Results 1 to 4 of 4

Math Help - trigo

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    381

    trigo

    Find the range of x :

     <br />
0<2\cos(x+\frac{\pi}{6})<1<br />

    From the graphical method , i got

    \frac{\pi}{6}<x<\frac{\pi}{3} , \frac{4\pi}{3}<x<\frac{3\pi}{2}

    My question is how to do it algebraically , i mean without the graphical method ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Divide by 2: 0<\cos\left(x+\frac{\pi}{6}\right)<\frac{1}{2}.

    If 0<x+\frac{\pi}{6}<\frac{\pi}{2} then the inequality can be written as

    \cos\frac{\pi}{2}<\cos\left(x+\frac{\pi}{6}\right)  <\cos\frac{\pi}{3}.

    On the interval \left[0,\frac{\pi}{2}\right] cosine is decreasing. Then

    \frac{\pi}{3}<x+\frac{\pi}{6}<\frac{\pi}{2}

    Substract \frac{\pi}{6} from all terms and you'll get \frac{\pi}{6}<x<\frac{\pi}{3}

    If \frac{3\pi}{2}<x+\frac{\pi}{6}<2\pi then we have

    \cos\frac{3\pi}{2}<\cos\left(x+\frac{\pi}{6}\right  )<\cos\frac{5\pi}{3}

    Cosine is increasing, then

    \frac{3\pi}{2}<x+\frac{\pi}{6}<\frac{5\pi}{3}

    Sunstract \frac{\pi}{6}\Rightarrow\frac{4\pi}{3}<x<\frac{3\p  i}{2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jan 2009
    Posts
    381
    Thanks .But how come when you say the cosine is decreasing, you just swap the positions of pi/3 and pi/6 ??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    If a function f is decreasing then x_1<x_2\Rightarrow f(x_1)>f(x_2)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigo Eqn
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 2nd 2009, 02:53 AM
  2. Trigo qn
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: October 8th 2008, 04:13 AM
  3. Trigo qn
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 7th 2008, 04:39 AM
  4. trigo sum/different~do not do~!
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 11th 2008, 06:43 AM
  5. trigo > i cant do it!
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 9th 2008, 05:43 AM

Search Tags


/mathhelpforum @mathhelpforum