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Math Help - Urgent! R-formulae! Please Help!!!!!!!!!

  1. #1
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    Urgent! R-formulae! Please Help!!!!!!!!!

    I need a miracle! Can someone pls help me! I need to noe WHEN and HOW to use the R-formulae! and WHAT the R-formuale is in the first place! THANKX!
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  2. #2
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    The R-formula is used when you have cos\theta \pm sin\theta~=~a~ where a is a non-zero value.

    Example;

    3sin\theta+4cos\theta~=~1

    Firstly set

    3sin\theta+4cos\theta~=~rsin(\theta+\alpha)

    3sin\theta+4cos\theta~=~r(sin\theta \cdot cos\alpha+cos\theta \cdot sin\alpha)

    sin\theta~terms: 3~=~rcos\alpha~\implies 9~=~r^2cos^2\alpha~~~[1]

    cos\theta~terms: 4~=~rsin\alpha~\implies 16~=~r^2sin^2\alpha~~~[2]

    [1]+[2]\rightarrow~25~=~r^2(cos^2\alpha+sin^2\alpha)

    \implies~25~=~r^2

    \implies~r~=~5

    Hence,

    5cos\alpha~=~3~~~~~,~~~~~5sin\alpha~=~4

     <br />
cos\alpha~=~\frac{3}{5}~~~~~,~~~~~sin\alpha~=~\fra  c{4}{5}<br />

    \implies~\alpha~\approx~53.13^o

    Thus,

     <br />
3sin\theta+4cos\theta~=~5sin(\theta+53.13^o)~=~1<br />

    The same technique is also used with rsin(\theta-\alpha)~,~rcos(\theta+\alpha) and rcos(\theta-\alpha)
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  3. #3
    Forum Admin topsquark's Avatar
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    Ahhhh. That's what the "R-formula" is supposed to be. I didn't know it had an official name.

    -Dan
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