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composition of approximation

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    Can anyone point me in the right direction for this:
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    (Original post by pippabethan)
    Can anyone point me in the right direction for this:
    If

    \sin(\theta) \approx \theta - \frac{1}{6}\theta^3

    then

    \sin(\frac{1}{2}\theta) \approx \frac{1}{2}\theta - \frac{1}{6}(\frac{1}{2}\theta)^3

    as \theta \mapsto \frac{1}{2}\theta. Similar mapping for cosine.
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    (Original post by RDKGames)
    Using equals signs as I can't find the Latex for approximations.
    \approx

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    (Original post by ghostwalker)
    \approx

    Oh what the hell! I tried that the other day and I got an error, checked the Latex page and it doesn't include that there so I gave up lol. Maybe used the wrong slash.
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    (Original post by RDKGames)
    If

    \sin(\theta) \approx \theta - \frac{1}{6}\theta^3

    then

    \sin(\frac{1}{2}\theta) \approx \frac{1}{2}\theta - \frac{1}{6}(\frac{1}{2}\theta)^3

    as \theta \mapsto \frac{1}{2}\theta. Similar mapping for cosine.
    Thank you! Got it after realising I needed to use the binomial expansion on the sec part
 
 
 
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