Results 1 to 2 of 2

Math Help - Complex numbers problem

  1. #1
    Junior Member rednest's Avatar
    Joined
    Mar 2008
    Posts
    36

    Cool Complex numbers problem

    Using De Moivre's Theorm, express tan 5\theta in terms of tan \theta.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by rednest View Post
    Using De Moivre's Theorm, express tan 5\theta in terms of tan \theta.
    De Moivre's theorem tells us that:

    (\cos(\theta)+i \sin(\theta))^5=\cos(5\theta)+i \sin(5\theta)

    Now I will write s for \sin(\theta) , c for \cos(\theta) and t for \tan(\theta). Then expanding the left hand side and equating real and imaginary parts we get:

     <br />
\cos(5\theta)=c^5-10c^3s^2+5c~s^4<br />

    and:

     <br />
\sin(5\theta)=5c^4s-10c^2s^3+s^5<br />
.

    Therefore:

     <br />
\tan(\theta)=\frac{5c^4s-10c^2s^3+s^5}{c^5-10c^3s^2+5c~s^4}<br />
.

    Now on the right divide top and bottom through by c^5 and you are done

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem with Complex numbers
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 19th 2010, 08:49 AM
  2. Complex numbers problem
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: March 31st 2010, 12:09 PM
  3. Problem with complex numbers
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 1st 2008, 07:11 AM
  4. Replies: 1
    Last Post: May 24th 2007, 03:49 AM
  5. a complex numbers problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 16th 2006, 01:51 PM

Search Tags


/mathhelpforum @mathhelpforum