Sine and cosine are a bit special because they are the real and imaginary part of the exponential function of an imaginary argument; that's why they reappear wh

Sine and cosine are a bit special because they are the real and imaginary part of the exponential function of an imaginary argument; that's why they reappear when taking the derivative multiple times, why they are exactly periodic, and why the sum of their squares equals 1. Tightly wound spirals, like those formed by the Airy functions and the Fresnel integrals, have almost the same shape as exact repetitions of a circle; graphs end up looking very similar.