Results 1 to 8 of 8

Math Help - Trigo Eqn

  1. #1
    gp3
    gp3 is offline
    Newbie
    Joined
    Nov 2009
    Posts
    19

    Unhappy Trigo Eqn

    How to solve this to get the angle?

    sin6x=3sin3x for 0 < x < 2pi

    this is how far i got:

    2sin3xcos3x = 3sin3x
    2sin3xcos3x/sin3x = 3
    2cos3x = 3
    cos3x = 3/2
    3x = cos-1 (3/2)

    But the calculator cant compute, gives me an error. Can someone see where i went wrong?

    Thanks!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by gp3 View Post
    How to solve this to get the angle?

    sin6x=3sin3x for 0 < x < 2pi

    this is how far i got:

    2sin3xcos3x = 3sin3x
    2sin3xcos3x/sin3x = 3
    2cos3x = 3
    cos3x = 3/2
    3x = cos-1 (3/2)

    But the calculator cant compute, gives me an error. Can someone see where i went wrong?

    Thanks!!!!
    HI

    you started off well .

    \sin 6x=3\sin 3x

    2\sin 3x\cos 3x=3\sin 3x **

    2\sin 3x\cos 3x-3\sin 3x=0

    \sin 3x(2\cos 3x-3)=0

    \sin 3x=0 OR \cos 3x=\frac{2}{3}

    Can you pick it up from here ? Just remember that the range is 0<x<2pi which implies 0<3x<6pi

    Note that at ** , you cant cancel off the sin 3x at both sides or else you would be missing solutions because you are ignoring the possibility of
    sin 3x=0

    Its like 2x^2=x , you cannot cancel the x so that x=1/2 , this is wrong .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    gp3
    gp3 is offline
    Newbie
    Joined
    Nov 2009
    Posts
    19
    yea, i know how to carry on. But if I have any more doubts, I will post them here. Thanks for your fast reply!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    gp3
    gp3 is offline
    Newbie
    Joined
    Nov 2009
    Posts
    19
    oh yea, i just spotted a mistake, i believe it should be cos3x = 3/2 and not cos3x = 2/3. And thus i cant solve cos3x = 3/2, it gives me an error.. help pls!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by gp3 View Post
    oh yea, i just spotted a mistake, i believe it should be cos3x = 3/2 and not cos3x = 2/3. And thus i cant solve cos3x = 3/2, it gives me an error.. help pls!
    oh yeah , my mistake , sorry .

    cos 3x=3/2 , it is undefined , because maximum for cos is 1 , anything over it would be undefined so you can just ignore this since it will not yield any solutions .
    Follow Math Help Forum on Facebook and Google+

  6. #6
    gp3
    gp3 is offline
    Newbie
    Joined
    Nov 2009
    Posts
    19
    hmm...so what i got for my answer is 0, pi/3, 2pi/3.

    But the solution they gave me was 0, pi/3, 2pi/3, pi, 4pi/3 and 5pi/3.

    tbh, i know the range is something like we have to go 2 rounds? or 3 rounds? for this question but how do you go about doing it? any idea on how to get the final 3 ?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by gp3 View Post
    hmm...so what i got for my answer is 0, pi/3, 2pi/3.

    But the solution they gave me was 0, pi/3, 2pi/3, pi, 4pi/3 and 5pi/3.

    tbh, i know the range is something like we have to go 2 rounds? or 3 rounds? for this question but how do you go about doing it? any idea on how to get the final 3 ?
    Well, since they say find all solutions for 0 < x < 2pi, that's what you're expected to do. Why did you stop at 2pi/3?

    The general solution to \sin (3x) = 0 is 3x = n \pi \Rightarrow x = \frac{n \pi}{3} where n is an integer. Use this to get all the solutions that lie in 0 < x < 2pi.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    gp3
    gp3 is offline
    Newbie
    Joined
    Nov 2009
    Posts
    19

    Wink

    lol....ok i got it now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trigo qns
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 9th 2008, 03:23 AM
  2. Trigo qn
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: October 8th 2008, 05:13 AM
  3. Trigo qn
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 7th 2008, 05:39 AM
  4. trigo sum/different~do not do~!
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 11th 2008, 07:43 AM
  5. trigo > i cant do it!
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 9th 2008, 06:43 AM

Search Tags


/mathhelpforum @mathhelpforum