# Taylor Series of cosx

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288 # Taylor Series of cosx

The Taylor series of the cosine function is given by:

cos(x) = 1 – (x^2)/2! + (x^4)/4! – (x^6)/6! + …

This series is an infinite series that can be used to approximate the value of the cosine function for a given value of x.

The Taylor series of a function is a representation of the function as an infinite sum of terms, where each term is obtained by taking the derivative of the function at a specific point (called the expansion point) and evaluating it at a given value of x.

For the cosine function, the expansion point is usually taken to be x = 0. This means that the Taylor series of the cosine function is obtained by taking the derivatives of the cosine function at x = 0 and evaluating them at a given value of x.

Here is the first few terms of the Taylor series of the cosine function:

cos(x) ≈ 1 – (x^2)/2 + (x^4)/24 – (x^6)/720 + …

You can see that the Taylor series of the cosine function is a power series, which means that it is a series of the form:

a_0 + a_1x + a_2x^2 + a_3*x^3 + …

where the coefficients a_0, a_1, a_2, … are obtained by taking the derivatives of the cosine function at the expansion point (in this case, x = 0).