Results 1 to 11 of 11

Thread: Help with trig addition and subtraction formulas.

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Help with trig addition and subtraction formulas.

    If $\displaystyle sin (\alpha) = -\frac {5}{13} $ and $\displaystyle tan ( \alpha) > 0 $ , find the exact value of $\displaystyle 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 $\displaystyle cos(\alpha)$

    and I don't understand why they are telling me $\displaystyle tan ( \alpha) > 0 $
    Last edited by dangsos; Dec 4th 2011 at 12:46 PM. Reason: additional info
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Re: Help with trig addition and subtraction formulas.

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

    using this formula I get sin(A-B) = -$\displaystyle \frac{5}{13}$ * $\displaystyle \frac{\sqrt{3}}{2}$ - cos$\displaystyle (\alpha)$ * $\displaystyle \frac{1}{2}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Belgium
    Posts
    1,254
    Thanks
    24

    Re: Help with trig addition and subtraction formulas.

    You have given that $\displaystyle \tan(\alpha)>0$ i.e $\displaystyle \frac{\sin(\alpha)}{\cos(\alpha)}>0$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Re: Help with trig addition and subtraction formulas.

    I don't understand. How does that help me find the missing peice $\displaystyle cos(\alpha)$ ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Belgium
    Posts
    1,254
    Thanks
    24

    Re: Help with trig addition and subtraction formulas.

    It means that $\displaystyle \cos(\alpha)<0$. I think it can be useful to use the identity $\displaystyle \cos(\alpha)=\pm \sqrt{1-\sin^2(\alpha)}$ (do you see the importance of $\displaystyle \cos(\alpha)<0$ now?)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3701

    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 $\displaystyle cos(\alpha)$ ?
    it tells you what quadrant $\displaystyle \alpha$ is in ... lets you know whether to make $\displaystyle \cos{\alpha}$ positive or negative.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Re: Help with trig addition and subtraction formulas.

    so using $\displaystyle \sqrt{1-sin^2(\alpha)}$ i get cos$\displaystyle (\alpha) = -\sqrt{\frac{144}{169}}$ correct?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Belgium
    Posts
    1,254
    Thanks
    24

    Re: Help with trig addition and subtraction formulas.

    Normally it has to be $\displaystyle \frac{-12}{13}$
    I think you can solve the exercice now ...
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Re: Help with trig addition and subtraction formulas.

    okay so with all that I get this

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

    my answer is $\displaystyle - \frac{5 * \sqrt{3} - 12}{26}$
    the book gives $\displaystyle \frac{12 * \sqrt{3} - 5}{26} $
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3701

    Re: Help with trig addition and subtraction formulas.

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

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

    try again ...
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Nov 2011
    Posts
    9

    Re: Help with trig addition and subtraction formulas.

    I always make the most simple mistakes >.< thank yo ufor correcting me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modular Addition and Subtraction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Sep 20th 2011, 10:59 PM
  2. Addition Subtraction
    Posted in the Algebra Forum
    Replies: 0
    Last Post: Aug 25th 2010, 05:43 PM
  3. Addition and Subtraction Formulas
    Posted in the Trigonometry Forum
    Replies: 13
    Last Post: Mar 16th 2010, 05:39 PM
  4. The Addition and subtraction Formulas
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Mar 16th 2010, 05:31 PM
  5. Addition/Subtraction of Cosine
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Mar 31st 2007, 08:05 PM

/mathhelpforum @mathhelpforum