For many real world use cases continuous positioning is required, allowing to avoid complex operations such as sinus. The most simple approach is to use our latitude (north/south) and longitude (west/east) position and remove the spheric aspects, e.g. by positioning the coordinates (0,0) in the upper-left corner of our world.
For doing so, the coordinates require a transformation from the center of the world illustration to the upper left corner.
X = Longitude shift = (longitude + 180)
Y = Latitude shift = sin(latitude * pi/180)
This procedure is defined by the (web) mercator projection.
Compare e.g., https://developers.google.com/maps/documentation/javascript/examples/map-coordinates
As tile size we use 6378137 meters as earth circumference for 1meter by 1meter patches.