Results 1 to 5 of 5

Math Help - Find all primary trig solutions

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    11

    Find all primary trig solutions

    Please help!

    "Find all primary solutions in
    sin6(theta)+sin3(theta) = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2008
    Posts
    11
    or at least tell me how to simplify or alter that equation, thanks
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    From
    NY - USA
    Posts
    28
    Quote Originally Posted by erockdontstop View Post
    Please help!

    "Find all primary solutions in
    sin6(theta)+sin3(theta) = 0

    sin(6x) + sin(3x) = 0

    sin(6x) = - sin(3x)

    \frac{sin(6x)}{-sin(3x)} = 1

    -2 cos(3x) = 1

    cos(3x) = -\frac{1}{2}

    3x = arccos(-\frac{1}{2})

    3x = \frac{2\pi}{3}

    x = \frac{2 \pi}{9}

    Now plug x in to the original equation to see if it equals 0

    sin(6(\frac{2\pi}{9}) + sin(3*(\frac{2\pi}{9}) = ?

    -\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} = 0

    remember that there are more solutions to this problem such as
    x = \pi,\frac{\pi}{3}, \frac{2 \pi}{3},  \frac{2 \pi}{9},\frac{2 \pi}{9},  \frac{4 \pi}{9} and so on
    Last edited by fonso_gfx; December 18th 2008 at 11:36 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2008
    Posts
    11
    [quote=fonso_gfx;238504] sin(6x) + sin(3x) = 0


    \frac{sin(6x)}{-sin(3x)} = 1

    -2 cos(3x) = 1

    how did you that?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2008
    From
    NY - USA
    Posts
    28
    [quote=erockdontstop;238509]
    Quote Originally Posted by fonso_gfx View Post
    sin(6x) + sin(3x) = 0


    \frac{sin(6x)}{-sin(3x)} = 1

    -2 cos(3x) = 1

    how did you that?
    I used the double angle formula

    sin(6x) = sin(2(3x)) = 2sin(3x)*cos(3x)

    Now when when you divide by -sin(3x) you get only

    -2cos(3x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig solutions
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 10th 2010, 08:29 AM
  2. Trig. All solutions?
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: November 25th 2009, 06:47 AM
  3. trig solutions
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 24th 2009, 12:54 PM
  4. Find all the solutions (Inverse Trig Funct.)
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 17th 2009, 11:46 PM
  5. Trig Solutions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 29th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum