Results 1 to 7 of 7

Math Help - cos^2(x) = 1/2 ... [o,2π)

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    2

    cos^2(x) = 1/2 ... [o,2π)

    Anyone have any idea how to solve it? Sqrt of both sides? But it's not a memory value angle... :\

    cos^2(x) = 1/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    \sqrt{cos^2x}=cos(x)=\sqrt{\frac{1}{2}}\rightarrow cos(x)=\frac{1}{\sqrt{2}}\rightarrow cos(x)=\frac{\sqrt{2}}{2}\rightarrow x=\frac{\pi}{4},\frac{7\pi}{4}
    Last edited by dwsmith; November 22nd 2010 at 08:51 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by dwsmith View Post
     cos(x)=\frac{\sqrt{2}}{2}=\frac{\pi}{4}
    I think you mean  \cos(x)=\frac{\sqrt{2}}{2}\implies x = \frac{\pi}{4}

    What about other solutions on [0,2\pi) ??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dwsmith View Post
    \sqrt{cos^2x}=cos(x)=\sqrt{\frac{1}{2}}\rightarrow cos(x)=\frac{1}{\sqrt{2}}\rightarrow cos(x)=\frac{\sqrt{2}}{2}\rightarrow x=\frac{\pi}{4},\frac{7\pi}{4}
    The other case to consider is \cos(x)=-\sqrt{\frac{1}{2}} and this is left for the OP to do.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member dhiab's Avatar
    Joined
    May 2009
    From
    ALGERIA
    Posts
    541
    Hello :
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    \displaystyle \left[cos\left(\frac{3\pi}{4}\right)\right]^2=\left(\frac{-\sqrt{2}}{2}\right)^2=\frac{1}{2}

    Therefore, the angles that incorporate the negative values satisfy the equation.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,458
    Thanks
    1868
    Quote Originally Posted by mathnoob2 View Post
    Anyone have any idea how to solve it? Sqrt of both sides? But it's not a memory value angle...
    As others have pointed out, yes, it is!

    :\

    cos^2(x) = 1/2
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum