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Math Help - Binomial Theorem?

  1. #1
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    Post Binomial Theorem?

    Expand (2 - 5sinx)^-4 in ascending powers of sin x up to and including the term in (sinx)^3. FInd the complete set of values of x in the interval 0 < x < 360 for which the expansion is valid.

    Can I let sin x be equal to some letter, use binomial and then back substitute? Thanks.
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  2. #2
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    Quote Originally Posted by yobacul View Post
    Expand (2 - 5sinx)^-4 in ascending powers of sin x up to and including the term in (sinx)^3. FInd the complete set of values of x in the interval 0 < x < 360 for which the expansion is valid.

    Can I let sin x be equal to some letter, use binomial and then back substitute? Thanks.
    Using a substitute is fine although I think there is a typo in your equation, are you sure the exponent is -4 and not 4?
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  3. #3
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    Binomial

    It is -4 yes, not 4. That's why I thought of binomial, since binomial can be used with negative powers, no? Or could one use the Maclaurin?
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  4. #4
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    Quote Originally Posted by yobacul View Post
    It is -4 yes, not 4. That's why I thought of binomial, since binomial can be used with negative powers, no? Or could one use the Maclaurin?
    The binomial theorem can be used to expand it but I don't see how it can be used to get a \sin^3(x) term.
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  5. #5
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    I think since you let sin x = y, and then use the binomial till y^3 and then backsubstitute to get (sin x)^3
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