"A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\\sim\\mathcal{U}(0,1)$ and $Y\\sim\\mathcal{U}(0,1)$, then $P[X^2+Y^2 \\le 1]=pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"