Recently, I finally started a hobby I've been thinking about for a long time, i.e., designing my own map projections. This one has such a simple but clever idea that I wouldn't be surprised to hear it's an already known one.
Basically, longitude is scaled by the cosine of the corresponding latitude, like in the sinusoidal projection. But then latitude is scaled by its own sine to avoid those sharp poles (and to emphasize the areas near the equator), and a constant to make it a circle.
So, does anyone know a pre-existing name for this? Alternatively, feel free to suggest a new name for it.
I'd quite like to see an oblique one that uses this great circle as the tangent line. It's the longest straight-line distance over land, and it'd be a straight line in the middle of the map if depicted like this