Here is a power series that can be used to calculate the cosine:


If you're not familiar with power series or alternating series, see the videos below.

What are power series?

What is an alternating series?

How can we use the power series to estimate the value of the cosine?


Let's find some of the first terms:


Each positive term makes our sum bigger, and each negative term makes our sum smaller, so we have:


Calculating the sums on both sides gives:


So cos(1) is about 0.54. This might be accurate enough for some applications. If we need better accuracy, we can add more terms and compare the underestimate and the overestimate.

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