High School East-West error at regular points on the Azimuthal Equidistant Map

[Miles Behind]

TL;DR

HELP ME get east west error for circles of latitude on the Azimuthal Equidistant projection as compared to the Globe.

Hello. I am conversing with Flat-Earth folks who tend to lean upon the Azimuthal Equidistant (AE) map centered on the North pole. I know that the AE map is a projection of the globe onto a flat surface, and is only accurate in distances north and south along lines of longitude. The east west distance error increases every mile away from the north pole, approaching silly amounts near the equator and Antarctic latitudes, and quickly increasing to infinity at the south pole. Can someone give me something that I can graph out on paper showing the (I suspect are exponential) error of east-west distances at multiple points between the north and south poles along circles of latitude? Perhaps give the distortion errors at 60N, 45N, 30N, Equator, 30S, 45S and 60 degrees south as a minimum (of course the east-west map error would be zero at the north pole, and infinite at the south pole). What measured distance error would be found for a short distance east and west at these points? Say along a 1 degree section? Is there a better way to do it?

Also. For a sphere with a circumference of 1 at its equator, what would be the circumference of the 30 degree, 45 degree, 60 degree north circles of latitude?

 

[Lnewqban]

... Also. For a sphere with a circumference of 1 at its equator, what would be the circumference of the 30 degree, 45 degree, 60 degree north circles of latitude?

 

[Miles Behind]

Excellent! Thank you much! By the way, what would the value be for 15 degrees north?

 

[Lnewqban]

You are welcome.
For 15 degrees north the value would be simply 1.0 x cos (15) = 0.9659.