Sine/cosine function and polynomial function

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Bruno Tolentino
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Some values of sine and cosine can ben expressed how the root of a polynomial of nth degree.

Example:http://www.wolframalpha.com/input/?i=cos((180/7)°)

(Roll the scroll still you find: "alternate forns" and see the associated polynomial: " x³ - 4 x² - 4 x + 1")

So, where I can find the mathematical relationship between the coefficients of a polynomial of nth degree with the argument of the function sine and cosine?

PS: ANY information is welcome!
 
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