Results 1 to 3 of 3

Thread: [SOLVED] Euler Expression

  1. #1
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175

    [SOLVED] Euler Expression

    Using Eulerís formula, express in terms of $\displaystyle sin\alpha$ and $\displaystyle cos\alpha$ for :

    $\displaystyle sin2\alpha$ and $\displaystyle cos2\alpha$

    I know that Euler's formula is :

    $\displaystyle e^{ix}$ = $\displaystyle cos\alpha$ + $\displaystyle isin\alpha$

    So I have come to the conclusion that:

    $\displaystyle cos2\alpha =Re[e^{2i\alpha}]$ and $\displaystyle sin2\alpha =Im[e^{2i\alpha}]$

    Is this correct and to answer this question do I leave it in this form?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    You must express $\displaystyle sin2\alpha$ and $\displaystyle cos2\alpha$ in terms of $\displaystyle sin\alpha$ and $\displaystyle cos\alpha$

    $\displaystyle cos2\alpha =Re[e^{2i\alpha}]$ and $\displaystyle e^{2i\alpha} = \left(e^{i\alpha}\right)^2 = (cos\alpha + i\:sin\alpha)^2$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    474
    Thanks
    5
    Quote Originally Posted by ronaldo_07 View Post
    Using Euler’s formula, express in terms of $\displaystyle sin\alpha$ and $\displaystyle cos\alpha$ for :

    $\displaystyle sin2\alpha$ and $\displaystyle cos2\alpha$

    I know that Euler's formula is :

    $\displaystyle e^{ix}$ = $\displaystyle cos\alpha$ + $\displaystyle isin\alpha$

    So I have come to the conclusion that:

    $\displaystyle cos2\alpha =Re[e^{2i\alpha}]$ and $\displaystyle sin2\alpha =Im[e^{2i\alpha}]$

    Is this correct and to answer this question do I leave it in this form?
    I think you need to use these Euler's formulas: $\displaystyle \sin \alpha = \frac{{{e^{ia}} - {e^{ - ia}}}}{{2i}}$ and $\displaystyle \cos \alpha = \frac{{{e^{ia}} + {e^{ - ia}}}}{2}$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Feb 20th 2010, 08:26 AM
  2. [SOLVED] Euler Method
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Jul 14th 2009, 08:46 PM
  3. [SOLVED] Two questions about Euler
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Apr 18th 2009, 05:47 PM
  4. [SOLVED] Number Theory:Euler phi function proofs
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: Feb 20th 2009, 12:39 AM
  5. ODE solved using Euler's equation
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: Jan 20th 2009, 10:35 AM

Search Tags


/mathhelpforum @mathhelpforum