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The algorithm for the cosine series, based on its Taylor series expansion around zero, is given by the formula:

[ \cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} ]

This means you can compute (\cos(x)) by summing terms of the form (\frac{(-1)^n x^{2n}}{(2n)!}) for (n = 0, 1, 2, \ldots) until the desired accuracy is achieved. The series converges for all real values of (x).

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10mo ago

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What is the algorithm for cosine series?

The cosine series, also known as the Taylor series expansion for cosine, is given by the infinite sum: (\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}). This formula represents the function (\cos(x)) as an infinite series of terms involving powers of (x) and factorials. To compute (\cos(x)) using this series, you can sum a finite number of terms until the desired accuracy is achieved. Each term alternates in sign and includes even powers of (x).


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