Brushless DC motors work like AC motors...
Well ... sort of/kind of ...
A brushless motor uses pulses of electricity, not a continuous sine wave. They COULD use a sine wave if the FREQUENCY of the sine wave could be easily changed
(a brushless motors speed is proportional to the frequency of the pulses of sine wave peaks).
It is VERY IMPORTANT that the motor speed and the frequency of the driver stay synchronized ! That is why there is a speed sensor
(actually, it is a position sensor) on the motor. It also requires a microprocessor (small, cheap) or other electronics to maintain this synchronization. If the motor slows down
(from a load) the pulses must slow down.
Interest footnote. Most brushless motors are "outunners". This means the output shaft is connect to a cup where the magnets are attached. It is easier to glue the magnet to the inside of the cup that is spinning around the various coils of wire that are being energized. The big win in the early days was no brush drag or wear. Very strong magnets and cheap electronics brought the technology to portable hand tools.
As mentioned, there are lots of good videos on YouTube about this.