Results 1 to 3 of 3

Thread: Solving sin(pi/3-2x) = sin(x-pi/6)

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    4

    Unhappy Solving sin(pi/3-2x) = sin(x-pi/6)

    Hi!

    Having problems getting correct answers for the equation
    $\displaystyle sin(pi/3-2x) = sin(x-pi/6)$

    Could someone help and point me to the right direction with this one ?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello thex10

    Welcome to Math Help Forum!
    Quote Originally Posted by thex10 View Post
    Hi!

    Having problems getting correct answers for the equation
    $\displaystyle sin(pi/3-2x) = sin(x-pi/6)$

    Could someone help and point me to the right direction with this one ?

    Thanks!
    The general solution of the equation:
    $\displaystyle \sin A = \sin B$
    is:
    $\displaystyle A = n\pi + (-1)^nB, n = 0 , \pm 1, \pm 2, ...$
    So for instance,
    When $\displaystyle n = 0,\; A = B$

    When $\displaystyle n = 1,\; A = \pi - B$


    When $\displaystyle n = 2,\; A = 2\pi + B$


    ... and so on

    So to solve the equation
    $\displaystyle \sin(\pi/3-2x) = \sin(x-\pi/6)$
    you first write down the general solution, as above, where
    $\displaystyle A = \pi/3 - 2x$
    and
    $\displaystyle B = x - \pi/6$
    which is:
    $\displaystyle \pi/3 - 2x =n\pi +(-1)^n(x - \pi/6)$
    and then see what happens when you take particular values for $\displaystyle n$.

    Can you continue from here?


    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    4
    Got it!

    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving for x
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 30th 2010, 01:30 PM
  2. Solving for x with sin
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: Aug 15th 2009, 05:40 PM
  3. Solving for x...
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jul 19th 2009, 01:16 PM
  4. Please help with solving for zero
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 12th 2009, 04:46 PM
  5. Replies: 3
    Last Post: Oct 11th 2006, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum