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Math Help - Product To Sum for trigonometry

  1. #1
    Member >_<SHY_GUY>_<'s Avatar
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    Question Product To Sum for trigonometry

    write:

    6sin[theta] * sin6[theta]
    as a sum or difference.

    write cos5[theta]+ cos3[theta] as a product
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by >_<SHY_GUY>_< View Post
    write:

    6sin[theta] * sin6[theta]
    as a sum or difference.

    write cos5[theta]+ cos3[theta] as a product
    do you know the product to sum and the sum to product formulas?


    \sin A \sin B = \frac 12 [ \cos (A - B) - \cos (A + B)]


    \cos A + \cos B = 2 \cos \frac {A + B}2 \cos \frac {A - B}2

    Hope that helps
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  3. #3
    Eater of Worlds
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    write cos5[theta]+ cos3[theta] as a product
    Use cos(u)+cos(v)=2cos\left(\frac{u+v}{2}\right)cos\le  ft(\frac{u-v}{2}\right)

    2cos\left(4{\theta}\right)cos({\theta})
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  4. #4
    Member >_<SHY_GUY>_<'s Avatar
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    Quote Originally Posted by Jhevon View Post
    do you know the product to sum and the sum to product formulas?


    \sin A \sin B = \frac 12 [ \cos (A - B) - \cos (A + B)]


    \cos A + \cos B = 2 \cos \frac {A + B}2 \cos \frac {A - B}2

    Hope that helps
    i used it, and got 3(-2cos[theta] - cos10[theta]) but the answer is 2 instead of -2... how?
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  5. #5
    Member >_<SHY_GUY>_<'s Avatar
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    Quote Originally Posted by galactus View Post
    Use cos(u)+cos(v)=2cos\left(\frac{u+v}{2}\right)cos\le  ft(\frac{u-v}{2}\right)

    2cos\left(4{\theta}\right)cos({\theta})
    when would you know when to use the double-angle formula and half angle formula? and how can you use the power reducing formula...they confuse me a lot
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by >_<SHY_GUY>_< View Post
    when would you know when to use the double-angle formula and half angle formula? and how can you use the power reducing formula...they confuse me a lot
    \cos^{2m}(x) or

    \sin^{2m}(x)

    where m\in\mathbb{N}

    \sin^{2m+1}(x)

    or \cos^{2m+1}(x)

    m\in\mathbb{Z^{+}}

    use pythagorean identity

    \sin\bigg(\frac{x}{2}\bigg)

    or \cos\bigg(\frac{x}{2}\bigg)

    use half-angle formulas

    \cos(2mx)

    or \sin(2mx)

    and m\in\mathbb{N}

    use double angle formuals

    NOTE the restrictions on m arent neccasary, but if m does not satisfy those conditions it is tricker because you get into radicals and such
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  7. #7
    Member >_<SHY_GUY>_<'s Avatar
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    Quote Originally Posted by Mathstud28 View Post
    \cos^{2m}(x) or

    \sin^{2m}(x)

    where m\in\mathbb{N}

    \sin^{2m+1}(x)

    or \cos^{2m+1}(x)

    m\in\mathbb{Z^{+}}

    use pythagorean identity

    \sin\bigg(\frac{x}{2}\bigg)

    or \cos\bigg(\frac{x}{2}\bigg)

    use half-angle formulas

    \cos(2mx)

    or \sin(2mx)

    and m\in\mathbb{N}

    use double angle formuals

    NOTE the restrictions on m arent neccasary, but if m does not satisfy those conditions it is tricker because you get into radicals and such

    Sorry... i didnt get one thing what you said...i just wanted to know when you use and not use those formulas
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by >_<SHY_GUY>_< View Post
    Sorry... i didnt get one thing what you said...i just wanted to know when you use and not use those formulas
    Thats what I told you...if you look closely the m just represents a natural number 1,2,3,4...

    So when you have a trig function in that form use which one I said
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