Results 1 to 2 of 2

Thread: sry for the trouble! another trigo problem!!

  1. #1
    cyy
    cyy is offline
    Newbie
    Joined
    Feb 2008
    Posts
    6

    Exclamation sry for the trouble! another trigo problem!!

    Hi sry for the previous double post, below is another porblem i faced:
    given: 0 <= x < pi ; 0 <= y; < pi
    ...


    sin^2x = sin^2y
    (sinx + siny )( sinx - siny ) = 0
    thus, how to get from above equation to form below 2 statements?
    x = y+2pi( k ) //where is the pi & k come from?
    x = -y+2pi( k )



    Thank You!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,152
    Thanks
    731
    Awards
    1
    Quote Originally Posted by cyy View Post
    Hi sry for the previous double post, below is another porblem i faced:
    given: 0 <= x < pi ; 0 <= y; < pi
    ...


    sin^2x = sin^2y
    (sinx + siny )( sinx - siny ) = 0
    thus, how to get from above equation to form below 2 statements?
    x = y+2pi( k ) //where is the pi & k come from?
    x = -y+2pi( k )



    Thank You!
    There is a problem with one of the solutions:

    Given two real numbers a and b, if ab = 0 then a = 0 and/or b = 0.

    So starting with
    $\displaystyle (sin(x) + sin(y) )( sin(x) - sin(y) ) = 0$

    We see that
    $\displaystyle sin(x) + sin(y) = 0$
    or
    $\displaystyle sin(x) - sin(y) = 0$

    The second is (almost) trivial, so I'll do the first.
    $\displaystyle sin(x) + sin(y) = 0$

    $\displaystyle sin(x) = -sin(y)$

    This can only happen when $\displaystyle x = y + (2k + 1) \pi$. If you don't see why then expand it:
    $\displaystyle sin(y + (2k + 1) \pi) = sin(x)~cos((2k + 1) \pi) + sin((2k + 1) \pi)~cos(y)$

    Now, 2k + 1 is odd, so $\displaystyle cos((2k +1) \pi) = -1$ and $\displaystyle sin((2k + 1)\pi) = 0$.

    Thus
    $\displaystyle x = y + (2k + 1) \pi$

    The other solution
    $\displaystyle x = y + 2k \pi$
    is correct.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trigo problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: Oct 23rd 2011, 08:43 AM
  2. trigo problem
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Dec 24th 2009, 07:08 AM
  3. trigo problem no. 23
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: Mar 22nd 2008, 06:59 AM
  4. another trigo problem
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: Mar 19th 2008, 09:25 PM
  5. trigo problem no.5
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jan 19th 2008, 11:32 PM

Search Tags


/mathhelpforum @mathhelpforum