Question 40736
{{{ N(e) = 6066 - 31*cos(2e) }}}


Chicago (42degrees):
{{{ N(e) = 6066 - 31cos(2e) }}}
{{{ N(e) = 6066 - 31cos(2*42) }}}
{{{ N(e) = 6066 - 31cos(84) }}}
N(e) = 6062.76 feet


North Pole (90 degrees):
{{{ N(e) = 6066 - 31cos(2e) }}}
{{{ N(e) = 6066 - 31cos(2*90) }}}
{{{ N(e) = 6066 - 31cos(180) }}}
{{{ N(e) = 6066 + 31 }}}
N(e) = 6097 feet


TRIG IDENTITY: 
{{{ cos(2e) = 2cos^2(e) - 1 }}} so we then get:


{{{ N(e) = 6066 - 31(2cos^2(e) - 1) }}}
{{{ N(e) = 6066 - 62cos^2(e) + 31 }}}
{{{ N(e) = 6097 - 62cos^2(e) }}}


When nautical mile = 6040feet:
{{{ N(e) = 6066 - 31cos(2e) }}}
{{{ 6040 = 6066 - 31cos(2e) }}}
{{{ -26 = - 31cos(2e) }}}
{{{ (-26)/(-31) = cos(2e) }}}
{{{ (26)/(31) = cos(2e) }}}
{{{ 2e = cos^(-1)((26)/(31)) }}}
2e = 33 degrees to 2significant places
--> e = 33/2
--> e = 16.5 degrees latitide


jon.