How do I simulate Cauchy distribution from Uniform distribution in (-pi/2, pi/2) in R? Not allowed to used any functions that already exist in R that generate Cauchy
You can do something that is called Inverse transform sampling, where you can use uniform distribution to generate other distribution that you want to obtain. It is really good to be familiar with this tool.
http://www.columbia.edu/~ks20/4404-Sigman/4404-Notes-ITM.pdf - it can be helpful for the first steps in this field.
When you generate this distribution, you can apply the result in your R environment.