Results 1 to 4 of 4

Math Help - Diffcult Trigonometry Equation Solving

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    35

    Diffcult Trigonometry Equation Solving

    Could anyone help me with this problem that I've been struggling with?

    Find all x such that:

    cos x + sin x = 1 + sin 2x, for 0 \< x \< 2x where \< is greater than or equal to.

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2008
    Posts
    106
    square both sides of the equation
    using some identities it simplifies down to

    \sin^2 2x+\sin 2x = 0

    solve that then test all the solutions you got in the original equation (squaring both sides causes some extra solutions to pop up)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by shinn View Post
    Could anyone help me with this problem that I've been struggling with?

    Find all x such that:

    cos x + sin x = 1 + sin 2x, for 0 \< x \< 2x where \< is greater than or equal to.

    Thanks in advance.
    Please note that (\sin(x)+\cos(x))^2=\sin^2(x)+\cos^2(x)+2 \sin(x) \cos(x)=1+\sin(2x)

    So your equation is :

    (\cos(x)+\sin(x))^2=(1+\sin(2x))^2

    1+\sin(2x)=(1+\sin(2x))^2

    (1+\sin(2x))(1+\sin(2x)-1)=0

    \sin(2x) \cdot (1+\sin(2x))=0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2008
    Posts
    35
    Wow that is neat...... never thought of squaring when trying to eliminate the 1............

    Thanks greatly for your help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Trigonometry
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 20th 2011, 09:15 PM
  2. Solving of Trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: January 3rd 2011, 07:19 AM
  3. Replies: 1
    Last Post: September 23rd 2010, 03:06 AM
  4. Replies: 2
    Last Post: April 12th 2009, 11:47 PM
  5. Solving trigonometry equation
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: May 15th 2008, 08:24 AM

Search Tags


/mathhelpforum @mathhelpforum