Suggest a method for generating normal random variables

Question

Suppose that R and U are independent continuous random variables where U has a Uniform distribution on [0, 1] and R has the density function

(a) Show that R² has an Exponential distribution.

(b) Define X = R cos(2πU) and Y = R sin(2πU). Show that X and Y are independent standard Normal random variables.

(c) Suggest a method for generating Normal random variables based on the results in part (a) and (b).