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Math Help - Help with trig addition and subtraction formulas.

  1. #1
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    Help with trig addition and subtraction formulas.

    If  sin (\alpha) = -\frac {5}{13} and  tan ( \alpha) > 0 , find the exact value of  sin (\alpha - \frac{\pi}{3}) .

    My first time using latex! Hopefully it makes my problem easier to read.

    EDIT:
    so the formula is sin(A-B)=(sinA)(cosB)-(cosA)(sinB)

    I guess I should mention I know how to get every value except cos(\alpha)

    and I don't understand why they are telling me  tan ( \alpha) > 0
    Last edited by dangsos; December 4th 2011 at 12:46 PM. Reason: additional info
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  2. #2
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    Re: Help with trig addition and subtraction formulas.

    sin(A-B)=(sinA)(cosB)-(cosA)(sinB)

    using this formula I get sin(A-B) = - \frac{5}{13} * \frac{\sqrt{3}}{2} - cos (\alpha) *  \frac{1}{2}
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  3. #3
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    Re: Help with trig addition and subtraction formulas.

    You have given that \tan(\alpha)>0 i.e \frac{\sin(\alpha)}{\cos(\alpha)}>0
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    Re: Help with trig addition and subtraction formulas.

    I don't understand. How does that help me find the missing peice  cos(\alpha) ?
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Help with trig addition and subtraction formulas.

    It means that \cos(\alpha)<0. I think it can be useful to use the identity \cos(\alpha)=\pm \sqrt{1-\sin^2(\alpha)} (do you see the importance of \cos(\alpha)<0 now?)
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  6. #6
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    Re: Help with trig addition and subtraction formulas.

    Quote Originally Posted by dangsos View Post
    I don't understand. How does that help me find the missing peice  cos(\alpha) ?
    it tells you what quadrant \alpha is in ... lets you know whether to make \cos{\alpha} positive or negative.
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  7. #7
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    Re: Help with trig addition and subtraction formulas.

    so using \sqrt{1-sin^2(\alpha)} i get cos (\alpha) = -\sqrt{\frac{144}{169}} correct?
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  8. #8
    MHF Contributor Siron's Avatar
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    Re: Help with trig addition and subtraction formulas.

    Normally it has to be \frac{-12}{13}
    I think you can solve the exercice now ...
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  9. #9
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    Re: Help with trig addition and subtraction formulas.

    okay so with all that I get this

    sin(A-B) = - \frac{5}{13} * \frac{\sqrt{3}}{2} - ( \frac{12}{13}) * \frac{1}{2}

    my answer is  - \frac{5 * \sqrt{3} - 12}{26}
    the book gives  \frac{12 * \sqrt{3} - 5}{26}
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  10. #10
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    Re: Help with trig addition and subtraction formulas.

    \sin{\alpha} \cdot \cos{\frac{\pi}{3}} - \cos{\alpha} \cdot \sin{\frac{\pi}{3}} =

    -\frac{5}{13} \cdot \frac{1}{2} - \left(-\frac{12}{13}\right) \cdot \frac{\sqrt{3}}{2}

    try again ...
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  11. #11
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    Re: Help with trig addition and subtraction formulas.

    I always make the most simple mistakes >.< thank yo ufor correcting me.
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