Fourier sine and cosine series

Fourier sine and cosine series are ways to express a wave-like function as a combination of different sines and cosines. Think of it like a recipe that tells you how to make the wave. A sine and a cosine are like two different types of waves -- one goes up and down, the other looks like the points of a star. By combining different proportions of these two waves, you can make different kinds of waves. Let's say we have a wave like this one:

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With a Fourier sine and cosine series, you can figure out how to make that wave using sine and cosine waves. You can look at the wave and figure out how much of each wave—sine or cosine—you need in order to make that wave.

Now, the Fourier sine and cosine series tells you how to mix those waves together and make the wave you want! It's like a recipe that tells you how much of each wave you need, and in what order you need to mix them together. So, when you see a wave like this one, you can use a Fourier sine and cosine series to figure out how to make it!