Vectors, components, sine and cosine in power series

Back in algebra II or so you probably started going over vectors.

To start off, you could describe a vector using an angle (like that on a compass) and a magnitude or as two components (i and j).

Later on, in three dimensions you could use i, j, and k components to describe a vector.

In earlier grades, teachers taught cosines and sines only in their relations to triangles, but it turns out that the sine and cosine functions can describe any function (this is related to power series).

Furthermore, a combination of sines and cosines can act as the basis of n-dimensional space.

Thus they prove to be useful far beyond describing triangles.