Results 1 to 3 of 3

Math Help - trigonometry problem

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    1

    trigonometry problem

    Find x of the equation sin5x+sin3x=cosx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2009
    From
    São Tomé
    Posts
    12

    help for the exercise

    Hello ngkh87,
    Here it is my point of view about the exercise.
    I hope you will understand!
    Bye!
    Attached Thumbnails Attached Thumbnails trigonometry problem-trig.-equation.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, ngkh87!

    My solution is similar to Lucio's . . .


    Solve for x\!:\;\;\sin5x+\sin3x\:=\:\cos x
    We have the Sum-to-Product Identity: . \sin A + \sin B \:=\:2\sin\left(\frac{A+B}{2}\right)\cos\left(\fra  c{A-B}{2}\right)
    . . which Lucio derived for us.


    The equation becomes: . 2\sin\left(\frac{5x+3x}{2}\right)\cos\left(\frac{5  x-3x}{2}\right) \:=\:\cos x

    And we have: . 2\sin4x\cos x \:=\:\cos x \quad\Rightarrow\quad 2\sin4x\cos x - \cos x \:=\:0

    Factor: . \cos x(2\sin4x-1) \:=\:0


    We have two equations to solve:


    . . \cos x \:=\:0 \quad\Rightarrow\quad \boxed{x \:=\:\tfrac{\pi}{2} + \tfrac{\pi}{2}n}


    . . 2\sin4x-1\:=\:0 \quad\Rightarrow\quad \sin4x \:=\:\tfrac{1}{2} \quad\Rightarrow\quad 4x \:=\:\begin{Bmatrix}\frac{\pi}{6} + 2\pi n \\ \\[-4mm] \frac{5\pi}{6} + 2\pi n \end{Bmatrix}
    . . Hence: . \boxed{x \;=\;\begin{Bmatrix}\frac{\pi}{24} + \frac{\pi}{2}n \\ \\[-3mm] \frac{5\pi}{24} + \frac{\pi}{2}n \end{Bmatrix}}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with trigonometry problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 22nd 2011, 10:07 AM
  2. trigonometry problem
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 9th 2009, 02:29 AM
  3. trigonometry problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 3rd 2008, 08:58 AM
  4. Trigonometry problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 16th 2007, 06:43 PM
  5. Trigonometry Problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 1st 2007, 10:50 AM

Search Tags


/mathhelpforum @mathhelpforum