Here are some properties that make the cosine base popular. It has the property that among a large set of bases, it roughly provides the best approximation of a given function [0]. Moreover, this approximation can be efficiently obtained by evaluating the function on Chebyshev nodes [1], followed by computing a discrete cosine transform [2].

[0]: https://doi.org/10.1093/comjnl/9.4.404

[1]: https://en.wikipedia.org/wiki/Chebyshev_nodes

[2]: https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-...