d^2/dx^2 sin(x) = -sin(x) This means that sin(x) is an eigenfunction of the second derivative operator in the infinite dimensional vector space of functions.

d^2/dx^2 sin(x) = -sin(x) This means that sin(x) is an eigenfunction of the second derivative operator in the infinite dimensional vector space of functions. This little fact makes numerically solving second-order differential equations using a sin(x) basis really cheap, just need to pay the upfront FFT cost... (O(n log n))