Our planet is spheroidal in shape, which means its surface is curved. So making a map of the Earth's surface involves taking something that is curved and projecting it onto something flat (such as a piece of paper or a computer screen). But this flattening inherently causes some distortion from reality. It is not possible for any one map projection to preserve all of the following: 1.) direction, 2.) shape, 3.) area, and 4.) distance. So when a cartographer chooses a particular map projection, they are choosing to preserve one or more of those traits at the expense of others.
Maps of the 48 states often use the Lambert Conformal Conic projection. Even if you are not familiar with that term, it is a map projection with which we are all quite familiar; many cartographers use it because it is a great choice for mapping the 48 states. It preserves shape well, and it comes reasonably close to preserving area and distance too. However, all map projections must distort something, and in the case of the LCC projection, the thing that gets distorted most is direction. Most maps of the 48 states omit graticules, and perhaps for that reason many people are not aware that directions are not consistent on an LCC map. The image below shows a conic map with graticules, and it serves to illustrate that the cardinal directions for a point on one side of the map have different angles than those same directions on the opposite side of the map:
That should also illustrate the fact that an LCC map should never include a north arrow! But since LCC maps usually omit graticules too, people tend to assume north is... well, just "up". As a result, I would say the following are the biggest misconceptions about direction in the U.S.:
In an attempt to correct those last three misconceptions, I created the infographics below. These images cannot be considered "maps", although they do resemble maps in the sense that the graphic elements are arranged geographically; and also some things have been distorted in order to emphasize certain truths.
For the first one, this is essentially what I did:
(You may have to tap on the images below in order to bring up a more legible version)
This second graphic was done in essentially the same way, although it is slightly more complicated:
I could have illustrated these same points with a map that uses a cylindrical projection (such as Mercator), but sometimes extraneous information (like state lines and coastlines) can obscure the main point. The method used here makes it easier to visually compare latitudes and longitudes of the selected states and cities.