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FP2 Maclaurins/Taylors Watch

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    Hi, I understand the basic method of this, but I'm confused on how to do it when there is a combined function
    e.g. Expanding ln(sinx) in taylors using (x-pi/6).
    I think you have to consider separaetly the expansion of lnx and sinx but I don't understand where to go from there. Any help appreciated thanks
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    Basically, imagine you have ln(u) instead of ln(x) and do the expansion in terms of u. I can't remember the series or I'd write it for you, but it's something like lnu = 1 - u + u^2 - u^3 + ... or whatever.

    Then do the expansion for sinx

    Now let u = sinx.

    So whereever you see u in your expansion of lnu, replace it with the expansion of sinx. It's messy, but it works apparently. So you'll have something like

    ln u = 1 - (sinx) + (sinx)^2 - (sinx)^3

    But instead of writing sinx, you write the expansion of sinx.
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    and the expansion of sin x would be just up to the terms it's asked for e.g. to x^3? and then you expand it all out?
    thank you by the way
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    (Original post by lilwhizzz)
    and the expansion of sin x would be just up to the terms it's asked for e.g. to x^3? and then you expand it all out?
    thank you by the way
    Yeah, expand both up to the require term. Then when you plug sinx into the lnu, you'll get something like u^3 = (x + x^2 + x^3)^3, after expanding, you'll have x^9 as well, which you just have to leave out. Hence it gets messy!
 
 
 
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