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  1. #1
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    Value

    Find the exact value of tan(`pi/12).

    Does this need to be done in radians or degrees or am I starting on the wrong track??
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by christenc05 View Post
    Find the exact value of tan(`pi/12).

    Does this need to be done in radians or degrees or am I starting on the wrong track??
    here are the two ways i'd go about this:

    (1) Note that $\displaystyle \tan \bigg( \frac {\pi}{12} \bigg) = \tan \bigg( \frac 12 \cdot \frac {\pi}6 \bigg)$

    now use the half angle formula for tangent, that is, the expansion for $\displaystyle \tan \frac {\theta}2$. here, $\displaystyle \theta = \frac {\pi}6$

    or

    (2) Note that $\displaystyle \tan \bigg( \frac {\pi}{12} \bigg) = \tan \bigg( \frac {4 \pi}{12} - \frac {3 \pi}{12} \bigg) = \tan \bigg( \frac {\pi}3 - \frac {\pi}4 \bigg)$.

    now use the addition formula for tangent


    can you continue?
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  3. #3
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    Quote Originally Posted by christenc05 View Post
    Find the exact value of tan(`pi/12).

    Does this need to be done in radians or degrees or am I starting on the wrong track??
    Use radians as the angle is in terms of $\displaystyle \pi$.

    $\displaystyle \tan \left( \frac{ \pi}{12} \right) = \tan \left( \frac{1}{2} \cdot \frac{ \pi}{6} \right)$

    You will need the half angle identity for tan for this problem.

    $\displaystyle \tan \left( \frac{\theta}{2} \right) = \frac{\sin \left( \frac{\theta}{2} \right)}{\cos \left( \frac{\theta}{2} \right)} $

    Multiply by $\displaystyle \frac{\cos \left( \frac{\theta}{2} \right)}{\cos \left( \frac{\theta}{2} \right)} $
    $\displaystyle \frac{\sin \left( \frac{\theta}{2} \right)}{\cos \left( \frac{\theta}{2} \right)} \cdot \frac{\cos \left( \frac{\theta}{2} \right)}{\cos \left( \frac{\theta}{2} \right)} \ \ \Rightarrow \ \ \frac{\sin \left( \theta \right)}{2 \cos^2 \left( \frac{\theta}{2} \right)} $

    $\displaystyle \therefore \tan \left( \frac{\theta}{2} \right) = \frac{\sin \theta }{1 + \cos \theta}$

    You should know $\displaystyle \sin \left( \frac{ \pi}{6} \right)$ and $\displaystyle \cos \left( \frac{ \pi}{6} \right)$.

    Bobak
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  4. #4
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    hi cristian005
    I don't know exact value of your formula.
    *************
    sharu
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    Last edited by CaptainBlack; Jul 9th 2008 at 01:38 AM. Reason: removed comercial advertising link
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by sharu View Post
    hi cristian005
    I don't know exact value of your formula.
    *************
    sharu
    Need natural backlink growth and residual referral traffic?
    URL removed we won't have that here however flattering it is to be a target for this form of advertising.

    RonL
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