Results 1 to 5 of 5

Math Help - Need help understanding this problem..

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    11

    Need help understanding this problem..

    Okay, I have to find all solutions to the equation and I'm stuck.

    sin(x + pi/4) = 1/2

    I unno what to do. Should I move that pi/4 to the right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Megaman View Post
    Okay, I have to find all solutions to the equation and I'm stuck.

    sin(x + pi/4) = 1/2

    I unno what to do. Should I move that pi/4 to the right?
    couple of hints ...

    \sin\left(\frac{\pi}{6} + 2k\pi\right) = \frac{1}{2}

    \sin\left(\frac{5\pi}{6} + 2k\pi \right) = \frac{1}{2}

    k is an integer
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    11
    Okay, I know that there are two possible solutions to this that being 30 degrees and 330 degrees. I don't understand where that 2kpi is coming from though. Is that like the same thing as 2pi being one circle while k is how many times it should loop? Anywho, I'm still confused over this. I got the answer by subtracting pi/4 from pi/6 and 5pi/6, which would make it -pi/12 and 7pi/12.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by Megaman View Post
    Okay, I know that there are two possible solutions to this that being 30 degrees and 330 degrees. I don't understand where that 2kpi is coming from though. Is that like the same thing as 2pi being one circle while k is how many times it should loop? Anywho, I'm still confused over this. I got the answer by subtracting pi/4 from pi/6 and 5pi/6, which would make it -pi/12 and 7pi/12.
    the original problem says to find all solutions for x ...

    x + \frac{\pi}{4} = \frac{\pi}{6} + 2k\pi

    x = 2k\pi - \frac{\pi}{12}<br />

    x + \frac{\pi}{4} = \frac{5\pi}{6} + 2k\pi <br />

    x = \frac{7\pi}{12} + 2k\pi
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293
    Quote Originally Posted by skeeter View Post
    the original problem says to find all solutions for x ...

    x + \frac{\pi}{4} = \frac{\pi}{6} + 2k\pi

    x = 2k\pi - \frac{\pi}{12}<br />

    x + \frac{\pi}{4} = \frac{5\pi}{6} + 2k\pi <br />

    x = \frac{7\pi}{12} + 2k\pi

    \sin{\left(x + \frac{\pi}{4}\right)} = \frac{1}{2}

    x + \frac{\pi}{4} = \arcsin{\left(\frac{1}{2}\right)}

    x + \frac{\pi}{4} = \left\{\frac{\pi}{6},\pi - \frac{\pi}{6}\right\} + 2\pi n where n is an integer, since sine is positive in the first and second quadrants.

    x + \frac{\pi}{4} = \left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\} + 2\pi n

    x = \left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\} + 2\pi n - \frac{\pi}{4}.


    Can you go from here?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help Understanding this problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 18th 2010, 11:27 PM
  2. Replies: 6
    Last Post: August 13th 2010, 01:03 AM
  3. Problem understanding the theorem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 5th 2010, 07:30 PM
  4. understanding SAT problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: July 30th 2007, 02:04 PM
  5. I'm not understanding this problem
    Posted in the Algebra Forum
    Replies: 5
    Last Post: February 1st 2007, 02:47 PM

Search Tags


/mathhelpforum @mathhelpforum