resolver synchros, what do we use them for ?

[flame_bringer]

i know that a synchro is a device that we use to measure the angular movment of a shaft , and i understand how a torque synchro and a control synchro work.
i also understand that a resolver synchro is used to split the polar signal to its cartesian coordinates but what i dont understand is , whats the purpose of doing this , and in what applications do we use resolver synchros usually in the aircraft .

Thanks in advance