Question

Assuming that Earth is a sphere of radius
6378 kilometers, what is the difference in latitude of two cities, one of which is 1190 kilometers due north of the other?

Answer 1

Lat = flat, so we're looking at East-West lines on a globe. Imagine an arrow from the center of the earth pointing to each city. What shape does this make? Roughly a triangle, right? If you neglect the curvature of the earth (is this a good assumption?), then you end up with a triangle for which you know three sides, but not the angles between them.

At this point, you can invoke the law of cosines to find the angle.
http://en.wikipedia.org/wiki/Law_of_cosines

The angle is roughly the difference in latitude between the cities.