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Math Help - Trig

  1. #1
    Member srirahulan's Avatar
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    Lightbulb Trig

    how to deduce cos rule, from sine rule??????
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  2. #2
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    Re: Trig

    In short, you don't. To derive the Cosine Rule, you draw in the height of your triangle and apply Pythagoras' Theorem to the resulting right-angle triangle.



    Or in the case of an obtuse-angle triangle...

    Trig-proveit.jpg

    We use the fact that \displaystyle \begin{align*} \sin{ \left( 180^{\circ} - \theta \right) } = \sin{(\theta)} \end{align*} and \displaystyle \begin{align*} \cos{ \left( 180^{\circ} - \theta \right) } = -\cos{(\theta)} \end{align*}, then by Pythagoras we have

    \displaystyle \begin{align*} \left[ a - b\cos{(\theta)} \right] ^2 + \left[ b\sin{(\theta)} \right] ^2 = c^2 \end{align*}

    which upon simplification gives the same result.
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