Box-Muller Method
If \(U_1,U_2\) are iid samples from \(U[0,1]\), and \[ X_1 = \sqrt{-2\log U_1}\cos(2\pi U_2) \] \[ X_2 = \sqrt{-2\log U_1}\cos(2\pi U_2) \]
Then \(X_1,X_2\) are iid draws from the standard Normal distribution.
If \(U_1,U_2\) are iid samples from \(U[0,1]\), and \[ X_1 = \sqrt{-2\log U_1}\cos(2\pi U_2) \] \[ X_2 = \sqrt{-2\log U_1}\cos(2\pi U_2) \]
Then \(X_1,X_2\) are iid draws from the standard Normal distribution.