# standart Cauchy distribution

Suppose that X has a standard uniform distribution. Show that Y=tan(2πX) has a standart Cauchy distribution.

## 1 Answer

Let's consider the cumulative distribution function of $Y$: $$P(Y\leq x) = P(\tan(2\pi X)\leq x).$$ You can probably continue from here to get the CDF of the Cauchy distribution by considering separately the cases where $x$ is positive or negative.