Assignment:
Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in degrees.
a) What is the length of a British nautical mile at Chicago (latitude of 42 degrees)?
b) What is the length of a British nautical mile at the North Pole (latitude of 90 degrees)?
Express N(e) in terms of cosine e only, do not use the double angle.
c) At what latitude north is the length of a British nautical mile found to be 6040 feet?
Provide complete and step by step solution for the question and show calculations and use formulas.