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Binomial Theoreom and Trigonometry

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Express cos^4Θ.sinΘ in the form asinΘ+bsin3Θ+csin5Θ

    2. Relevant equations
    cosrΘ = 1/2(z^r + z^-r)
    sinrΘ = 1/2i(z^r - z^-r)

    3. The attempt at a solution
    So far I think I have this.

    32i(sinΘ)(cos^4Θ) = (z-z^-1)(z+z^-1)^4

    I am unsure how to multiply and manipulate out the brackets to get what I want, which I think is something along the lines of.

    p(z - z^-1) + q(z^3 - z^-3) + r(z^5 - z^-5)

    Basically need to know the best way to deal with the brackets to get it in that form^
    If anything is hard to understand because of my notation, let me know and ill try clarify.

  2. jcsd
  3. Mar 9, 2010 #2


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    If you know the binomial theorem, you can use it to expand (z+1/z)^4 quickly, but multiplying everything out by hand isn't too bad either.
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