Results 1 to 3 of 3

Math Help - Tan 2 theta

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    28

    Tan 2 theta

    I know from my conic that Tan2\Theta=\frac{1}{4}, can you show me how I arrive at:

    Cos2\Theta=\frac{4}{\sqrt17} from the above please so that I can work out my transformed conic.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, bigroo!

    \text{I know from my conic that: }\:\tan2\theta\:=\:\dfrac{1}{4}

    \text{Can you show me how I arrive at: }\:\cos2\theta\:=\:\dfrac{4}{\sqrt17}}

    We have: . \tan2\theta \:=\:\dfrac{1}{4} \:=\:\dfrac{opp}{adj}

    \,2\theta is in a right triangle with: . opp = 1,\;adj = 4


    Code:
          *
          |   *        __
          |       *   √17
        1 |           *
          |               *
          |              2@   *
          * - - - - - - - - - - - *
                      4

    Pythagorus says: . hyp^2 \:=\:1^2 + 4^2 \:=\:17 \quad\Rightarrow\quad hyp \:=\:\sqrt{17}

    Therefore: . \cos2\theta \;=\;\dfrac{adj}{hyp} \;=\;\dfrac{4}{\sqrt{17}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2009
    Posts
    28
    Thank you soroban, it was basic Pythagorus after all. I guess I was looking too deep.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 29th 2010, 09:24 AM
  2. Replies: 2
    Last Post: March 29th 2010, 06:38 AM
  3. Replies: 3
    Last Post: February 6th 2009, 03:19 PM
  4. Replies: 1
    Last Post: January 23rd 2009, 09:53 AM
  5. Solve sin4(theta) = cos2(theta)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 8th 2008, 10:23 AM

Search Tags


/mathhelpforum @mathhelpforum