Sine/cosine function and polynomial function

In summary, the conversation discusses the relationship between polynomials and trigonometric functions, specifically sine and cosine. The example provided shows how some values of sine and cosine can be expressed as the root of a polynomial of nth degree. The question then asks where to find the mathematical relationship between the coefficients of a polynomial and the argument of sine and cosine. The speaker notes that not every polynomial is related to a trigonometric function, despite some trigonometric functions being related to polynomials.
  • #1
Bruno Tolentino
97
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!
 
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  • #2
Im not sure that every polynomial is related to a trig function just because some trig functions are related to polynomials.
 
  • #3
I wrote some.

More tips?
 

1. What is the difference between sine and cosine functions?

The sine and cosine functions are both trigonometric functions that describe the relationship between the sides and angles of a right triangle. The main difference between them is that the sine function describes the relationship between the opposite side and the hypotenuse of a right triangle, while the cosine function describes the relationship between the adjacent side and the hypotenuse.

2. How do you graph a polynomial function?

To graph a polynomial function, first determine the degree of the polynomial, which is the highest power of the variable in the function. Then, plot several points on the graph by substituting different values for the variable and solving for the corresponding output. Finally, connect the points to form a smooth curve. It is also helpful to identify any x-intercepts, y-intercepts, and the end behavior of the graph.

3. What is the period of a sine or cosine function?

The period of a sine or cosine function is the length of one complete cycle of the function. For a sine function, the period is 2π, and for a cosine function, the period is also 2π. This means that the graph of a sine or cosine function will repeat itself every 2π units along the x-axis.

4. How do you find the zeros of a polynomial function?

The zeros of a polynomial function are the values of the variable that make the output of the function equal to zero. To find the zeros, set the function equal to zero and solve for the variable. The solutions to this equation will be the zeros of the function. It is also helpful to use the Rational Zero Theorem to identify potential rational zeros and then use synthetic division to test them.

5. What is the difference between a polynomial function and a rational function?

A polynomial function is a function that can be written as a sum of constants and variables raised to non-negative integer powers. A rational function, on the other hand, is a function that can be written as the quotient of two polynomial functions. This means that a rational function may have negative and/or fractional powers of the variable, while a polynomial function will only have non-negative integer powers.

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