Problem 6. (Mercator Projection) The Mercator projection is a conformal (angle preserving) projection that maps latitude and longitude to rectangular coordinates (x, y). It is widely used for example, in nautical charts and in the maps that you print from the web. The projection is defined by the equations x = 0 and y = ln((1 + sin )/(1 sin ))/2, where 0 is the longitude of the point in the center of the map. Write a program mercator.py that takes three floats 0, , and as command-line arguments and writes its projection, ie, the x and y values, separated by a space. Note that the equations use degrees, whereas Pythons trigonometric functions use radians. Use math.radians() to convert degrees to radians. Use your program to compute the Mercator projection of Boston (42.36 N and 71.06 W) with the center of the map being the prime meridian (0).

$ python mercator.py 0 42.36 -71.06

-71.06 0.817646151942

mercator.py =

# mercator.py: Takes three floats l0, phi, and l as command-line arguments and # prints its projection, i.e., the x and y values separated by a space, # calculated using x=l-l0 and y=ln(1+sin(phi)/(1-sin(phi)))/2.

import math import stdio import sys