Results 1 to 6 of 6

Math Help - Even or odd

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    21

    Even or odd

    Hey guys.

    I've got this function.

    g (x) = 1 - cos (pi - 2x)

    I must prove this is an even function.

    All I got was g (-x) = 1 - cos (pi + 2x), but I can't pass this point. Where do I go from here? Any help would be appreciated. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Alvy View Post
    Hey guys.

    I've got this function.

    g (x) = 1 - cos (pi - 2x)

    I must prove this is an even function.

    All I got was g (-x) = 1 - cos (pi + 2x), but I can't pass this point. Where do I go from here? Any help would be appreciated. Thank you.
    Hi Alvy,

    use the fact that

    cos({\pi}-2x)=-cos(-2x)

    cos(-2x)=cos(2x)

    cos({\pi}+2x)=-cos(2x)
    Last edited by Archie Meade; May 3rd 2010 at 08:24 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by Alvy View Post
    Hey guys.

    I've got this function.

    g (x) = 1 - cos (pi - 2x)

    I must prove this is an even function.

    All I got was g (-x) = 1 - cos (pi + 2x), but I can't pass this point. Where do I go from here? Any help would be appreciated. Thank you.
    hi

    this is an even function . If you graph it , you will see that the function is symmetrical about the y-axis .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by Archie Meade View Post
    Hi Alvy,

    use the fact that

    cos({\pi}-2x)=-cos(-2x)
    sorry , understood .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2010
    Posts
    21
    Thank you very much, Archie Meade and mathaddict. I got it. One last question, if I may.

    I must find g(x), knowing that sen(2x) = 1/3, and x E [pi/4, pi/2].

    What's the path here? I'm confused. Thank you.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Alvy View Post
    Thank you very much, Archie Meade and mathaddict. I got it. One last question, if I may.

    I must find g(x), knowing that sen(2x) = 1/3, and x E [pi/4, pi/2].

    What's the path here? I'm confused. Thank you.
    sin(2x)=\frac{1}{3}

    2x=sin^{-1}\left(\frac{1}{3}\right)=19.47^o

    This is too small given the domain.

    However sin(2x)=sin({\pi}-2x)

    Hence 180^o-2x=19.47^o

    This gives a valid x.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum