Sine/cosine function and polynomial function

Click For Summary
Sine and cosine values can be expressed as roots of nth-degree polynomials, demonstrating a mathematical relationship between trigonometric functions and polynomial equations. An example provided illustrates this connection, showing a specific cosine value linked to a cubic polynomial. The discussion seeks to explore the coefficients of these polynomials in relation to the arguments of sine and cosine functions. There is uncertainty about the extent of this relationship, with a suggestion that not all polynomials may relate to trigonometric functions. Further insights and information on this topic are encouraged.
Bruno Tolentino
Messages
96
Reaction score
0
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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

High School What are cosine and sine functions called in relation to Pi?
  • · Replies 6 ·
Replies
6
Views
3K
Sine Function with Alternating Peaks and Wavelengths
  • · Replies 3 ·
Replies
3
Views
2K
Roots of a polynomial mixed with a trigonometric function
  • · Replies 14 ·
Replies
14
Views
2K
How to find sines/cosines without memorization?
  • · Replies 7 ·
Replies
7
Views
3K
MHB Law of sines: Unambiguous case
  • · Replies 4 ·
Replies
4
Views
3K
MHB Rational roots, functions, modeling.
  • · Replies 5 ·
Replies
5
Views
5K
Don't understand the fundamentals of this problem using MVT
  • · Replies 1 ·
Replies
1
Views
2K
Finding the minimal polynomial of primitive 15th root of 1
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Splitting ring of polynomials - why is this result unfindable?
  • · Replies 9 ·
Replies
9
Views
2K
Cryptographic attacks as minimization of degree 4 polynomial
  • · Replies 7 ·
Replies
7
Views
2K