If you begin at a location with the coordinates 0 degree lat. and 0 degree long., and first travelling east 1/3 of the way around the world, and then turning and going north 1/3 of the way to the north pole, what are the coordinates of your new location?

We can consider east and north direction as x and y axes respectively.

latitude 0 and longitude 0 be the origin.

Let 'a' be the total way around the world

so, if I travel east 1/3 of the way around the world, x co-ordinate = 1/3 a

if I travel north 1/3 of the way around the world, y co-ordinate = 1/3 a

So the coordinates of your new location are (1/3 a, 1/3 a)