Need help finding the function of an expansion

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SUMMARY

The function expansion presented is -(5/16)x^7 + (21/16)x^5 - (35/16)x^3 + (35/16)x, which resembles a polynomial rather than a sine function. The discussion highlights the importance of understanding the nature of the expansion, suggesting that it may represent a finite polynomial rather than a Taylor series. A key point raised is the need for clarity on the term "expansion," as it typically refers to infinite series in the context of functions like sine. The polynomial nature of the expression is confirmed by its finite number of terms.

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delta59
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Homework Statement



can anybody help with finding the function whos expansion is this -(5/16)x^7+(21/16)x^5-(35/16)x^3+(35/16)x

I looks like a function of sin(X) but I just can't nail down what it is.


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The Attempt at a Solution

 
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delta59 said:

Homework Statement



can anybody help with finding the function whos expansion is this -(5/16)x^7+(21/16)x^5-(35/16)x^3+(35/16)x

I looks like a function of sin(X) but I just can't nail down what it is.

Have you looked at the graph?
graph5.jpg

It doesn't look like a sine curve to me, more like a polynomial of some sort, heh heh.
 
What do you mean by "expansion"? Since you have powers of x I would have thought "Taylor's series" but the Taylor's series of any thing other than a polynomial is an infinite series. Any finite "expansion" in powers of x is just the polynomial it looks like. And if you mean this to be the first seven terms of a power series, you will have to tell us what the general coefficient is.
 
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