Results 1 to 4 of 4

Math Help - Finding the cosine of 72* the hard way

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    2

    Finding the cosine of 72* the hard way

    Alright, so let's say that w = cis(72*)

    Using demoivre's theorem, w^5 = 1

    What I'm hung up on, now, is showing that w^4+w^3+w^2+w+1=0, I'm supposed to use something I already know about polynomials (synthetic division?), and knowing that both w and 1 are roots of f(x) = x^5 -1, but I'm drawing a total blank.

    All help is very much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Kwerk View Post
    Alright, so let's say that w = cis(72*)

    Using demoivre's theorem, w^5 = 1

    What I'm hung up on, now, is showing that w^4+w^3+w^2+w+1=0, I'm supposed to use something I already know about polynomials (synthetic division?), and knowing that both w and 1 are roots of f(x) = x^5 -1, but I'm drawing a total blank.

    All help is very much appreciated.
    x^5-1=(x-1)(x^4+x^3+x^2+x+1)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    2
    Okay I get that, now I have to turn that into w^2 + w^3 = (w + w^4)^2 - 2
    somehow. I think I'm supposed to expand (w+w^4) ^2 into w^8+2w^5+w^2, but after than I'm lost again.
    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 Kwerk View Post
    Alright, so let's say that w = cis(72*)

    Using demoivre's theorem, w^5 = 1

    What I'm hung up on, now, is showing that w^4+w^3+w^2+w+1=0, I'm supposed to use something I already know about polynomials (synthetic division?), and knowing that both w and 1 are roots of f(x) = x^5 -1, but I'm drawing a total blank.

    All help is very much appreciated.
    Read the attachment I have (quickly) prepared for you and work your way through it.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 16th 2011, 03:06 AM
  2. Replies: 1
    Last Post: June 22nd 2011, 01:43 PM
  3. finding sine, cosine, and tangent of theta
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 8th 2011, 01:51 PM
  4. Replies: 3
    Last Post: May 2nd 2010, 10:20 PM
  5. A hard question of finding angle
    Posted in the Geometry Forum
    Replies: 4
    Last Post: October 5th 2009, 09:24 PM

Search Tags


/mathhelpforum @mathhelpforum