Why is the cosine function not a polynomial???

Question

I know that a cosine function isn't a polynomial, but I can't seem to name any specific reasons why. Please help!

Answer 1

You could assume that cosine was a polynomial of degree n where n is a positive integer. The Fundamental Thm of Algebra tells us that it would have at most n roots (zeroes). However, the cosine function has an infinite number of roots so it cannot be a polynomial (this is a very informal proof by contradiction).

Answer 2

The reason that the cosine function is not a polynomial because there is no highest finite degree of the polynomial if you write cosine as a polynomial. The degree is infinite so it is not a polynomial. If the degree would be finite like f(x)=x^1000000 then f(x) is a polynomial.

Answer 3

The harmonic oscillator Schroedinger equation is complicated to sparkling up. What people do is anticipate the answer has the form of a polynomial situations an errors function. while that's finished the polynomials become Hermite polynomials.

Answer 4

Polynomial, by definition, is an algebraic expression with non-negative integral powers of all the variables involved and clearly cosine(x) cannot be expressed in terms of x with integral power.

Answer 5

because it is a function that needs something inside of it..ie; you can't write cos by itself it needs something inside like cosx. Other functions that are not polynomials are abs value, tan, ln, etc. A polynomial is usually a variable raised to a power.

Answer 6

For starters, it's periodic and bounded. Any non-constant polynomial will eventually go to +∞ or -∞ as x -> ∞, and is therefore neither periodic nor bounded.