# Using numpy for various math operations
import numpy as np  # allows numpy functions to be accessed with the
                    # shortcut name np

# Compute the traversal length of a line of latitude in kilometers
# Note: numpy trig functions expect their inputs (arguments)
# to be in radian measure (not degrees)

r = 6378206.4 # Clarke 1866 estimate of earth radius in meters
circumferenceEq = 2 * np.pi * r # circumference of earth along equator
myLat = 45              # user's latitude (change to whatever you like)
phi = np.radians(myLat) # convert a latitude in degrees to radians
                        # and store as phi. This is necessary because
                        # np.cos() assumes its argument is in radians.
traversalAtPhiM = circumferenceEq * np.cos(phi) 
traversalAtPhiKM = traversalAtPhiM / 1000.0
print 'For a latitude of ' + str(myLat) + ' degrees, the traversal is ' \
      + str(traversalAtPhiKM) + ' km'

# Starting with an angle in degrees, find its sine.
# Then take the inverse sine (arcsine) of the sine
# to get back to the original angle. How close do you
# get? We'll use radians all the way through so that
# we don't get more chances for rounding error.
myAngle = np.pi / 3.0 # pi / 3.0 is the radian equivalent of 60 degrees
sinMyAngle = np.sin(myAngle)
arcsinSinMyAngle = np.arcsin(sinMyAngle)
print 'For the angle ' + str(myAngle) + '(in radians), its sin is ' \
      + str(sinMyAngle) + ' and the arcsin of the sin is ' \
      + str(arcsinSinMyAngle) + ' which has a difference of ' \
      + str(myAngle - arcsinSinMyAngle) + ' from the original angle ' \
      + '(which is ' + str(np.degrees(myAngle)) + ' in degrees)'