Results 1 to 5 of 5

Math Help - Orthogonal Functions

  1. #1
    jut
    jut is offline
    Junior Member
    Joined
    Jul 2007
    Posts
    33

    Orthogonal Functions

    I'm to show that sin(x) is orthogonal to sin(x).

    From class, we're told that f(x) and g(x) are orthogonal if
    \int _{-\pi }^{\pi }f (x) g(x)dx=0

    I am confused to begin with because when I graph sin(x)sin(x) I see that the area under the curve from -pi to pi is not zero. Can someone help me here please.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by jut View Post
    I'm to show that sin(x) is orthogonal to sin(x).

    From class, we're told that f(x) and g(x) are orthogonal if
    \int _{-\pi }^{\pi }f (x) g(x)dx=0

    I am confused to begin with because when I graph sin(x)sin(x) I see that the area under the curve from -pi to pi is not zero. Can someone help me here please.
    It's not true that sin(x) is orthogonal to sin(x). Read the question again. Perhaps it's asking you to show that sin(x) is orthogonal to cos(x)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    jut
    jut is offline
    Junior Member
    Joined
    Jul 2007
    Posts
    33
    Check out my attachment; i copied it straight from the h.w. pdf.

    I'm thinking it's a mistake. I emailed the professor.

    ps - what is your signature all about?
    Attached Thumbnails Attached Thumbnails Orthogonal Functions-pr3.png  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,238
    Thanks
    1795
    A function is never orthogonal to itself! That would be like saying a vector is perpendicular to itself.

    The problem is asking you to show that the functions sin(nx) and sin(mx) are orthogonal for m \ne n.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by jut View Post
    Check out my attachment; i copied it straight from the h.w. pdf.

    I'm thinking it's a mistake. I emailed the professor.

    ps - what is your signature all about?
    The question says "Show that the functions \sin kx,\ \cos kx,\ k = 0,1,2\ldots are orthogonal." You should interpret this as meaning that any two distinct functions from that set are orthogonal. A function can only be orthogonal to itself if it is the zero function.

    (However, there is a slight inaccuracy in the wording of the question, because it specifies the possibility k=0 for both the sine and the cosine series. The function \sin 0x is the zero function, and so it should probably not have been included.)

    Re: signature. It was conjectured by Euler in 1769 that a k'th power cannot be expressed as the sum of fewer than k k'th powers. But Euler, unusually for him, was wrong. The first counterexample was the identity 27^5 + 84^5 + 110^5 + 133^5 = 144^5. This was discovered in 1906 (calculated by hand, way before the invention of computers) and published in a volume to commemorate the 400th anniversary of the University of Aberdeen. The identity 95800^4 + 217519^4 + 414560^4 = 422481^4 is more recent (1988). In each of those cases, a k'th power is the sum of k–1 k'th powers. It is still not known whether a k'th power can be the sum of k–2 (or fewer) k'th powers.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 15th 2011, 05:32 AM
  2. Orthogonal basic && basic for the orthogonal complement
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 5th 2009, 07:33 AM
  3. Orthogonal functions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 7th 2009, 07:38 AM
  4. Prove these functions are orthogonal
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 20th 2009, 06:59 PM
  5. how do u find the functions orthogonal to this
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2009, 01:20 AM

Search Tags


/mathhelpforum @mathhelpforum