine and/or sinusterms?
    I should use Eulers formula, and control it by putting x=0 before and after I've done it.

    Don't really know how to start, looked all the chapters in my book but still can't figure it out, think it's the ² term that makes me confused.

    Any tip?
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  2. #2
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    Hi andreynr6

    I'm not sure about the Euler formula, but I can use trigonometry manipulation to write 2sin²5xcos3x as a sum of cosine terms.

    2 \sin^2 5x \cos 3x

    =2\left(\frac{1}{2}-\frac{1}{2} \cos 10x\right) \cos 3x

    =\cos 3x - \cos 3x \cos 10x

    =\cos 3x - \frac{1}{2}(\cos 13x + \cos 7x)
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  3. #3
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    ah, I did something like you also, but noticed my little mistake thanks to you.

    Yeah, think I skip Euler for this time

    Thanks!

    /andrey, not so good in English.....yet
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  4. #4
    Senior Member pacman's Avatar
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    I don't know what you are apt to, but this may help . . . .

    2 sin^2 (5x) cos (3x) = 16sin^2 (x) cos (x) (cos 2x - 1/2)(cos 2x + cos 4x + 1/2)^2

    graph below,
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  5. #5
    Senior Member pacman's Avatar
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    or this one, because it depends on what you want to obtain . . . .

    2 sin^2 5x cos 3x = 8[sin^2 (5x/2)][cos^2 (5x/2)][2cos^2 (3x/2) - 1]

    factoring it will do . . .
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  6. #6
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    how did you do the first one? I wanna know, so I can do it myself..
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  7. #7
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    Solved it.

    Here's the solution, thanks to all of you.
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  8. #8
    Senior Member pacman's Avatar
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    ah, now i know what you wanted
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