Factor, 56 bytes

[ normal-random-float 2pi random 2dup cos * -rot sin * ]

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Verifying correctness:

enter image description here

Factor, 56 bytes

[ normal-random-float 2pi random 2dup cos * -rot sin * ]

Try it online!

Verifying correctness:

enter image description here

Explanation

 ! 1 0.1
normal-random-float ! 1.091729295255315
2pi ! 1.091729295255315 6.283185307179586
random ! 1.091729295255315 4.669140230445313
2dup ! 1.091729295255315 4.669140230445313 1.091729295255315 4.669140230445313
cos ! 1.091729295255315 4.669140230445313 1.091729295255315 -0.04323526873134136
* ! 1.091729295255315 4.669140230445313 -0.04720120946224146
-rot ! -0.04720120946224146 1.091729295255315 4.669140230445313
sin ! -0.04720120946224146 1.091729295255315 -0.9990649185802335
* ! -0.04720120946224146 -1.090708439475907