Results 1 to 5 of 5

Math Help - Trigonometry

  1. #1

  2. #2
    Newbie
    Joined
    Feb 2014
    From
    Baguio, Philippines
    Posts
    9
    Thanks
    4

    Re: Trigonometry

    Is that 7 different equations and do you want the answers in Radians? What part do you not understand, do you know where these terms lie on the Quadrant graph for starters?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,462
    Thanks
    950

    Re: Trigonometry

    it's just spam. They don't really care about an answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,548
    Thanks
    1418

    Re: Trigonometry

    $\displaystyle \begin{align*} \sin{ \left( \frac{\pi}{14} \right)} \sin{ \left( \frac{3\pi}{14} \right) } \sin{ \left( \frac{5\pi}{14} \right) } \sin{ \left( \frac{7\pi}{14} \right) } \sin{ \left( \frac{9\pi}{14} \right) } \sin{ \left( \frac{11\pi}{14} \right) } \sin{ \left( \frac{13\pi}{14} \right) } &= \cos{ \left( \frac{3\pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{ \pi}{7} \right) } \sin{ \left( \frac{\pi}{2} \right) } \sin{ \left( \frac{5\pi}{14} \right) } \sin{ \left( \frac{3\pi}{14} \right) } \sin{ \left( \frac{\pi}{14} \right) } \\ &= \cos{ \left( \frac{3\pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{ \pi}{7} \right) } \cdot 1 \cdot \cos{ \left( \frac{ \pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{3\pi}{7} \right) } \\ &= \cos{ \left( \frac{3\pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{\pi}{7} \right) } \left[ -\cos{ \left( \frac{6\pi}{7} \right) } \right] \left[ - \cos{ \left( \frac{5\pi}{7} \right) } \right] \left[ - \cos{ \left( \frac{4\pi}{7} \right) } \right] \\ &= - \cos{ \left( \frac{\pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{3\pi}{7} \right) } \cos{ \left( \frac{4\pi}{7} \right) } \cos{ \left( \frac{5\pi}{7} \right) } \cos{ \left( \frac{6\pi}{7} \right) } \end{align*}$

    Now using the identity $\displaystyle \begin{align*} \prod_{ k = 1}^{n - 1} \cos{ \left( \frac{k\pi}{n} \right) } &= \frac{\sin{ \left( \frac{\pi n }{2} \right) } }{2^{n-1}} \end{align*}$ we have

    $\displaystyle \begin{align*} - \cos{ \left( \frac{\pi}{7} \right) } \cos{ \left( \frac{2\pi}{7} \right) } \cos{ \left( \frac{3\pi}{7} \right) } \cos{ \left( \frac{4\pi}{7} \right) } \cos{ \left( \frac{5\pi}{7} \right) } \cos{ \left( \frac{6\pi}{7} \right) } &= -\prod_{k = 1}^6{ \cos{ \left( \frac{k\pi}{7} \right) } } \\ &= - \frac{\sin{ \left( \frac{7\pi}{2} \right) }}{2^6} \\ &= - \frac{(-1)}{64} \\ &= \frac{1}{64} \end{align*}$
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    829
    Thanks
    209

    Re: Trigonometry

    Trigonometry-09-mar-14-1.pngTrigonometry-09-mar-14-2.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry to Memorize, and Trigonometry to Derive
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: August 21st 2013, 12:03 PM
  2. HELP :::::: trigonometry PLEASE
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 30th 2012, 08:49 AM
  3. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: September 10th 2009, 02:12 PM
  4. Trigonometry 2
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 16th 2009, 02:09 PM
  5. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 5th 2008, 01:15 PM

Search Tags


/mathhelpforum @mathhelpforum