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Math Help - Eccentric angle

  1. #1
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    Eccentric angle

    I'm stuck on this question:

    The eccentric angle corresponding to the point (2,1) on the ellipse with equation x^2+9y^2=13 is theta (don't know how to do the symbol). Find tan theta.

    When I attempted the question I got 1/2, but the answer is 3/2. Please can someone explain why.
    Last edited by free_to_fly; December 19th 2007 at 02:44 AM.
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    I'm stuck on this question:

    The eccentric angle corresponding to the point (2,1) on the ellipse with equation x^2+9y^2=13 is theta (don't know how to do the symbol). Find tan theta.

    When I attempted the question I got 1/2, but the answer is 3/2. Please can someone explain why.
    Hello,

    parametrize the equation of an ellipse with it's center in the origin, the major semiaxis a and the minor semiaxis b:
    \left|\begin{array}{l}x=a \cdot \cos(\theta) \\ y = b \cdot \sin(\theta)\end{array}\right.~\implies~\left|\beg  in{array}{l}\frac xa= \cos(\theta) \\ \frac yb =  \sin(\theta)\end{array}\right.

    Now divide the second equation by the first equation:

    \frac{\sin(\theta)}{\cos(\theta)}=\tan(\theta)=\df  rac{\frac yb}{\frac xa}=\frac{a \cdot y}{b  \cdot x} Plug in the values you already know:

    \tan(\theta)=\frac{\sqrt{13} \cdot 1}{\frac13 \cdot \sqrt{13}\cdot 2} = \frac32
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