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Math Help - double - angled formulas

  1. #1
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    Joined
    Dec 2011
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    9

    double - angled formulas

    Hey everyone!,

    If anyone could help me with this, with explanation that would be great, thanks


    (i) Using an appropriate double-angle formula, express sin(4θ) in
    terms of sin(2θ) and cos(2θ).

    (ii) Using your answer to part(b)(i) and appropriate double-angle
    formulas, derive the formula
    sin(4θ) = 4 sin θ cos3 θ − 4 sin3 θ cos θ.

    for (i) i've worked out (dunno if right)

    sin(4θ) = using terms of sin(2θ) = 2sin(2θ)cos(θ)

    using terms of cos(2θ) = 1 - 2sin^2(2θ)

    but not sure how they would help for part (ii)

    seems to be testing my skills in re-arranging the formulas
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  2. #2
    Newbie
    Joined
    Dec 2011
    Posts
    9

    Re: double - angled formulas

    Hi skeeter, had a look and this is what i come up with let us know,

    2(2sintcost)(cos^2t-sin^2t) =

    (2sintcost) * cos^2t = 2sintcostcos^2t = 2sintcos^3t

    (2sintcost) * sin^2t = 2sintcostsin^2t = 2sin^3tcost

    =

    2(2sintcos^3t - 2sin^3tcost)

    =

    4sintcos^3t - 4sin^3tcost which is the answer, (broken down right?) thanks for letting us know about the (^)!
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