Results 1 to 6 of 6

Math Help - trigo equation

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    381

    trigo equation

    This seems easy but i am not quite sure ..

    4\cos \frac{7}{2}\theta\cos \theta\cos \frac{1}{2}\theta=0

    For 0<\theta<360

    so i think

    \cos \frac{7}{2}\theta=0 , \theta = 180/7 , 540/7

    \cos \theta=0 , \theta=90 , 270

    \cos \frac{1}{2}\theta=0 , \theta = 180

    Am i correct >
    Last edited by mr fantastic; October 7th 2009 at 01:00 AM. Reason: Added latex tags to some of the code
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    see the graph, i think 7 times it crossed the x-axis, more roots are missing. The graph looks symetric . . .
    Attached Thumbnails Attached Thumbnails trigo equation-ok.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    a better graph, see
    Attached Thumbnails Attached Thumbnails trigo equation-ok-1.gif  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jan 2009
    Posts
    381
    Quote Originally Posted by pacman View Post
    see the graph, i think 7 times it crossed the x-axis, more roots are missing. The graph looks symetric . . .
    Sorry but that doesn't really help . Do you spot any mistake in my working ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,686
    Thanks
    617
    Hello, thereddevils!

    Left out a few solutions . . .


    4\!\cdot\!\cos\left(\tfrac{7}{2}\theta\right)\!\cd  ot\!\cos(\theta)\!\cdot\!\cos\left(\tfrac{1}{2}\th  eta\right)\:=\:0\quad\text{for }0^o\,<\,\theta\,<\,360^o
    \cos\left(\tfrac{7}{2}\theta\right) \:=\:0 \quad\Rightarrow\quad \tfrac{7}{2}\theta \;=\;90^o + 180^on  \quad\Rightarrow\quad \theta \:=\:\frac{180^o + 360^on}{7}


    . . For n = 0,1,2,3,4,5,6, we have:

    . . . . \frac{180^o}{7} \:=\:25\tfrac{5}{7}^o

    . . . . \frac{540^o}{7} \:=\: 77\tfrac{1}{7}^o

    . . . . \frac{900^o}{7} \:=\: 128\tfrac{4}{7}^o

    . . . . \frac{1260^o}{7} \:=\: 180^o

    . . . . \frac{1620^o}{7} \:=\: 231\tfrac{3}{7}^o

    . . . . \frac{1980^o}{7} \:=\: 282\tfrac{6}{7}^o

    . . . . \frac{2340^o}{7} \:=\: 334\tfrac{2}{7}^o



    \cos(\theta) \:=\:0 \quad\Rightarrow\quad \theta \:=\:90^o,\:270^o



    \cos\left(\tfrac{1}{2}\theta\right) \:=\:0 \quad\Rightarrow\quad \tfrac{1}{2}\theta \:=\:90^o + 180^on

    . . \theta \:=\:180^o + 360 ^on \quad\Rightarrow\quad \theta \:=\:180^o

    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    Thanks soroban, that explain why there are 9 roots in my graph.
    . .
    . . . .
    . . . .
    . . . .
    . . . .
    . . . .

    .

    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. New Trigo-equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 17th 2009, 03:36 PM
  2. Tan : Trigo-equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 16th 2009, 07:10 AM
  3. Trigo-equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 12th 2009, 06:16 AM
  4. Trigo-equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 7th 2009, 03:14 AM
  5. trigo equation
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: September 11th 2008, 05:07 AM

Search Tags


/mathhelpforum @mathhelpforum