Cosine Function Taylor Series Expansion - Formula and Explanation

The Taylor series expansion of cos(x) is given by:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

This can be expressed in summation notation as:

cos(x) = Σ((-1)^n * x^(2n)) / (2n)!

where n is a natural number (including 0), and Σ represents the infinite sum starting from n=0.

This formula shows that the cosine function can be approximated by an infinite series of terms involving powers of x. Each term in the series corresponds to a derivative of cos(x) evaluated at x=0, divided by the corresponding factorial.