Results 1 to 2 of 2

Thread: Cos 36 degrees to simplest radical form?!

  1. May 25th 2010, 03:48 AM #1
    zacharyrod
    zacharyrod is offline
    Newbie zacharyrod's Avatar
    Joined
    Oct 2009
    From
    Seoul, Korea
    Posts
    10

    Exclamation Cos 36 degrees to simplest radical form?!

    How would I find the simplest radical form of 36 degrees? The attatchment displays the situation.
    Attached Thumbnails Attached Thumbnails Cos 36 degrees to simplest radical form?!-scan0002.jpg  
    Follow Math Help Forum on Facebook and Google+
  2. May 25th 2010, 11:44 PM #2
    Grandad
    Grandad is offline
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello zacharyrod
    Quote Originally Posted by zacharyrod View Post
    How would I find the simplest radical form of 36 degrees? The attatchment displays the situation.
    This is all to do with the Golden Ratio.

    In the diagram, let BC = x. Then AD= DC = x (since \triangle's BDC and ADC are isosceles). Therefore BD = 1 - x.

    Now use the fact that the \triangle's ABC and BDC are similar:
    \frac{AC}{BC}=\frac{BC}{BD}

    \Rightarrow \frac{1}{x}=\frac{x}{1-x}

    \Rightarrow 1-x = x^2

    \Rightarrow x^2+x-1=0

    \Rightarrow x = \frac{-1+\sqrt{5}}{2}, taking the positive root
    and now
    \cos 36^o = \frac{\tfrac12AC}{DC}
    =\frac{1}{-1+\sqrt5}

    =\frac{1+\sqrt5}{4}
    Grandad
    Follow Math Help Forum on Facebook and Google+
« proof of sine series | Please help with Trig question! »

Similar Math Help Forum Discussions

  1. simplest form
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 21st 2009, 03:56 PM
  2. Can you convert a decimal to a radical in simplest form?
    Posted in the Calculators Forum
    Replies: 7
    Last Post: June 21st 2009, 09:09 PM
  3. solve roots and expres in simplest radical form
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 12th 2008, 04:49 PM
  4. solve & express in simplest radical form
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 10th 2008, 03:34 PM
  5. simplest form
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 3rd 2007, 04:26 AM

Search Tags


/mathhelpforum @mathhelpforum