How does an API (air position indicator) work?
The API uses not only heading and airspeed but they are fed to mechanisms within the instrument that solve the navigation problem using sine, cosine and secant functions. The output was latitude and longitude from the departure or a known fix (geographical position) to give the no wind position of the airplane. This was then used by the navigator to give a dedreconing position by plotting the last known wind vector from the no wind position.