You would also have to not use a phone in general, since your carrier always knows where you are, by the nature of how cellular networks work. Your phone has a unique hardware identifier that is linked to your identity, and every tower knows which phones pinged it recently. Two towers are two points in a triangle, and you're the third.
Carriers constantly perform triangulation and keep records of phones' coordinates, which of course can be subpoenaed, and may be available more freely to government agencies, depending on how much abusive surveillance your local government does. Carriers have also sold this information to data brokers in the past.