Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.

The Taylor expansion/theorem is used to express any function as a power series about a certain point. Using the given formula of the Taylor expansion, we can approximate a trigonometric function (for example, Sin(x)) to increasing orders. By drawing each of these onto overlaying graphs, we can see that as the order of our Taylor expansion increases, we achieve a function that is closer to the original function (Sin(x)). It is important to understand that this is how computers/calculators calculate trigonometric functions.