#R, 60 56 53 49 bytes

An extra 4 bytes thanks to @JayCe and changing it to a function.

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

function(n,y=acos(runif(n)))runif(n)*2*pi+c(y,-y)

Try it online!

R, 60 56 53 49 bytes

An extra 4 bytes thanks to @JayCe and changing it to a function.

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

function(n,y=acos(runif(n)))runif(n)*2*pi+c(y,-y)

Try it online!

#R, 60 56 53

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

x=runif(n<-scan())*2*pi;y=acos(runif(n));cat(x+y,x-y)

#R, 60 56 53 49 bytes

An extra 4 bytes thanks to @JayCe and changing it to a function.

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

function(n,y=acos(runif(n)))runif(n)*2*pi+c(y,-y)

Try it online!

#R, 60 56 53

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

x=runif(n<-scan())*2*pi;y=acos(runif(n));cat(x+y,x-y)

#R, 60 56 53

Using the same basic formula as the others. R uses the Mersenne-Twister method by default, but others can be set. Outputs a space separated list.

x=runif(n<-scan())*2*pi;y=acos(runif(n));cat(x+y,x-y)