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Math Help - R formulae (double angle formulae) URGENT

  1. #1
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    Question R formulae (double angle formulae) URGENT

    Q) Express 3 sin x + 4 cos x in the form R cos (x-a) a is alpha

    any idea i think we must change the sinx into cos x
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  2. #2
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    This problem can easily be solved my comparing coefficients.

    First start by stating your identity.

    R \cos(x - \alpha)  \equiv  3 \sin x + 4 \cos x

    It is important that you understand exactly what \equiv means before you go ahead, if you don't just say.

    Expand the left hand side using the compound angle formula.

    R \cos x \cos \alpha + R \sin x \sin \alpha \equiv  3 \sin x + 4 \cos x

    compare coefficients to get

    R \cos \alpha = 4
    R \sin \alpha = 3

    do you want to try and finish off form here ?

    let me know how it goes form here.

    Bobak
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  3. #3
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    oh ok i forget wat its mean

    (how u post these sign [alpha and other])
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  4. #4
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    Quote Originally Posted by bobak View Post
    This problem can easily be solved my comparing coefficients.

    First start by stating your identity.

    R \cos(x - \alpha)  \equiv  3 \sin x + 4 \cos x

    It is important that you understand exactly what \equiv means before you go ahead, if you don't just say.

    Expand the left hand side using the compound angle formula.

    R \cos x \cos \alpha + R \sin x \sin \alpha \equiv  3 \sin x + 4 \cos x

    compare coefficients to get

    R \cos \alpha = 4
    R \sin \alpha = 3

    do you want to try and finish off form here ?

    let me know how it goes form here.

    Bobak

    forget wat this \equiv means

    explain brief how u compare these coefficient to get

    R \cos \alpha = 4
    R \sin \alpha = 3

    quick plz
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  5. #5
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    Quote Originally Posted by manutd4life View Post
    oh ok i forget wat its mean

    (how u post these sign [alpha and other])
    you forget what \equiv, it should be covered somewhere in your textbook. It means that both sides of the expression are equal for all values of x. that is to say that the left hand side is identical to the right hand side.

    If two expressions are identical then the coefficients  \sin x and  \cos x respectively are the same. the coefficient of  \sin x on the left hand side is  R \sin \alpha and on he right hand side it is 3.

    are you following ?

    Bobak
    Last edited by bobak; May 20th 2008 at 04:22 PM.
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  6. #6
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    is this answer good:

    5 \cos(x - 36.9)
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  7. #7
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    Quote Originally Posted by manutd4life View Post
    is this answer good:

    5 \cos(x - 36.9)
    Well done.


    Just remember that is for an angle in degrees. Do you know how to adjust the result for radians ?

    Bobak
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  8. #8
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    Just remember that is for an angle in degrees. Do you know how to adjust the result for radians ?

    Bobak
    No dont how

    (another question)
    can u help me in one more question??
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  9. #9
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    Quote Originally Posted by manutd4life View Post
    No dont how

    (another question)
    can u help me in one more question??
    Well if you haven't covered radians in school yet it is not important (yet).

    If you want to ask another question start a new thread.

    Bobak
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