Sine/cosine function and polynomial function

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SUMMARY

The discussion centers on the mathematical relationship between sine/cosine functions and polynomial functions of nth degree. It highlights that certain values of sine and cosine can be expressed as roots of specific polynomials, exemplified by the polynomial x³ - 4x² - 4x + 1 associated with cos(180/7°). Participants seek to understand the connection between polynomial coefficients and the arguments of sine and cosine functions, emphasizing that not all polynomials relate to trigonometric functions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with polynomial functions and their degrees.
  • Basic knowledge of mathematical roots and coefficients.
  • Experience with mathematical software like Wolfram Alpha for visualizing functions.
NEXT STEPS
  • Research the relationship between trigonometric identities and polynomial equations.
  • Explore the concept of Chebyshev polynomials and their connection to trigonometric functions.
  • Learn about the roots of unity and their applications in trigonometry.
  • Investigate the use of Taylor series for approximating sine and cosine functions.
USEFUL FOR

Mathematicians, students studying calculus or algebra, and anyone interested in the interplay between trigonometric and polynomial functions.

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!
 
Mathematics news on Phys.org
Im not sure that every polynomial is related to a trig function just because some trig functions are related to polynomials.
 
I wrote some.

More tips?
 

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