Draw a diagram of the planet clearly marking the equator with a horizontal line that circles about the planet in the plane of the midpoint between the North and South Poles. Sketch the radius of the circle as a straight line that extends from the perimeter of the circle to the mid-point of the entire sphere at a zero degree angle. Label the radius as "R."
Draw a circle of latitude in the same way that you sketched the equator in Step 1, except with the plane translated upward or downward from the equator such that it traces out a plane that runs parallel to the plane marked by the equator. The circle of latitude should clearly show a smaller perimeter than that of the circle denoted by the equator.
Draw the radius of the circle of latitude. This line will be located in the plane traced out by this circle, such that the radius extends from the perimeter to the north-south planetary axis at a zero degree angle. Label this radius as "r."
Sketch the radius of the Earth again as a straight line that connects the mid-point of the planetary sphere to the perimeter of the circle of latitude that you drew in Step 2. Label the angle between this radius (R) and the circle of latitude radius (r) as L. This quantity is the latitude.
Write the relationship among R, r, and L. From basic trigonometry, it can be seen from our diagram that r = R(cos(L)) when considering the triangle formed between r, R and the segment of the north-south axis that connects these two segments. We can solve this equation for L using basic algebra, ending up with L = arccos(r/R), where "arccos" is the inverse cosine function. Plug the given value for the latitude radius and the radius of the Earth (6,371 kilometers) into the inverse cosine equation to calculate L.