Results 1 to 2 of 2

Math Help - Simple sinx...

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    1

    Question Simple sinx...

    Hello everyone who reads this... please help me to solve this
    sin(5x) / sin(x) = ? ...if I know that sin(3x) / sin(x) = 6 / 5
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    \sin^3 x = -\frac{1}{4}\:\sin 3x + \frac{3}{4} \:\sin x

    Therefore
    \sin^2 x = -\frac{1}{4}\:\frac{\sin 3x}{\sin x} + \frac{3}{4} = -\frac{1}{4}\:\frac{6}{5} + \frac{3}{4} = \frac{9}{20}

    Now
    \sin^5 x = \frac{1}{16}\:\sin 5x - \frac{5}{16} \:\sin 3x + \frac{5}{8} \:\sin x

    Therefore
    \sin^4 x = \frac{1}{16}\:\frac{\sin 5x}{\sin x} - \frac{5}{16} \:\frac{\sin 3x}{\sin x} + \frac{5}{8}

    \left(\frac{9}{20}\right)^2 = \frac{1}{16}\:\frac{\sin 5x}{\sin x} - \frac{5}{16} \:\frac{6}{5} + \frac{5}{8}

    \frac{1}{16}\:\frac{\sin 5x}{\sin x} = -\left(\frac{9}{20}\right)^2 - \frac{5}{16} \:\frac{6}{5} + \frac{5}{8} = -\frac{19}{400}

    Finally
    \frac{\sin 5x}{\sin x} = -16\:\frac{19}{400} = -\frac{19}{25}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ((1+sinx+icosx)/(1+sinx-icos))^n
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 28th 2011, 07:06 PM
  2. Replies: 1
    Last Post: March 25th 2011, 12:27 AM
  3. Prove:(tanx/(1+tanx)) = (sinx/(sinx+cosx))
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: February 2nd 2011, 08:46 PM
  4. Integral of Ln(Sinx)/Sinx
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 11th 2010, 02:18 AM
  5. find y' if y=(sinx)^2 + 2^(sinx)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 23rd 2009, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum